on a new class of completely integrable nonlinear wave equations i infinitely many conservation laws we point out a class of nonlinear wave equations which admit infinitely many conserved quantities these equations are characterized by a pair of exact one forms the implication that they are closed gives rise to equations the characteristics and riemann invariants of which are readily obtained the construction of the conservation laws requires the solution of a linear second order equation which can be reduced to canonical form using the riemann invariants the hodograph transformation results in a similar linear equation we discuss also the symplectic structure and backlund transformations associated with these equations

an improved stable adaptive fuzzy control method stable adaptive fuzzy control is a self tuning concept for fuzzy controllers that uses a lyapunov based learning algorithm thus guaranteeing stability of the system plant controller learning algorithm and convergence of the plant output to a given reference signal in the paper two new methods for stable adaptive fuzzy control are presented the first method is an extension of an existing concept it is shown that a major drawback of that concept the necessity for new adaptation at every change of the reference signal can be avoided by a simple modification the main focus of the paper is on the presentation of a second method which extends the applicability of stable adaptive fuzzy control to a broader class of nonlinear plants this is achieved by an improved controller structure adopted from the neural network domain performance and limitations of the proposed methods as well as some practical design aspects are discussed and illustrated with simulation results

output feedback control of nonlinear systems using direct adaptive fuzzy neural controller in this paper a direct adaptive fuzzy neural output feedback controller dafoc for a class of uncertain nonlinear systems is developed under the constraint that only the system output is available for measurement an output feedback control law and an update law are derived for on line tuning the weighting factors of the dafoc by using strictly positive real lyapunov theory the stability of the closed loop system compensated by the dafoc can be verified moreover the proposed overall control scheme guarantees that all signals involved are bounded and the output of the closed loop system asymptotically tracks the desired output trajectory to demonstrate the effectiveness of the proposed method simulation results are illustrated in this paper

fuzzy adaptive control of a certain class of siso discrete time processes in this manuscript we address the problem of the stability of a certain class of siso discrete time processes controlled by an adaptive fuzzy controller by using lyapunov stability theory these results were recently obtained for adaptive neural controllers and are extended here to adaptive fuzzy controllers of sugeno s type in order to achieve tracking of a reference signal with this kind of fuzzy system we allow both the membership functions and the consequent part of the rules to be adjusted by a parameter adaptation law we first present the gradient based steepest descent adaptation law and we argue that this gradient based adaptation law can be simplified dramatically thereafter we show the asymptotic stability of the overall system the convergence of the tracking error to zero when using this simplified parameters adjustment law unfortunately this result can only be proved when the outputs of the fuzzy controller can be expanded to the first order around the optimal parameter values that allow perfect tracking that is when the parameters are initialized not too far from their optimal values local stability however when the set of tunable parameters is restricted to the set appearing in the linear consequent part of the rules i e the membership functions of the premises are not modified and when the reference signal is the delayed desired output the stability result is strictly valid the parameters do not have to be initialized around the perfectly tuned values in this case the algorithm can be simplified further by only considering the sign of the derivative of the output of the process in terms of its last influential input

direct adaptive control of partially known nonlinear systems a direct adaptive control strategy for a class of single input single output nonlinear systems is presented the major advantage of the proposed method is that a detailed dynamic nonlinear model is not required for controller design the only information required about the plant is measurements of the state variables the relative degree and the sign of a lie derivative which appears in the associated input output linearizing control law unknown controller functions are approximated using locally supported radial basis functions that are introduced only in regions of the state space where the closed loop system actually evolves lyapunov stability analysis is used to derive parameter update laws which ensure under certain assumptions the state vector remains bounded and the plant output asymptotically tracks the output of a linear reference model the technique is successfully applied to a nonlinear biochemical reactor model

adaptive nn control for a class of strict feedback discrete time nonlinear systems in this paper both full state and output feedback adaptive neural network nn controllers are presented for a class of strict feedback discrete time nonlinear systems firstly lyapunov based full state adaptive nn control is presented via backstepping which avoids the possible controller singularity problem in adaptive nonlinear control and solves the noncausal problem in the discrete time backstepping design procedure after the strict feedback form is transformed into a cascade form another relatively simple lyapunov based direct output feedback control is developed the closed loop systems for both control schemes are proven to be semi globally uniformly ultimately bounded

canonical structures for dispersive waves in shallow water the canonical hamiltonian structure of the equations of fluid dynamics obtained in the boussinesq approximation are considered new variational formulations of these equations are proposed and it is found that as in the case of the kdv equation and the equations governing long waves in shallow water they are degenerate lagrangian systems therefore in order to cast these equations into canonical form it is again necessary to use dirac s theory of constraints it is found that there are primary and secondary constraints which are second class and it is possible to construct the hamiltonian in terms of canonical variables among the examples of boussinesq equations that are discussed are the equations of whitham broer kaup which kupershmidt has recently expressed in symmetric form and shown to admit tri hamiltonian structure

observer based direct adaptive fuzzy neural control for nonaffine nonlinear systems in this paper an observer based direct adaptive fuzzy neural control scheme is presented for nonaffine nonlinear systems in the presence of unknown structure of nonlinearities a direct adaptive fuzzy neural controller and a class of generalized nonlinear systems which are called nonaffine nonlinear systems are instead of the indirect one and affine nonlinear systems given by leu et al by using implicit function theorem and taylor series expansion the observer based control law and the weight update law of the fuzzy neural controller are derived for the nonaffine nonlinear systems based on strictly positive real spr lyapunov theory the stability of the closed loop system can be verified moreover the overall adaptive scheme guarantees that all signals involved are bounded and the output of the closed loop system will asymptotically track the desired output trajectory to demonstrate the effectiveness of the proposed method simulation results are illustrated in this paper

inverse variational problem and canonical structure of burgers equations it is demonstrated that burgers equations which are often believed to describe dissipative systems are non lagrangian following bateman s analysis of damped harmonic oscillator an action is defined to look for a lagrangian representation for equations in the burgers hierarchy the associated higher order lagrangian densities are found to be degenerate such that the hamiltonian structure could be studied by a repackaging of ostrogradski formalism and dirac s theory of constraints

asymptotic tracking of uncertain systems with continuous control using adaptive bounding this paper presents a robust adaptive control design method for a class of multiple input multiple output uncertain nonlinear systems in the presence of parametric and nonparametric uncertainties and bounded disturbances using the approximation properties of the unknown continuous nonlinearities and the adaptive bounding technique the developed controller achieves asymptotic convergence of the tracking error to zero while ensuring boundedness of parameter estimation errors the algorithm does not assume the knowledge of any bound on the unknown quantities in designing the controller it is based on an integral technique involving the filtered tracking error and produces a continuous control theoretical developments are illustrated via simulation results

adaptive control of a class of nonlinear pure feedback systems using fuzzy backstepping approach a controller is proposed for the robust backstepping control of a class of nonlinear pure feedback systems using fuzzy logic the proposed control scheme utilizes fuzzy logic systems to learn the behavior of the unknown plant dynamics filtered signals are employed to circumvent algebraic loop problems encountered in the implementation of the usual controllers and the approximation errors can be efficiently counteracted by employing smooth robust compensators most importantly the uniform ultimate boundedness of all signals in the closed loop system can be guaranteed and a priori knowledge of the plant dynamics is no longer required furthermore the proposed method can be used for adaptive control of a large class of single input single output nonlinear systems in both strict feedback and pure feedback forms and has great potential in many diverse applications the performance of the proposed approach is demonstrated through three simulation examples including one nonlinear pure feedback and two nonlinear strict feedback systems

on a new class of completely integrable nonlinear wave equations ii multi hamiltonian structure the multi hamiltonian structure of a class of nonlinear wave equations governing the propagation of finite amplitude waves is discussed infinitely many conservation laws had earlier been obtained for these equations starting from a primary hamiltonian formulation of these equations the necessary and sufficient conditions for the existence of bi hamiltonian structure are obtained and it is shown that the second hamiltonian operator can be constructed solely through a knowledge of the first hamiltonian function the recursion operator which first appears at the level of bi hamiltonian structure gives rise to an infinite sequence of conserved hamiltonians it is found that in general there exist two different infinite sequences of conserved quantities for these equations the recursion relation defining higher hamiltonian structures enables one to obtain the necessary and sufficient conditions for the existence of the k 1 st hamiltonian operator which depends on the kth hamiltonian function the infinite sequence of conserved hamiltonians are common to all the higher hamiltonian structures the equations of gas dynamics are discussed as an illustration of this formalism and it is shown that in general they admit tri hamiltonian structure with two distinct infinite sets of conserved quantities the isothermal case of 1 is an exceptional one that requires separate treatment this corresponds to a specialization of the equations governing the expansion of plasma into vacuum which will be shown to be equivalent to poisson s equation in nonlinear acoustics

stable neural controller design for unknown nonlinear systems using backstepping we propose from an adaptive control perspective a neural controller for a class of unknown minimum phase feedback linearizable nonlinear system with known relative degree the control scheme is based on the backstepping design technique in conjunction with a linearly parametrized neural network structure the resulting controller however moves the complex mechanics involved in a typical backstepping design from off line to online with appropriate choice of the network size and neural basis functions the same controller can be trained online to control different nonlinear plants with the same relative degree with semi global stability as shown by the simple lyapunov analysis meanwhile the controller also preserves some of the performance properties of the standard backstepping controllers simulation results are shown to demonstrate these properties and to compare the neural controller with a standard backstepping controller

alternative bi hamiltonian structures for wdvv equations of associativity the wdvv equations of associativity in two dimensional topological field theory are completely integrable third order monge ampere equations which admit bi hamiltonian structure the time variable plays a distinguished role in the discussion of hamiltonian structure whereas in the theory of wdvv equations none of the independent variables merits such a distinction wdvv equations admit very different alternative hamiltonian structures under different possible choices of the time variable but all these various hamiltonian formulations can be brought together in the framework of the covariant theory of symplectic structure they can be identified as different components of the covariant witten zuckerman symplectic 2 form current density where a variational formulation of the wdvv equation that leads to the hamiltonian operator through the dirac bracket is available

uncertainty performance and model dependency in approximate adaptive nonlinear control we consider systems satisfying a matching condition that are functionally known up to weighted l sup 2 and l sup spl infin measures of uncertainty a modified lq measure of control and state transient performance is given and the performance of a class of approximate model based adaptive controllers is studied an upper performance bound is derived in terms of the uncertainty models the stability and state transient bounds require only the la uncertainty model control effort bounds require both l sup 2 and l sup spl infin uncertainty models and various structural properties of the model basis sufficient conditions are given to ensure that the performance is bounded independently of the model basis size

the generalized gabor scheme of image representation in biological and machine vision a scheme suitable for visual information representation in a combined frequency position space is investigated through image decomposition into a finite set of two dimensional gabor elementary functions gef the scheme is generalized to account for the position dependent gabor sampling rate oversampling logarithmic frequency scaling and phase quantization characteristic of the visual system comparison of reconstructed signal highlights the advantages of the generalized gabor scheme in coding typical bandlimited images it is shown that there exists a tradeoff between the number of frequency components used per position and the number of such clusters sampling rate utilized along the spatial coordinate

learning from adaptive neural dynamic surface control of strict feedback systems learning plays an essential role in autonomous control systems however how to achieve learning in the nonstationary environment for nonlinear systems is a challenging problem in this paper we present learning method for a class of n th order strict feedback systems by adaptive dynamic surface control dsc technology which achieves the human like ability of learning by doing and doing with learned knowledge to achieve the learning this paper first proposes stable adaptive dsc with auxiliary first order filters which ensures the boundedness of all the signals in the closed loop system and the convergence of tracking errors in a finite time with the help of dsc the derivative of the filter output variable is used as the neural network nn input instead of traditional intermediate variables as a result the proposed adaptive dsc method reduces greatly the dimension of nn inputs especially for high order systems after the stable dsc design we decompose the stable closed loop system into a series of linear time varying perturbed subsystems using a recursive design the recurrent property of nn input variables is easily verified since the complexity is overcome using dsc subsequently the partial persistent excitation condition of the radial basis function nn is satisfied by combining a state transformation accurate approximations of the closed loop system dynamics are recursively achieved in a local region along recurrent orbits then the learning control method using the learned knowledge is proposed to achieve the closed loop stability and the improved control performance simulation studies are performed to demonstrate the proposed scheme can not only reuse the learned knowledge to achieve the better control performance with the faster tracking convergence rate and the smaller tracking error but also greatly alleviate the computational burden because of reducing the number and complexity of nn input variables

dirac constraints in field theory lifts of hamiltonian systems to the cotangent bundle to every hamiltonian system is associated a degenerate lagrangian formulation following dirac s theory of constraints one finds a family of lifts of the system to the cotangent bundle of the underlying manifold the lifted system admits a reduction to the original equation such that the original hamiltonian formulation is the pullback of the canonical symplectic form invariants of the original equation can be lifted to invariants of the extended system this procedure is applied to integrable systems such as the korteweg de vries equation

learning continuous trajectories in recurrent neural networks with time dependent weights the paper is concerned with a general learning with arbitrary criterion and state dependent constraints of continuous trajectories by means of recurrent neural networks with time varying weights the learning process is transformed into an optimal control framework where the weights to be found are treated as controls a learning algorithm based on a variational formulation of pontryagin s maximum principle is proposed this algorithm is shown to converge under reasonable conditions to an optimal solution the neural networks with time dependent weights make it possible to efficiently find an admissible solution i e initial weights satisfying state constraints which then serves as an initial guess to carry out a proper minimization of a given criterion the proposed methodology may be directly applicable to both classification of temporal sequences and to optimal tracking of nonlinear dynamic systems numerical examples are also given which demonstrate the efficiency of the approach presented

paper nonlinear adaptive model following control the use of discontinuous control in adaptive model following continuous control systems with nonlinear time varying plant is described the first approach is based on the theory of variable structure systems hyperstability theory is the basis of the second scheme the third one results by combining the previous approaches the link among the three approaches is explored by studying the error dynamics practical implementation and applications are discussed

robustifying nonlinear systems using high order neural network controllers a robust control methodology for affine control of nonlinear dynamical systems is developed in this paper a correction control signal is added to a nominal controller designed to guarantee a desired performance for the corresponding nominal system to render the actual system uniformly and ultimately bounded the control signal is smooth and does not require a priori knowledge of an upper bound on the modeling error and or optimal weight values simulations performed on a simple nonlinear system illustrate the approach

stable sequential identification of continuous nonlinear dynamical systems by growing radial basis function networks this paper presents a sequential identification scheme for continuous nonlinear dynamical systems using neural networks the nonlinearities of the dynamical systems are assumed to be unknown the identification model is a gaussian radial basis function neural network that grows gradually to span the appropriate state space and of sufficient complexity to provide an approximation to the dynamical system the sequential identification algorithm for continuous dynamical nonlinear systems is developed in the continuous time framework instead of in discrete time the approach different from the conventional methods of optimizing a cost function attempts to ensure stability of the overall system while the neural network learns the system dynamics the stability and convergence of the overall identification scheme are guaranteed by parameter adjustment laws developed using the lyapunov synthesis approach to ensure that the modelling error can be reduced arbitrarily a one to one mapping is proposed so that th

comparison of some neural network and scattered data approximations the inverse manipulator kinematics example this paper compares the application of five different methods for the approximation of the inverse kinematics of a manipulator arm from a number of joint angle cartesian coordinate training pairs the first method is a standard feedforward neural network with error backpropagation learning the next two methods are derived from an extended kohonen map algorithm that we combine with shepard interpolation for the forward computation we compare the method of ritter et al for the learning of the extended kohonen map to our own scheme based on gradient descent optimization we also study three scattered data approximation algorithms they include two variants of the radial basis function rbf method hardy s multiquadrics and gaussian rbf we further develop our own local polynomial fit method that could be considered as a modification of mclain s method we propose extensions to the considered scattered data approximation algorithms to make them suitable for vector valued multivariable functions such as the mapping of cartesian coordinates into joint angle coordinates

adaptive learning control for finite interval tracking based on constructive function approximation and wavelet using a constructive function approximation network an adaptive learning control alc approach is proposed for finite interval tracking problems the constructive function approximation network consists of a set of bases and the number of bases can evolve when learning repeats the nature of the basis allows the continuous adaptive learning of parameters when the network undergoes any structural changes and consequently offers the flexibility in tuning the network structure the expandability of the bases guarantees precision of the function approximation and avoids the trial and error procedure in structure selection for any fixed structure network two classes of unknown nonlinear functions namely either global l2 or local l2 with a known bounding function are taken into consideration using the lyapunov method the existence of solution and the convergence property of the proposed alc system are discussed in a rigorous manner by virtue of the celebrated orthonormal and multiresolution properties wavelet network is used as the universal function approximator with the weights tuned by the proposed adaptive learning mechanism

brief paper novel adaptive neural control design for nonlinear mimo time delay systems in this paper we address the problem of adaptive neural control for a class of multi input multi output mimo nonlinear time delay systems in block triangular form based on a neural network nn online approximation model a novel adaptive neural controller is obtained by constructing a novel quadratic type lyapunov krasovskii functional which not only efficiently avoids the controller singularity but also relaxes the restriction on unknown virtual control coefficients the merit of the suggested controller design scheme is that the number of online adapted parameters is independent of the number of nodes of the neural networks which reduces the number of the online adaptive learning laws considerably the proposed controller guarantees that all closed loop signals remain bounded while the output tracking error dynamics converges to a neighborhood of the origin a simulation example is given to illustrate the design procedure and performance of the proposed method

multiplication free radial basis function network for the purpose of adaptive function approximation a new radial basis function network is proposed which is nonlinear in its parameters the goal is to reduce significantly the computational effort for a serial processor by avoiding multiplication in both the evaluation of the function model and the computation of the parameter adaptation the approximation scheme makes use of a grid based gaussian basis function network due to the local support of digitally implemented gaussian functions the function representation is parametric local and therefore well suited for an online implementation on a microcomputer a gradient descent based nonlinear learning algorithm is presented and the convergence of the algorithm is proved

canonical formulation of shallow water waves the author introduces a new potential and use it with the velocity potential to construct a new variational principle for long surface waves in shallow water applying dirac s theory of constraints the author casts it into canonical form and obtain an explicit expression for the exact hamiltonian

generalized hermite interpolation via matrix valued conditionally positive definite functions in this paper we consider a broad class of interpolation problems for both scalarand vector valued multivariate functions subject to linear side conditions such as being divergence free where the data are generated via integration against compactly supported distributions we show that by using certain families of matrix valued conditionally positive definite functions such interpolation problems are well poised that is the interpolation matrices are invertible as a sample result we show that a divergence free vector field can be interpolated by a linear combination of convolutions of the data generating distributions with a divergence free 3 x 3 matrix valued conditionally positive definite function in addition we obtain norm estimates for inverses of interpolation matrices that arise in a class of multivariate hermite interpolation problems

quaternion based adaptive output feedback attitude control of spacecraft using chebyshev neural networks this paper investigates the problem of output feedback attitude control of an uncertain spacecraft two robust adaptive output feedback controllers based on chebyshev neural networks cnn termed adaptive neural networks nn controller i and adaptive nn controller ii are proposed for the attitude tracking control of spacecraft the four parameter representations quaternion are employed to describe the spacecraft attitude for global representation without singularities the nonlinear reduced order observer is used to estimate the derivative of the spacecraft output and the cnn is introduced to further improve the control performance through approximating the spacecraft attitude motion the implementation of the basis functions of the cnn used in the proposed controllers depends only on the desired signals and the smooth robust compensator using the hyperbolic tangent function is employed to counteract the cnn approximation errors and external disturbances the adaptive nn controller ii can efficiently avoid the over estimation problem i e the bound of the cnns output is much larger than that of the approximated unknown function and hence the control input may be very large existing in the adaptive nn controller i both adaptive output feedback controllers using cnn can guarantee that all signals in the resulting closed loop system are uniformly ultimately bounded for performance comparisons the standard adaptive controller using the linear parameterization of spacecraft attitude motion is also developed simulation studies are presented to show the advantages of the proposed cnn based output feedback approach over the standard adaptive output feedback approach

a consistent boundary condition for vorticity streamfunction simulation of wall bounded vortex flow this paper was motivated by a computational effort to model the aircraft wake vortex hazard near airports those flows can usually be approximated as a pair of two dimensional incompressible vortices interacting with an infinite solid wall the present numerical model uses a vorticity streamfunction formulation to simulate the two dimensional problem since vorticity generation near the wall alters the evolution of the secondary and tertiary vortices directly accurate modeling of the wall region is critical a local relationship between vorticity and streamfunction for a wall boundary condition has been established from a new point of view by specifying the streamfunction at the boundary grid lifted away from the solid wall the new method has utilized taylor series expansions near the wall boundary although the resulting expressions are only first order accurate the critical importance of physical and mathematical consistency has been achieved numerical test cases are discussed in the paper

stable adaptive neuro control design via lyapunov function derivative estimation a new approach to the tracking problem for affine in the control nonlinear dynamical systems whose nonlinearities are assumed to be unknown is presented in this paper the philosophy of the developed technique is based on estimating the derivative of an unknown lyapunov function exploiting the approximation capabilities of the linear in the weights neural network structures a novel resetting strategy guarantees the boundedness away from zero of certain signals the uniform ultimate boundedness of the tracking error to an arbitrarily small set plus the boundedness of all other signals in the closed loop is guaranteed

hamiltonian structure of real monge ampere equations the variational principle for the real homogeneous monge ampere equation in two dimensions is shown to contain three arbitrary functions of four variables there exist two different specializations of this variational principle where the lagrangian is degenerate and furthermore contains an arbitrary function of two variables the hamiltonian formulation of these degenerate lagrangian systems requires the use of dirac s theory of constraints as in the case of most completely integrable systems the constraints are second class and dirac brackets directly yield the hamiltonian operators thus the real homogeneous monge ampere equation in two dimensions admits two classes of infinitely many hamiltonian operators namely a family of local as well as another family non local hamiltonian operators and symplectic 2 forms which depend on arbitrary functions of two variables the simplest non local hamiltonian operator corresponds to the kac moody algebra of vector fields and functions on the unit circle hamiltonian operators that belong to either class are compatible with each other but between classes there is only one compatible pair in the case of real monge ampere equations with constant right hand side this compatible pair is the only pair of hamiltonian operators that survives then the complete integrability of all these real monge ampere equations follows by magri s theorem some of the remarkable properties we have obtained for the hamiltonian structure of the real homogeneous monge ampere equation in two dimensions turn out to be generic to the real homogeneous monge ampere equation and the geodesic flow for the complex homogeneous monge ampere equation in arbitrary number of dimensions hence among all integrable nonlinear evolution equations in one space and one time dimension the real homogeneous monge ampere equation is distinguished as one that retains its character as an integrable system in multiple dimensions

approximation based control of nonlinear mimo time delay systems approximation based control is presented for a class of multi input multi output mimo nonlinear systems in block triangular form with unknown state delays neural networks nns are utilized to approximate and compensate for unknown functions in the system dynamics including the unknown bounds of the functions of delayed states the use of a separation technique removes the need for any assumption on the function of delayed states and allows the handling of multiple delays in each function of delayed states by combining the use of lyapunov krasovskii functionals and adaptive nn backstepping the proposed control guarantees that all closed loop signals remain bounded while the outputs converge to a neighborhood of the desired trajectories simulation results demonstrate the effectiveness of the proposed scheme

control of chaotic dynamical systems using radial basis function network approximators abstract this paper presents a general control method based on radial basis function networks rbfns for chaotic dynamical systems for many chaotic systems that can be decomposed into a sum of a linear and a nonlinear part under some mild conditions the rbfn can be used to well approximate the nonlinear part of the system dynamics the resulting system is then dominated by the linear part with some small or weak residual nonlinearities due to the rbfn approximation errors thus a simple linear state feedback controller can be devised to drive the system response to a desirable set point in addition to some theoretical analysis computer simulations on two representative continuous time chaotic systems the duffing and the lorenz systems are presented to demonstrate the effectiveness of the proposed method

complete discrete 2 d gabor transforms by neural networks for image analysis and compression a three layered neural network is described for transforming two dimensional discrete signals into generalized nonorthogonal 2 d gabor representations for image analysis segmentation and compression these transforms are conjoint spatial spectral representations which provide a complete image description in terms of locally windowed 2 d spectral coordinates embedded within global 2 d spatial coordinates in the present neural network approach based on interlaminar interactions involving two layers with fixed weights and one layer with adjustable weights the network finds coefficients for complete conjoint 2 d gabor transforms without restrictive conditions in wavelet expansions based on a biologically inspired log polar ensemble of dilations rotations and translations of a single underlying 2 d gabor wavelet template image compression is illustrated with ratios up to 20 1 also demonstrated is image segmentation based on the clustering of coefficients in the complete 2 d gabor transform

adaptive output feedback control of nonlinear systems using neural networks a direct adaptive output feedback control design procedure is developed for highly uncertain nonlinear systems that does not rely on state estimation the approach is also applicable to systems of unknown but bounded dimension in particular we consider single input single output nonlinear systems whose output has known but otherwise arbitrary relative degree this includes systems with both parameter uncertainty and unmodeled dynamics the result is achieved by extending the universal function approximation property of linearly parameterized neural networks to model unknown system dynamics from input output data the network weight adaptation rule is derived from lyapunov stability analysis and guarantees that the adapted weight errors and the tracking error are bounded numerical simulations of an output feedback controlled van der pol oscillator coupled with a linear oscillator is used to illustrate the practical potential of the theoretical results

reproducing kernel hilbert space approach for the online update of radial bases in neuro adaptive control classical work in model reference adaptive control for uncertain nonlinear dynamical systems with a radial basis function rbf neural network adaptive element does not guarantee that the network weights stay bounded in a compact neighborhood of the ideal weights when the system signals are not persistently exciting pe recent work has shown however that an adaptive controller using specifically recorded data concurrently with instantaneous data guarantees boundedness without pe signals however the work assumes fixed rbf network centers which requires domain knowledge of the uncertainty motivated by reproducing kernel hilbert space theory we propose an online algorithm for updating the rbf centers to remove the assumption in addition to proving boundedness of the resulting neuro adaptive controller a connection is made between pe signals and kernel methods simulation results show improved performance

variational estimation in spatiotemporal systems from continuous and point process observations spatiotemporal models are ubiquitous in science and engineering yet estimation in these models from discrete observations remains computationally challenging we propose a practical novel approach to inference in spatiotemporal processes both from continuous and from discrete point process observations the method is based on a finite dimensional reduction of the spatiotemporal model followed by a mean field variational approximate inference approach to cater for the point process case a variational laplace approach is proposed which yields tractable computations of approximate variational posteriors results show that variational bayes is a viable and practical alternative to statistical methods such as expectation maximization or markov chain monte carlo

adaptive control of a class of nonlinear systems with nonlinearly parameterized fuzzy approximators recently through the use of parameterized fuzzy approximators various adaptive fuzzy control schemes have been developed to deal with nonlinear systems whose dynamics are poorly understood an important class of parameterized fuzzy approximators is constructed using radial basis function rbf as a membership function however some tuneable parameters in rbf appear nonlinearly and the determination of the adaptive law for such parameters is a nontrivial task in this paper we propose a new adaptive control method in an effort to tune all the rbf parameters thereby reducing the approximation error and improving control performance global boundedness of the overall adaptive system and tracking to within a desired precision are established with the new adaptive controller simulations performed on a simple nonlinear system illustrate the approach

neural networks based adaptive control for nonlinear time varying delays systems with unknown control direction this paper investigates a neural network nn state observer based adaptive control for a class of time varying delays nonlinear systems with unknown control direction an adaptive neural memoryless observer in which the knowledge of time delay is not used is designed to estimate the system states furthermore by applying the property of the function tanh2 e the function can be defined at 0 and introducing a novel type appropriate lyapunov krasovskii functional an adaptive output feedback controller is constructed via backstepping method which can efficiently avoid the problem of controller singularity and compensate for the time delay it is highly proven that the closed loop systems controller designed by the nn basis function property new kind parameter adaptive law and nussbaum function in detecting the control direction is able to guarantee the semi global uniform ultimate boundedness of all signals and the tracking error can converge to a small neighborhood of zero the characteristic of the proposed approach is that it relaxes any restrictive assumptions of lipschitz condition for the unknown nonlinear continuous functions and the proposed scheme is suitable for the systems with mismatching conditions and unmeasurable states finally two simulation examples are given to illustrate the effectiveness and applicability of the proposed approach

bayesian nonparametric adaptive control using gaussian processes most current model reference adaptive control mrac methods rely on parametric adaptive elements in which the number of parameters of the adaptive element are fixed a priori often through expert judgment an example of such an adaptive element is radial basis function networks rbfns with rbf centers preallocated based on the expected operating domain if the system operates outside of the expected operating domain this adaptive element can become noneffective in capturing and canceling the uncertainty thus rendering the adaptive controller only semiglobal in nature this paper investigates a gaussian process based bayesian mrac architecture gp mrac which leverages the power and flexibility of gp bayesian nonparametric models of uncertainty the gp mrac does not require the centers to be preallocated can inherently handle measurement noise and enables mrac to handle a broader set of uncertainties including those that are defined as distributions over functions we use stochastic stability arguments to show that gp mrac guarantees good closed loop performance with no prior domain knowledge of the uncertainty online implementable gp inference methods are compared in numerical simulations against rbfn mrac with preallocated centers and are shown to provide better tracking and improved long term learning

a general fuzzy scheme for nonlinear processes with stability analysis abstract in this paper we develop a general fuzzy control scheme for nonlinear processes assuming little knowledge about the dynamics of the controlled process the proposed scheme starts by probing the process at different points in its operating region to generate a fuzzy quantisation a simple local controller is then designed at each fuzzy locality a fuzzy inference mechanism then links up tje local controllers to form a global controller which can be further refined by the learning algorithm by employing a newly developed structure adaptive fuzzy modelling scheme the appropriate fuzzy rule base for the inference mechanism can be extracted stably and efficiently the conditions for the stability of the global controller are rigourously established simulation results are presented to illustrate the effectiveness of the scheme

dirac s theory of constraints in field theory and the canonical form of hamiltonian differential operators a simple algorithm for constructing the canonical form of hamiltonian systems of evolution equations with constant coefficient hamiltonian differential operators is given the result of the construction is equivalent to the canonical system derived using dirac s theory of constraints from the corresponding degenerate lagrangian

two mode adaptive fuzzy control with approximation error estimator in this paper we propose a two mode adaptive fuzzy controller with approximation error estimator in the learning mode the controller employs some modified adaptive laws to tune the fuzzy system parameters and an approximation error estimator to compensate for the inherent approximation error in the operating mode the fuzzy system parameters are fixed only the estimator is updated online mathematically we show that the closed loop system is stable in the sense that all the variables are bounded in both modes we also establish mathematical bounds on the tracking error state vector control signal and the rms error using these bounds we show that controller s design parameters can be chosen to achieve desired control performance after that an algorithm to automatically switch the controller between two modes is presented finally simulation studies of an inverted pendulum system and a chua s chaotic circuit demonstrate the usefulness of the proposed controller

bi hamiltonian structures of d boussinesq and benney lax equations the dispersionless boussinesq and benney lax equations are equations of hydrodynamic type which can be obtained as reductions of the dispersionless kadomtsev petviashvili equation we find that for the three component reduction the dispersionless boussinesq and benney lax equations are the same up to a diffeomorphism this equivalence becomes manifest when the equations of motion are cast into the form of a triplet of conservation laws furthermore in this form we are able to recognize a non trivial scaling symmetry of these equations which plays an important role in the construction of their bi hamiltonian structure we exhibit a pair of compatible hamiltonian operators which belong to a restricted class of dubrovin and novikov operators appropriate to a system of conservation laws the recursion operator for this system generates three infinite sequences of conserved hamiltonians

integrated design of a linear neuro adaptive controller in the presence of norm bounded uncertainties adaptive neural controllers are often criticised for the lack of clear and easy design methodologies that relate adaptive neural network nn design parameters to performance requirements this study proposes a methodology for the design of an integrated linear adaptive model reference controller that guarantees component wise boundedness of the tracking error within an a priori specified compact domain the approach is based on the design of a robust invariant ellipsoidal set where both the nn reconstruction error and the neuro adaptive control are considered as bounded persistent uncertainties we show that all the performance and control requirements for the closed loop system can be expressed as linear matrix inequality constraints this brings the advantage that feasibility and optimal design parameters can be effectively computed while solving a linear optimisation problem an advantage of the method is that it allows a systematic and quantitative evaluation of the interplay between the design param

adaptive fuzzy tracking control for a class of pure feedback stochastic nonlinear systems with non lower triangular structure this paper considers the problem of the adaptive fuzzy tracking control for a class of nonaffine stochastic nonlinear systems without lower triangular form by using fuzzy logic systems universal approximation property an adaptive fuzzy controller is proposed which guarantees that all the signals in the closed loop system are bounded in the sense of mean quartic value and the output tracking error eventually converges to a small neighborhood around the origin simulation results are provided to illustrate the effectiveness of the proposed scheme

adaptive neural network control for a class of low triangular structured nonlinear systems in this paper a class of unknown perturbed nonlinear systems is theoretically stabilized by using adaptive neural network control the systems with disturbances and nonaffine unknown functions have low triangular structure which generalizes both strict feedback uncertain systems and pure feedback ones there do not exist any effective methods to stabilize this kind of systems with some new conclusions for nussbaum gain functions ngf and the idea of backstepping semiglobal uniformal and ultimate boundedness of all the signals in the closed loop is proved at equilibrium point the two problems control directions and control singularity are well dealt with the effectiveness of proposed scheme is shown by simulation on a proper nonlinear system

an improvement on stable adaptive control for a class of nonlinear systems in the work of zhang et al an excellent neural network controller is provided by introducing a modified lyapunov function to eliminate the singularity issue completely in this note we focus on the improvement on the work of zhang et al for a class of unknown nonlinear systems

brief paper localized adaptive bounds for approximation based backstepping recent research has established the utility of adaptive bounds on model uncertainty in adaptive approximation based control such bounds have utility both for robust control law design and for self organizing approximators that could adjust the number of basis elements n by adding additional approximation resources in the regions where the approximation error bound is large existing adaptive bounding methods utilize algorithms with global forgetting in this article we investigate methods to develop bounds on approximation accuracy that involve local forgetting the importance of local versus global forgetting is motivated in the text and illustrated with an example

identification and control of a nonlinear discrete time system based on its linearization a unified framework this paper presents a unified theoretical framework for the identification and control of a nonlinear discrete time dynamical system in which the nonlinear system is represented explicitly as a sum of its linearized component and the residual nonlinear component referred to as a higher order function this representation substantially simplifies the procedure of applying the implicit function theorem to derive local properties of the nonlinear system and reveals the role played by the linearized system in a more transparent form under the assumption that the linearized system is controllable and observable it is shown that 1 the nonlinear system is also controllable and observable in a local domain 2 a feedback law exists to stabilize the nonlinear system locally and 3 the nonlinear system can exactly track a constant or a periodic sequence locally if its linearized system can do so with some additional assumptions the nonlinear system is shown to have a well defined relative degree delay and zero dynamics if the zero dynamics of the linearized system is asymptotically stable so is that of the nonlinear one and in such a case a control law exists for the nonlinear system to asymptotically track an arbitrary reference signal exactly in a neighborhood of the equilibrium state the tracking can be achieved by using the state vector for feedback or by using only the input and the output in which case the nonlinear autoregressive moving average narma model is established and utilized these results are important for understanding the use of neural networks as identifiers and controllers for general nonlinear discrete time dynamical systems

further results on adaptive control for a class of nonlinear systems using neural networks zhang et al presented an excellent neural network nn controller for a class of nonlinear control designs the singularity issue is completely avoided based on a modified lyapunov function their lemma illustrates the existence of an ideal control which is important in establishing the nn approximator in this paper we provide a lyapunov function to realize an alternative ideal control which is more direct and simpler the major contributions of this paper are divided into two parts first it proposes a control scheme which results in a smaller dimensionality of nn than that of zhang et al in this way the proposed nn controller is easier to implement and more reliable for practical purposes second by removing certain restrictions from the design reported by zhang et al we further develop a new nn controller which can be applied to a wider class of systems

dynamic structure neural networks for stable adaptive control of nonlinear systems an adaptive control technique using dynamic structure gaussian radial basis function neural networks that grow in time according to the location of the system s state in space is presented for the affine class of nonlinear systems having unknown or partially known dynamics the method results in a network that is economic in terms of network size for cases where the state spans only a small subset of state space by utilizing less basis functions than would have been the case if basis functions were centered on discrete locations covering the whole relevant region of state space additionally the system is augmented with sliding control so as to ensure global stability if and when the state moves outside the region of state space spanned by the basis functions and to ensure robustness to disturbances that arise due to the network inherent approximation errors and to the fact that for limiting the network size a minimal number of basis functions are actually being used adaptation laws and sliding control gains that ensure system stability in a lyapunov sense are presented together with techniques for determining which basis functions are to form part of the network structure the effectiveness of the method is demonstrated by experiment simulations

multi hamiltonian structure of equations of hydrodynamic type the discussion of the hamiltonian structure of two component equations of hydrodynamic type is completed by presenting the hamiltonian operators for euler s equation governing the motion of plane sound waves of finite amplitude and another quasilinear second order wave equation there exists a doubly infinite family of conserved hamiltonians for the equations of gas dynamics that degenerate into one namely the benney sequence for shallow water waves infinite sequences of conserved quantities for these equations are also presented in the case of multicomponent equations of hydrodynamic type it is shown that kodama s generalization of the shallow water equations admits bi hamiltonian structure

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

robust integral of neural network and error sign control of mimo nonlinear systems this paper presents a novel state feedback control scheme for the tracking control of a class of multi input multioutput continuous time nonlinear systems with unknown dynamics and bounded disturbances first the control law consisting of the robust integral of a neural network nn output plus sign of the tracking error feedback multiplied with an adaptive gain is introduced the nn in the control law learns the system dynamics in an online manner while the nn residual reconstruction errors and the bounded disturbances are overcome by the error sign signal since both of the nn output and the error sign signal are included in the integral the continuity of the control input is ensured the controller structure and the nn weight update law are novel in contrast with the previous effort and the semiglobal asymptotic tracking performance is still guaranteed by using the lyapunov analysis in addition the nn weights and all other signals are proved to be bounded simultaneously the proposed approach also relaxes the need for the upper bounds of certain terms which are usually required in the previous designs finally the theoretical results are substantiated with simulations

a neural approach for control of nonlinear systems with feedback linearization several schemes for feedback linearization using neural networks have been investigated and compared then an approach to design a neurocontroller in the sense of feedback linearization is introduced the contents include 1 full input output linearization when a system has relative degree n 2 partial input output linearization when a system has relative degree r r n and 3 approximate linearization when the involutivity condition does not hold corresponding programs and examples are given to illustrate the proposed methodology

adaptive neural control for a class of nonlinear systems with uncertain hysteresis inputs and time varying state delays in this paper adaptive variable structure neural control is investigated for a class of nonlinear systems under the effects of time varying state delays and uncertain hysteresis inputs the unknown time varying delay uncertainties are compensated for using appropriate lyapunov krasovskii functionals in the design and the effect of the uncertain hysteresis with the prandtl ishlinskii pi model representation is also mitigated using the proposed control by utilizing the integral type lyapunov function the closed loop control system is proved to be semi globally uniformly ultimately bounded sguub extensive simulation results demonstrate the effectiveness of the proposed approach

fuzzy adaptive controller for mimo nonlinear systems with known and unknown control direction this paper investigates fuzzy adaptive control schemes for a class of multi input multi output mimo unknown nonlinear systems with known and unknown sign of the control gain matrix three fuzzy adaptive control schemes are developed in the design of the second and third controller we will exploit a decomposition of the control gain matrix into a symmetric positive definite matrix a diagonal matrix with diagonal entries 1 or 1 and a unity upper triangular matrix the nussbaum type function is used to deal with the unknown control direction i e the unknown sign of the control gain matrix for updating the parameters of the fuzzy system an adaptation proportional integral pi law is proposed theoretical results are illustrated through two simulation examples

direct adaptive nn control of a class of nonlinear systems in this paper direct adaptive neural network nn control is presented for a class of affine nonlinear systems in the strict feedback form with unknown nonlinearities by utilizing a special property of the affine term the developed scheme avoids the controller singularity problem completely all the signals in the closed loop are guaranteed to be semiglobally uniformly ultimately bounded and the output of the system is proven to converge to a small neighborhood of the desired trajectory the control performance of the closed loop system is guaranteed by suitably choosing the design parameters simulation results are presented to show the effectiveness of the approach

a model reference adaptive control scheme for pure feedback nonlinear systems a model reference adaptive control mrac scheme is presented for nonlinear systems in a pure feedback canonical form with unknown parameters the present of parameter uncertainty in the system causes imperfect linearization i e it introduces nonlinear additive terms in the transformed coordinates under some mild technical assumptions global convergence of the output error is established for all initial estimates of the parameter vector lying in an open neighborhood of the true parameters in the parameter space

stable adaptive control for a class of nonlinear systems using a modified lyapunov function investigates the adaptive control design for a class of nonlinear systems using lyapunov s stability theory the proposed method is developed based on a novel lyapunov function which removes the possible controller singularity problem in some of the existing adaptive control schemes using feedback linearization techniques the resulting closed loop system is proven to be globally stable and the output tracking error converges to an adjustable neighborhood of zero

global adaptive neural control for strict feedback time delay systems with predefined output accuracy this paper focuses on the stabilization problem for a class of nonlinear strict feedback systems with disturbances and time delay by constructing some nonnegative functionals a multiswitching based adaptive backstepping neural state feedback controller is designed compared with all the existing control methodologies for the uncertain time delay systems the outstanding merits of the proposed control scheme are presented as follows first the controller guarantees that all the signals in the closed loop system remain globally bounded meanwhile the system output achieves an accuracy that is given a priori according to the practical requirements second in contrast to the classical adaptive backstepping neural control schemes we analyze the convergence of the tracking error by using barbalat s lemma instead of lyapunov stability theory third the main technical novelty is to construct three new nth order continuously differentiable functions which are used to design the actual controller the virtual control variables and the adaptive laws two simulation examples are provided to illustrate the effectiveness and advantage of the proposed control scheme

brief lq performance bounds for adaptive output feedback controllers for functionally uncertain nonlinear systems we consider functionally uncertain systems which can be written in an output feedback form where the nonlinearities are functions of the output only the uncertainty is described by a weighted l 2 norm about a nominal system and an approximate adaptive design is given which ensures output practical stability the main result requires knowledge of the weighted l 2 uncertainty level an upper bound on the lq performance of the output transient and the control input is derived where the cost penalises the output transient and the control effort on the time interval where the output lies outside the prescribed neighbourhood of zero to which we achieve convergence

robust adaptive neural control for a class of perturbed strict feedback nonlinear systems this paper presents a robust adaptive neural control design for a class of perturbed strict feedback nonlinear system with both completely unknown virtual control coefficients and unknown nonlinearities the unknown nonlinearities comprise two types of nonlinear functions one naturally satisfies the triangularity condition and can be approximated by linearly parameterized neural networks while the other is assumed to be partially known and consists of parametric uncertainties and known bounding functions with the utilization of iterative lyapunov design and neural networks the proposed design procedure expands the class of nonlinear systems for which robust adaptive control approaches have been studied the design method does not require a priori knowledge of the signs of the unknown virtual control coefficients leakage terms are incorporated into the adaptive laws to prevent parameter drifts due to the inherent neural network approximation errors it is proved that the proposed robust adaptive scheme can guarantee the uniform ultimate boundedness of the closed loop system signals the control performance can be guaranteed by an appropriate choice of the design parameters simulation studies are included to illustrate the effectiveness of the proposed approach

a novel robust adaptive fuzzy tracking control for a class of nonlinearmulti input multi output systems robust adaptive fuzzy tracking control of a class of uncertain multi input multi output nonlinear systems with coupled interconnections is considered in this paper takagi sugeno t s fuzzy systems are used to approximate the unknown system functions a novel adaptive control scheme is developed on the basis of the so called dynamic surface control and minimal learning parameters techniques the proposed scheme has following two key features first the number of parameters updated online for each subsystem is reduced to one and both problems of curse of dimension for high dimensional systems and explosion of complexity inherent in the conventional backstepping methods are circumvented second the potential controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques is overcome it is shown via lyapunov theory that all the signals in the closed loop system are semiglobally uniformly ultimately bounded finally simulation results via two examples are presented to demonstrate the effectiveness and advantages of the proposed scheme

a self organizing fuzzy control approach for bank to turn missiles abstract in this paper an adaptive fuzzy autopilot is developed for bank to turn btt missiles we propose a self organizing rotated fuzzy basis function control system that is more flexible than fuzzy basis function expansion in that not only the output weights but also the shapes of fuzzy basis functions can be tuned another characteristic of this autopilot is to incorporate the terminal attractor controller into the autopilot to speed up the convergence rate the global stability analysis established in the lyapunov sense shows that the states and tracking errors of the btt missile are uniformly bounded finally there are two simulation examples to demonstrate the effectiveness of the proposed autopilot the purpose of the first example is to indicate the better performance including faster convergence speed and lower steady state error obtained by autopilots with terminal attractors as compared with that autopilot without terminal attractor another simulation result proves that btt missile can manipulate under various flight conditions in our scenarios and shows the superior tracking performance

persistency of excitation in identification using radial basis function approximants in this paper identification algorithms whose convergence and rate of convergence hinge on the regressor vector being persistently exciting are discussed it is then shown that if the regressor vector is constructed out of radial basis function approximants it will be persistently exciting provided a kind of ergodic condition is satisfied in addition bounds on parameters associated with the persistently exciting regressor vector are provided these parameters are connected with both the convergence and rates of convergence of the algorithms involved

nonlinear adaptive control using neural networks and multiple models in this paper adaptive control of a class of nonlinear discrete time dynamical systems with boundedness of all signals is established by using a linear robust adaptive controller and a neural network based nonlinear adaptive controller and switching between them by a suitably defined switching law the linear controller when used alone assures boundedness of all the signals but not satisfactory performance the nonlinear controller may result in improved response but may also result in instability by using a switching scheme it is demonstrated that improved performance and stability can be simultaneously achieved

spatiotemporal system identification with continuous spatial maps and sparse estimation we present a framework for the identification of spatiotemporal linear dynamical systems we use a state space model representation that has the following attributes 1 the number of spatial observation locations are decoupled from the model order 2 the model allows for spatial heterogeneity 3 the model representation is continuous over space and 4 the model parameters can be identified in a simple and sparse estimation procedure the model identification procedure we propose has four steps 1 decomposition of the continuous spatial field using a finite set of basis functions where spatial frequency analysis is used to determine basis function width and spacing such that the main spatial frequency contents of the underlying field can be captured 2 initialization of states in closed form 3 initialization of state transition and input matrix model parameters using sparse regression the least absolute shrinkage and selection operator method and 4 joint state and parameter estimation using an iterative kalman filter sparse regression algorithm to investigate the performance of the proposed algorithm we use data generated by the kuramoto model of spatiotemporal cortical dynamics the identification algorithm performs successfully predicting the spatiotemporal field with high accuracy whilst the sparse regression leads to a compact model

adaptive neural control for output feedback nonlinear systems using a barrier lyapunov function in this brief adaptive neural control is presented for a class of output feedback nonlinear systems in the presence of unknown functions the unknown functions are handled via on line neural network nn control using only output measurements a barrier lyapunov function blf is introduced to address two open and challenging problems in the neuro control area 1 for any initial compact set how to determine a priori the compact superset on which nn approximation is valid and 2 how to ensure that the arguments of the unknown functions remain within the specified compact superset by ensuring boundedness of the blf we actively constrain the argument of the unknown functions to remain within a compact superset such that the nn approximation conditions hold the semiglobal boundedness of all closed loop signals is ensured and the tracking error converges to a neighborhood of zero simulation results demonstrate the effectiveness of the proposed approach

stable multi input multi output adaptive fuzzy neural control in this letter stable direct and indirect adaptive controllers are presented that use takagi sugeno t s fuzzy systems 1985 conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal vector for a class of continuous time multi input multi output mimo square nonlinear plants with poorly understood dynamics the direct adaptive scheme allows for the inclusion of a priori knowledge about the control input in terms of exact mathematical equations or linguistics while the indirect adaptive controller permits the explicit use of equations to represent portions of the plant dynamics we prove that with or without such knowledge the adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of the reference inputs we do not impose any initialization conditions on the controllers and guarantee convergence of the tracking error to zero

direct adaptive fuzzy tracking control for a class of perturbed strict feedback nonlinear systems in this paper a novel direct adaptive fuzzy tracking control scheme is presented for a class of perturbed strict feedback nonlinear systems with unknown virtual control coefficients based on the mamdani type fuzzy logic system online approximation capability a direct adaptive fuzzy tracking controller is developed by using the backstepping approach the proposed design scheme guarantees that all the signals in the resulting closed loop system are uniform ultimate bounded and the tracking error converges to an arbitrarily small neighborhood of the origin in addition the number of the online adaptive parameters is not more than the order of the considered system and the possible controller singularity problem is removed by introducing the modified integral lyapunov functions finally two simulation examples are used to demonstrate the effectiveness of the proposed control scheme

robust local stability of multilayer recurrent neural networks we derive a condition for robust local stability of multilayer recurrent neural networks with two hidden layers the stability condition follows from linking theories about linearization robustness analysis of linear systems under nonlinear perturbation and matrix inequalities a characterization of the basin of attraction of the origin is given in terms of the level set of a quadratic lyapunov function similar to the nl sub q theory the local stability is imposed around the origin and the apparent basin of attraction is made large by applying the criterion while the proven basin of attraction is relatively small due to conservatism of the criterion modification of the dynamic backpropagation by the new stability condition is discussed and illustrated by simulation examples

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

stabilization of feedback linearizable systems using a radial basis function network the main obstacle in the practical use of the feedback linearization is the difficulty in obtaining a linearizing feedback and a coordinate transformation map finding a desired transformation map and feedback turns out to be finding an integrating factor for an annihilating one form in this work we develop numerical algorithms for an integrating factor and the corresponding zero form employing a radial basis function rbf neural network as an interpolation method for the data resulted from the numerical algorithms the authors obtained an approximate integrating factor and zero form in closed forms finally they construct a stabilizing controller based on a linearized system with the use of the approximate integrating factor and zero form

neural network based dobc for a class of nonlinear systems with unmatched disturbances in this brief the problem of composite anti disturbance tracking control for a class of strict feedback systems with unmatched unknown nonlinear functions and external disturbances is investigated a disturbance observer based control dobc in combination with a neural network scheme and back stepping method is developed to achieve a composite anti disturbance controller design that provides guaranteed performance in the proposed method a conventional disturbance observer and a radial basis function neural network rbfnn are combined into a new disturbance observer to estimate the unmatched disturbances as compared with conventional dobc methods the primary merit of the proposed method is that the unknown nonlinear functions are approximated using the rbfnn technique and not regarded as part of the disturbances or estimated by a conventional disturbance observer hence the proposed method can obtain higher control accuracy than the conventional dobc methods this advantage is validated by simulation studies

conservation laws for shallow water waves on a sloping beach shallow water waves are governed by a pair of nonlinear partial differential equations we transfer the associated homogeneous and nonhomogeneous systems corresponding to constant and sloping depth respectively to the hodograph plane where we find all the nonsimple wave solutions and construct infinitely many polynomial conversation laws we also establish correspondence between conservation laws and hodograph solutions as well as backlund transformations by using the linear nature of the problems on the hodograph plane