parameterization and adaptive control of multivariable noncanonical t s fuzzy systems this paper conducts a new study for adaptive takagi sugeno t s fuzzy approximation based control of multi input and multi output mimo noncanonical form nonlinear systems canonical form nonlinear systems have explicit relative degree structures whose approximation models can be directly used to derive desired parameterized controllers noncanonical form nonlinear systems usually do not have such a feature nor do their approximation models which are also in noncanonical forms this paper shows that it is desirable to reparameterize noncanonical form t s fuzzy system models with smooth membership functions for adaptive control and such system reparameterization can be realized using relative degrees a concept yet to be studied for mimo noncanonical form t s fuzzy systems this paper develops an adaptive feedback linearization scheme for control of such general system models with uncertain parameters by first deriving various relative degree structures and normal forms for such systems then a reparameterization procedure is developed for such system models based on which adaptive control designs are derived with desired stability and tracking properties analyzed a detailed example is presented with simulation results to show the new control design procedure and desired control system performance

output feedback direct adaptive fuzzy controller based on frequency domain methods this paper describes a design method that guarantees the stability of an adaptive fuzzy control system the system consists of an unstable plant with an irrational transfer function a takagi sugeno fuzzy adaptive controller a nonlinear reference model and an adaptation mechanism the gradient based adaptation mechanism changes the consequents of the controller rules in such a way that the closed loop system behaves like the reference model the proposed design procedure utilizes frequency domain methods in the forms of the nyquist and circle criteria it is assumed that the function of the fuzzy controller is a nonlinearity described by a sector condition this condition means that the controller function lies between two lines passing through the origin in this method the function of the fuzzy controller is verified during online adaptation therefore it stays in the allowed sector this method is illustrated by an example of a control system containing an unstable plant with a transport delay the main contribution of this paper is to use frequency methods combined with adaptive fuzzy control these methods have previously been used for nonadaptive fuzzy control but in this paper they are used for the first time for adaptive fuzzy control

a fast adaptive diffusion wavelet method for burger s equation abstract a fast adaptive diffusion wavelet method is developed for solving the burger s equation the diffusion wavelet is developed in 2006 coifman and maggioni 2006 and its most important feature is that it can be constructed on any kind of manifold classes of operators which can be used for construction of the diffusion wavelet include second order finite difference differentiation matrices the efficiency of the method is that the same operator is used for the construction of the diffusion wavelet as well as for the discretization of the differential operator involved in the burger s equation the diffusion wavelet is used for the construction of an adaptive grid as well as for the fast computation of the dyadic powers of the finite difference matrices involved in the numerical solution of burger s equation in this paper we have considered one dimensional and two dimensional burger s equation with dirichlet and periodic boundary conditions for each test problem the cpu time taken by fast adaptive diffusion wavelet method is compared with the cpu time taken by finite difference method and observed that the proposed method takes lesser cpu time we have also verified the convergence of the given method

adaptive fuzzy tracking control of nonlinear time delay systems with dead zone output mechanism based on a novel smooth model this paper presents a novel fuzzy adaptive controller for controlling a class of dead zone output nonlinear systems with time delays a new approximate model is first designed to describe a special dead zone phenomenon encountered by the output mechanism of nonlinear systems and the proposed smooth model can be conveniently fused with available adaptive fuzzy control techniques in addition the coupling effect that the dead zone output and the time delayed states coexist in a common coupling function makes the tracking control design more complicated to further address this difficulty a compensation method using mean value theorem with lyapunov krasovskii function is presented in this paper by using the proposed output dead zone model and based on lyapunov synthesis a new optimized algorithm is developed to guarantee the prescribed convergence of tracking error and the boundedness of all the signals in the closed loop systems simulations have been implemented to verify the performance of the proposed fuzzy adaptive controller

modified neural dynamic surface approach to output feedback of mimo nonlinear systems we report an adaptive output feedback dynamic surface control dsc maintaining the prescribed performance for a class of uncertain nonlinear systems with multiinput and multioutput designing neural network observers and modifying the dsc method achieves several control objectives first to achieve output feedback control the finite time echo state networks esn observer with fast convergence is designed to obtain the online system states thus the immeasurable states in traditional state feedback control are estimated and the unknown functions are approximated by esn then a modified dsc approach is developed by introducing a high order sliding mode differentiator to replace the first order filter in each step thus the effect of filter performance on closed loop stability is reduced furthermore the input to state stability guarantees that all signals of the whole closed loop system are semiglobally uniformly ultimately bounded specifically the performance functions make the tracking errors converge to a compact set around equilibrium two numerical examples illustrated the proposed control scheme with satisfactory results

approaches to t s fuzzy affine model based reliable output feedback control for nonlinear ito stochastic systems this paper deals with the problem of reliable and robust mathscr h infty static output feedback sof controller synthesis for continuous time nonlinear stochastic systems with actuator faults the nonlinear stochastic plant is expressed by an ito type takagi sugeno fuzzy affine model with parametric uncertainties and a markov process is employed to model the occurrence of actuator fault the purpose is to design an admissible piecewise sof controller such that the resulting closed loop system is stochastically stable with a prescribed disturbance attenuation level in an mathscr h infty sense specifically based on a markovian lyapunov function combined with ito differential formula s procedure and some matrix inequality convexification procedures two new approaches to the reliable sof controller analysis and synthesis are proposed for the underlying stochastic fuzzy affine systems it is shown that the existence of desired reliable controllers is fully characterized in terms of strict linear matrix inequalities finally simulation examples are presented to illustrate the effectiveness and advantages of the developed methods

adaptive fuzzy output feedback control for switched nonstrict feedback nonlinear systems with input nonlinearities this paper studies adaptive fuzzy output feedback tracking control problem for nonstrict feedback switched nonlinear systems the switched systems under consideration contain unknown nonlinearities unmeasured states and unknown deadzones fuzzy logic systems are utilized to approximate the unknown nonlinearities and a switched fuzzy state observer is designed and thus the immeasurable states are estimated via it in the framework of observer based output feedback control and by using the certainty equivalence deadzone inverse a novel adaptive fuzzy output feedback control design method with the parameters adaptation laws is developed the stability of the closed loop system and the convergence of the tracking error are proved based on lyapunov function and the average dwell time methods two simulation examples are provided to check the effectiveness of the proposed approach

observer based adaptive fuzzy tracking control of nonlinear systems with time delay and input saturation this paper studies the problem of adaptive output tracking control for a class of nonlinear systems subject to unknown time delay and input saturation to address the delay and the input saturation some reasonable assumptions and an auxiliary system are introduced the fuzzy logic approach is employed to approximate the unknown functions in the system an observer is designed to estimate the unavailable system states the dynamic surface control dsc technique is utilized to avoid the problem of explosion of complexity by combining the backstepping and dsc methods a bounded control input is designed to ensure that all signals of the closed loop system are bounded and the tracking error can fluctuate around the origin within a small neighborhood finally two examples are presented to demonstrate the effectiveness and potential of the proposed new design techniques

on the defect of additivity of fuzzy measures it is well known that fuzzy measures are non additive in this paper we introduce the concept of defect which gives us the degree of non additivity of fuzzy measures for large classes of fuzzy measures this defect is calculated and estimated three kinds of applications are given to the approximative calculation of some fuzzy integrals to the best approximation of a fuzzy measure by classical measures and to the introduction of an invariant at translations distance on the set of fuzzy measures

adaptive fuzzy reliable control for switched uncertain nonlinear systems based on closed loop reference model abstract this paper investigates an input to state practical stability isps problem for a class of switched strict feedback nonlinear systems with closed loop reference model the considered systems are with unmodeled dynamics dynamic disturbances and actuator failures fuzzy logical systems flss are utilized to approximate the unknown functions different from the open loop model reference adaptive control a feedback gain term is introduced into the reference model to improve the transient performance of the considered systems especially when actuator failures occur and switchings take place by combining the small gain approach and backstepping technique an adaptive fuzzy control method is proposed it is shown that under the developed control scheme the tracking error converges to a small neighborhood of the origin while all the signals of the closed loop system are semi globally uniformly ultimately bounded sguub simulation study is given to illustrate the effectiveness of our 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

adaptive fuzzy identification and control for a class of nonlinear pure feedback mimo systems with unknown dead zones the adaptive fuzzy identification and control problems are considered for a class of multi input multi output nonlinear systems with unknown functions and unknown dead zone inputs the main characteristics of the considered systems are that 1 they are composed of n subsystems and each subsystem is in nested lower triangular form 2 dead zone inputs are in nonsymmetric nonlinear form and 3 dead zone inputs appear nonlinearly in the systems and their parameters are not required to be known the controller design for this class of systems is a difficult and complicated task because of the existences of unknown functions the couplings among the nested subsystems and the dead zone inputs in the controller design the fuzzy logic systems are employed to approximate the unknown functions and the differential mean value theorem is used to separate dead zone inputs to compensate for dead zone inputs the compensative terms are designed in the controllers the stability of the closed loop system is proved via the lyapunov stability theorem a simulation example is provided to validate the feasibility of the approach

fuzzy filter design for ito stochastic systems with application to sensor fault detection the paper deals with the robust fault detection problem for takagi sugeno t s fuzzy ito stochastic systems our aim is to develop a robust fault detection approach to the t s fuzzy systems with brownian motion by using a general observer based fault detection filter as a residual generator the robust fault detection is formulated as a filtering problem attention is focused on the design of both the fuzzy rule independent and the fuzzy rule dependent fault detection filters guaranteeing a prescribed noise attenuation level in an hinfin sense sufficient conditions are proposed to guarantee the mean square asymptotic stability with an hinfin performance for the fault detection system the corresponding solvability conditions for the desired fuzzy rule independent and fuzzy rule dependent fault detection filters are also established finally a numerical example is provided to illustrate the effectiveness of the proposed theory

h_ bm infty fuzzy control for systems with repeated scalar nonlinearities and random packet losses this paper is concerned with the h infin fuzzy control problem for a class of systems with repeated scalar nonlinearities and random packet losses a modified takagi sugeno t s fuzzy model is proposed in which the consequent parts are composed of a set of discrete time state equations containing a repeated scalar nonlinearity such a model can describe some well known nonlinear systems such as recurrent neural networks the measurement transmission between the plant and controller is assumed to be imperfect and a stochastic variable satisfying the bernoulli random binary distribution is utilized to represent the phenomenon of random packet losses attention is focused on the analysis and design of h infin fuzzy controllers with the same repeated scalar nonlinearities such that the closed loop t s fuzzy control system is stochastically stable and preserves a guaranteed h infin performance sufficient conditions are obtained for the existence of admissible controllers and the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one subject to linear matrix inequalities which can be readily solved by using standard numerical software two examples are given to illustrate the effectiveness of the proposed design method

robust backstepping control of a class of nonlinear systems using fuzzy logic abstract fuzzy logic fl controllers for the robust back stepping control of a class of nonlinear systems in both continuous and discrete time are presented control action is employed to achieve tracking performance for unknown nonlinear system novel parameter tuning algorithms are obtained that are similar to modification in the case of continuous time adaptive control uniform ultimate boundedness of the tracking error and the fuzzy parameter estimates are presented without using the persistency of excitation pe condition initialization of the fuzzy parameters is straightforward simulation results justify the theoretical conclusions

adaptive fuzzy tracking control for a class of uncertain nonaffine nonlinear systems with dead zone inputs this paper considers the problem of adaptive fuzzy tracking control for a class of uncertain nonaffine nonlinear systems with mismatched external disturbances parameter uncertainties and nonsymmetric dead zone inputs without the help of the dead zone inverse function and by incorporating the implicit function theorem both the adaptive state feedback tracking controller and the adaptive output feedback tracking controller based on high gain observer are designed by utilizing fuzzy logic systems fls to approximate the appropriate nonlinear control input functions a compounded disturbance is defined in terms of the external disturbance parameter uncertainty nonsymmetric dead zone input and approximation error of fls under the condition that the upper bound of the compounded disturbance is unknown novel adaptive laws are introduced to estimate and tune the unknown controller parameters on line furthermore on the basis of lyapunov stability analysis it is also proved that the presented control methods can guarantee that all the closed loop system error signals are uniformly ultimately bounded finally two simulation examples are provided to demonstrate efficiency of the proposed adaptive fuzzy tracking control approaches

adaptive dynamic surface control for stabilization of parametric strict feedback nonlinear systems with unknown time delays the robust stabilization method via the dynamic surface control dsc is proposed for uncertain nonlinear systems with unknown time delays in parametric strict feedback form that is the dsc technique is extended to state time delay nonlinear systems with linear parametric uncertainties the proposed control system can overcome not only the problem of ldquoexplosion of complexityrdquo inherent in the backstepping design method but also the uncertainties of the unknown time delays by choosing appropriate lyapunov krasovskii functionals in addition we prove that all the signals in the closed loop system are semiglobally uniformly bounded finally an example is provided to illustrate the effectiveness of the proposed control system

adaptive output feedback control for nonlinear time delay systems by fuzzy approximation approach in this paper the problem of adaptive fuzzy tracking control via output feedback for a class of uncertain single input single output siso strict feedback nonlinear systems with unknown time delay functions is investigated dynamic surface control technique is used to avoid the problem of explosion of complexity which is caused by repeated differentiation of certain nonlinear functions in the backstepping design process in addition the fuzzy logic systems are utilized to approximate the unknown and desired control input signals directly instead of the unknown nonlinear functions the designed controller can guarantee all the signals in the closed loop system to be semiglobally uniformly ultimately bounded and the tracking error to converge to a small neighborhood of the origin simulations results are provided to demonstrate the effectiveness of the proposed methods

space time spectral element methods for one dimensional nonlinear advection diffusion problems abstract the following space time galerkin spectral element methods are developed and applied to solve the burgers equation with small viscosity a coupled methods consisting of an explicit method for hyperbolic dominated equations and an implicit method for parabolic dominated equations b two splitting methods which solve the hyperbolic substep explicitly and the parabolic one implicitly one uses spectral elements in the explicit part and the other uses the adams bashforth multistep method a subcycling technique in which several convective steps are taken for each implicit viscous step was also investigated for the two splitting methods a stability analysis of the four methods is performed and subsequent results are debated a convergence study and a comparison of computer execution time for the four methods is made and the results are discussed comparative study leads to the conclusion that the space time spectral element splitting method with subcycling is superior to the other methods presented in terms of robustness and computer execution time the number of subcycles should be kept low 2 3 in order to avoid significant loss of accuracy the coupled explicit method is also applied to the solution of the one dimensional coupled continuity momentum and energy equations for non isothermal flow of an ideal gas with temperature dependent properties in a cylindrical duct of variable radius

brief paper backstepping controller design for a class of stochastic nonlinear systems with markovian switching a more general class of stochastic nonlinear systems with irreducible homogenous markovian switching are considered in this paper as preliminaries the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a lyapunov function the state feedback controller is designed by regarding markovian switching as constant such that the closed loop system has a unique solution and the equilibrium is asymptotically stable in probability in the large the output feedback controller is designed based on a quadratic plus quartic form lyapunov function such that the closed loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded in probability solution in the biased case

new results on h_ infty tracking control based on the t s fuzzy model for sampled data networked control system this study deals with the problem of h infty tracking control for a sampled data networked control system based on a takagi sugeno fuzzy model an error model is established by combining the input delay and parallel distributed compensation techniques so as to transform the sampling period of a sampler a signal transmission delay and data packet dropouts to the refreshing interval of a zero order hold the method introduces a new augmented lyapunov krasovskii functional to derive a sufficient condition to ensure a prescribed h infty tracking performance with less conservativeness than others a fuzzy controller can easily be designed using the condition a numerical example demonstrates the validity of the method

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

new space time spectral and structured spectral element methods for high order problems abstract we propose new space time spectral and structured spectral element methods for high order problems by matrix decomposition we introduce a family of new basis functions which leads to a diagonal system for the fourth order problems with constant coefficients based on new basis functions in space and a dual petrov galerkin formulation in time we propose a new space time spectral method for a time dependent problem and proved their spectral accuracy both in space and time numerical results demonstrate their high efficiency and coincide well with theoretical analysis further to ultimately promote the numerical performance and efficiency we exploit the idea of locally simultaneous diagonalization to provide new structured spectral element methods for high order problems besides to increase the flexibility a c 1 conforming rectangular spectral method in analogy to argyris or bell triangular elements are proposed for fourth order equations which serves as a preparative work towards conforming quadrilateral spectral elements for high order equations

the semi approximate approach for solving burgers equation with high reynolds number this paper presents the solution of burgers equation involving very high reynolds number re 5 we use semi implicit time difference scheme to reduce burgers equation to two point non linear ordinary differential equation and solved it by matched asymptotic expansion method

adaptive output neural network control for a class of stochastic nonlinear systems with dead zone nonlinearities this paper investigates the problem of adaptive output neural network nn control for a class of stochastic nonaffine and nonlinear systems with actuator dead zone inputs first based on the intermediate value theorem a novel design scheme that converts the nonaffine system into the corresponding affine system is developed in particular the priori knowledge of the bound of the derivative of the nonaffine and nonlinear functions is removed then by employing nns to approximate the appropriate nonlinear functions the corresponding adaptive nn tracking controller with the adjustable parameter updated laws is designed through a backstepping technique furthermore it is shown that all the closed loop signals are bounded in probability and the system output tracking error can converge to a small neighborhood in the sense of a mean quartic value finally experimental simulations are provided to demonstrate the efficiency of the proposed adaptive nn tracking control method

sampled data fuzzy control for a class of nonlinear systems with missing data and disturbances this paper considers the sampled data fuzzy control of nonlinear systems in strict feedback form with disturbances and random missing input data we propose a novel method in which a state observer and a disturbance observer are combined to construct a sampled data fuzzy output feedback controller the stochastic variables with a bernoulli distributed sequence are used to model missing input data fuzzy logic systems are applied to approximate nonlinearities without requiring prior knowledge the relation between observer gain and sampling period is established the output feedback controller designed guarantees that the nonlinear system is globally stable a simulation example of four degrees of freedom robotic arm is used to demonstrate the effectiveness and applicability of the proposed control scheme

adaptive compensation for infinite number of time varying actuator failures in fuzzy tracking control of uncertain nonlinear systems the problem of direct adaptive compensation for infinite number of time varying actuator failures faults is of both theoretical and practical importance in the fuzzy tracking control of uncertain nonlinear systems however due to the technical difficulties so far very limited result is available in addressing such an issue which thus motivates us to propose a new fuzzy control methodology in this paper the proposed scheme is established from the techniques of projection adaptation design a new piecewise lyapunov function analysis and an optimized fuzzy adaptation it is shown that all the closed loop signals are bounded and the steady state tracking error converges to a residual around zero irrespective of a possibility that there are infinite number of time varying actuator failures simulations are provided to illustrate the effectiveness and applicability of the proposed scheme

stable indirect fuzzy adaptive control this paper investigates new fuzzy model based observer adaptive control for multi input multi output continuous time nonlinear systems the proposed adaptive scheme uses takagi seguno ts fuzzy models to estimate the plant states and dynamics using stability arguments it is shown that the proposed scheme is globally asymptotically stable the observation and tracking errors are shown to converge asymptotically to zero despite the presence of external disturbances and approximation errors the performance of the developed approach is illustrated by simulation on two link robot model

adaptive robust control for fuzzy mechanical systems constraint following and redundancy in constraints motion control for uncertain mechanical systems is considered emphasis is on constraint following while the constraint may be redundant the uncertainty in the system which is possibly fast time varying is bounded the bound is unknown but is assumed to be within a prescribed fuzzy set an adaptive robust control is proposed based on the fuzzy property of the uncertainty both the mechanical system and the control are deterministic and hence not if then fuzzy rule based the performance of the resulting controlled system is twofold first some deterministic performance is guaranteed regardless of the value of the uncertainty second the minimization of a fuzzy based performance index is guaranteed based on an optimal choice of a control design parameter the effectiveness of the design procedure is illustrated by the simulation control of a digging excavator

fuzzy adaptive control for a class of nonlinear systems an adaptive tracking control architecture is proposed for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamic is either unknown or impossible the architecture employs fuzzy systems to approximate nonlinear functions uses fuzzy sliding controller to compensate for the plant uncertainties global asymptotic stability is established in the lyapunov sense with the tracking errors converging to a neighborhood of zero

adaptive fuzzy backstepping control for a class of nonlinear systems with sampled and delayed measurements this paper investigates the adaptive fuzzy backstepping control and h infty performance analysis for a class of nonlinear systems with sampled and delayed measurements in the control scheme a fuzzy estimator fe model is used to estimate the states of the controlled plant while the fuzzy logic systems are used to approximate the unknown nonlinear functions in the nonlinear system the controller is obtained based on the fe model by combining the backstepping technique with the classic adaptive fuzzy control method in the stability analysis all the signals in the closed loop system are guaranteed to be semiglobally uniformly ultimately bounded suub and the outputs of the system are proven to converge to a small neighborhood of origin furthermore the h infty performance is investigated and the outputs of the closed loop system are bounded in the h infty sense two examples are given to illustrate the effectiveness of the proposed control scheme

quommutator deformations of spl n 1 we analyze the witten woronowicz s type deformations of the lie superalgebras spl n 1 and obtain deformations parametrized by n n 1 2 independent parameters for n 2 and by three parameters for n 2 for some of these algebras finite dimensional representations can be constructed in terms of finite difference operators providing operators that are relevant for the classification of quasiexactly solvable finite difference equations

a novel adaptive fuzzy variable structure control for a class of nonlinear uncertain systems via backstepping abstract this paper presents a new design of adaptive fuzzy variable structure control to solve the traditional problem of model reference adaptive control mrac for a class of single input single output minimum phase uncertain nonlinear systems via backstepping instead of taking the tedious coordinate transformation and yielding a hard high gain controller we introduce smooth b spline type membership functions into the controller so as to compensate for the uncertainties much softer i e in a much smoother and locally weighted manner to be rigorous it is shown that the stability of the closed loop system can be assured and the tracking error can globally approach to an arbitrary preset dead zone range in order to demonstrate the effectiveness of the developed novel controller an example is extensively simulated to provide quite satisfactory performance

spectral element method in time for rapidly actuated systems in this paper the spectral element se method is applied in time to find the entire time periodic or transient solution of time dependent differential equations the time periodic solution is computed by enforcing periodicity of the element set of particular interest are periodic forcing functions possessing high frequency content to maintain the spectral accuracy for such forcing functions an h refinement scheme is employed near the semi discontinuity without increasing the number of degrees of freedom time discretization by spectral elements is applied initially to a standard form of a set of linear first order differential equations subject to harmonic excitation and an excitation admitting rapid variation other case studies include the application of the se approach to parabolic and hyperbolic partial differential equations the first order form of these equations is obtained through semi discretization using conventional finite element spectral element and finite difference schemes element clustering h refinement is applied to maintain the high accuracy and efficiency in the region of the forcing function admitting rapid variation the convergence in time of the method is demonstrated in some cases machine precision is obtained with 25 degrees of freedom per cycle finally the method is applied to a weakly nonlinear problem with time periodic solution to demonstrate its future applicability to the analysis of limit cycle oscillations in aeroelastic systems

a space time spectral method for the time fractional diffusion equation in this paper we consider the numerical solution of the time fractional diffusion equation essentially the time fractional diffusion equation differs from the standard diffusion equation in the time derivative term in the former case the first order time derivative is replaced by a fractional derivative making the problem global in time we propose a spectral method in both temporal and spatial discretizations for this equation the convergence of the method is proven by providing a priori error estimate numerical tests are carried out to confirm the theoretical results thanks to the spectral accuracy in both space and time of the proposed method the storage requirement due to the global time dependence can be considerably relaxed and therefore calculation of the long time solution becomes possible

optimal adaptive fuzzy ftc design for strict feedback nonlinear uncertain systems with actuator faults abstract in this paper the optimal fault tolerant control ftc design problem is investigated for strict feedback nonlinear systems the considered nonlinear systems contain actuator faults which are bias fault and gain fault the problem of actuator faults is solved by utilizing the adaptive compensation technique applying the backstepping design technique a main fault tolerant controller is established via the designed main fault tolerant control strategy the controlled nonlinear system can be converted to an equivalent nonlinear system in affine form subsequently a fuzzy logic system fls is introduced to approximate the unknown cost function and an adaptive fuzzy feedback optimal controller is developed the whole adaptive fuzzy fault tolerant optimal control scheme consists of a main controller and a feedback optimal controller based on the lyapunov theory it is proved that all the signals in the closed loop system are bounded the system output can track a bounded reference signal in addition the proposed control method can guarantee the cost function is the smallest simulation results are provided to illustrate the effectiveness of the proposed fault tolerant optimal control scheme

space time spectral method for a weakly singular parabolic partial integro differential equation on irregular domains abstract the spectral method is proposed for the partial integro differential equations with a weakly singular kernel on irregular domains the space discretization is based on the nodal spectral element method using the lagrange polynomials basis associated with the gauss lobatto legendre quadrature nodes also the model is discretized in time with the legendre spectral galerkin method the discretization leads to conversion of the problem to a sylvester matrix equation which can be solved efficiently by the qz algorithm gardiner et al 1992 the convergence of the method is proven by providing a priori l 2 error estimate numerical results illustrate the efficiency and spectral accuracy of the proposed method

dynamic surface control for a class of nonlinear systems a method is proposed for designing controllers with arbitrarily small tracking error for uncertain mismatched nonlinear systems in the strict feedback form this method is another synthetic input technique similar to backstepping and multiple surface control methods but with an important addition spl tau 1 low pass filters are included in the design where spl tau is the relative degree of the output to be controlled it is shown that these low pass filters allow a design where the model is not differentiated thus ending the complexity arising due to the explosion of terms that has made other methods difficult to implement in practice the backstepping approach while suffering from the problem of explosion of terms guarantees boundedness of tracking errors globally however the proposed approach while being simpler to implement can only guarantee boundedness of tracking error semiglobally when the nonlinearities in the system are non lipschitz

on some nonlinear extensions of the angular momentum algebra deformations of the lie algebras so 4 so 3 1 and e 3 that leave their so 3 subalgebra undeformed and preserve their coset structure are considered it is shown that such deformed algebras are associative for any choice of the deformation parameters their casimir operators are obtained and some of their unitary irreducible representations are constructed for vanishing deformation the unitary irreducible representations of the deformed algebras transform into those of the corresponding lie algebras that contain each of the so 3 unitary irreducible representations at most once it is also proved that similar deformations of the lie algebras su 3 sl 3 r and of the semidirect sum of an abelian algebra t 5 and so 3 do not lead to associative algebras

robust h_ infty fuzzy output feedback control with multiple probabilistic delays and multiple missing measurements in this paper the robust h control problem is investigated for a class of uncertain discrete time fuzzy systems with both multiple probabilistic delays and multiple missing measurements a sequence of random variables all of which are mutually independent but obey the bernoulli distribution is introduced to account for the probabilistic communication delays the measurement missing phenomenon occurs in a random way the missing probability for each sensor satisfies a certain probabilistic distribution in the interval here the attention is focused on the analysis and design of h fuzzy output feedback controllers such that the closed loop takagi sugeno t s fuzzy control system is exponentially stable in the mean square the disturbance rejection attenuation is constrained to a given level by means of the h performance index intensive analysis is carried out to obtain sufficient conditions for the existence of admissible output feedback controllers which ensures the exponential stability as well as the prescribed h performance the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one that is solved by the semi definite program method simulation results are utilized to demonstrate the effectiveness of the proposed design technique in this paper

adaptive control of a class of nonlinear systems with fuzzy logic an adaptive tracking control architecture is proposed 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 employs fuzzy systems which are expressed as a series expansion of basis functions to adaptively compensate for the plant nonlinearities global asymptotic stability of the algorithm is established in the lyapunov sense with tracking errors converging to a neighborhood of zero simulation results for an unstable nonlinear plant are included to demonstrate that incorporating the linguistic fuzzy information from human experts results in superior tracking performance

adaptive fuzzy reliable tracking control for a class of uncertain nonlinear time delay systems with abrupt non affine faults abstract this paper investigates the problem of approximation based adaptive reliable tracking control for a class of uncertain nonlinear strict feedback systems the considered system is with unknown time delays and abrupt non affine nonlinear faults to eliminate the effect of unknown time delays the finite covering lemma and fuzzy logic systems are utilized and the traditional lyapunov krasovskii function is abandoned with the help of mean value theorem the non affine nonlinear faults are decoupled for the strictness of system based on the property of nussbaum function the problem of unknown control directions and control gains is solved finally a novel adaptive fault tolerant control scheme with the feedback information of not only the current states but also the past states is designed it is guaranteed that all the signals in the closed loop system are semi global uniformly bounded and the tracking error converges to a small neighborhood of the origin simulation results from a practical example of isothermal continuous stirred tanks reactors are given to demonstrate the effectiveness of the proposed control scheme

observer based adaptive neural network control for nonlinear stochastic systems with time delay this paper considers the problem of observer based adaptive neural network nn control for a class of single input single output strict feedback nonlinear stochastic systems with unknown time delays dynamic surface control is used to avoid the so called explosion of complexity in the backstepping design process radial basis function nns are directly utilized to approximate the unknown and desired control input signals instead of the unknown nonlinear functions the proposed adaptive nn output feedback controller can guarantee all the signals in the closed loop system to be mean square semi globally uniformly ultimately bounded simulation results are provided to demonstrate the effectiveness of the proposed methods

observer based adaptive fuzzy control for siso nonlinear systems abstract the observer based indirect and direct adaptive fuzzy controllers are developed for a class of siso uncertain nonlinear systems the proposed approaches do not need the availability of the state variables by designing the state observer the adaptive fuzzy systems which are used to model the unknown functions can be constructed using the state estimations thus a new hybrid adaptive fuzzy control method is proposed by combining the above adaptive fuzzy system with the h control technique based on lyapunov stability theorem the proposed adaptive fuzzy control system can guarantee the stability of the whole closed loop systems and obtain good tracking performance as well the proposed methods are applied to an inverted pendulum system and a chaotic system and achieve satisfactory simulation results

observer based fuzzy adaptive control for strict feedback nonlinear systems in this paper a new fuzzy adaptive control approach is developed for a class of siso strict feedback nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is introduced for state estimation as well as system identification under the framework of the backstepping design fuzzy adaptive output feedback control is constructed recursively it is proven that the proposed fuzzy adaptive control approach guarantees the semi global boundedness property for all the signals and the tracking error to a small neighborhood of the origin simulation studies are included to illustrate the effectiveness of the proposed approach

stable adaptive control using fuzzy systems and neural networks stable direct and indirect adaptive controllers are presented which use takagi sugeno fuzzy systems conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous time nonlinear plants with poorly understood dynamics the indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller we prove that with or without such knowledge both adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of a reference input in addition for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation the performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

hybrid fuzzy adaptive output feedback control design for uncertain mimo nonlinear systems with time varying delays and input saturation in this paper a hybrid fuzzy adaptive output feedback control design approach is proposed for a class of multiinput and multioutput strict feedback nonlinear systems with unknown time varying delays unmeasured states and input saturation first fuzzy logic systems are employed to approximate unknown nonlinear functions in the system next a smooth function is used to approximate the input saturation and an adaptive fuzzy state observer is constructed to solve the problem of unmeasured states based on the designed adaptive fuzzy state observer a serial parallel estimation model is established by applying adaptive fuzzy dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial parallel estimation model a new fuzzy controller with the composite parameters adaptive laws is developed based on lyapunov krasovskii functional it is proved that all variables of the closed loop system are bounded and the system outputs can follow the given bounded reference signals as close as possible a simulation example is provided to further show the effectiveness of this novel control scheme

adaptive fuzzy quantized control of time delayed nonlinear systems with communication constraint abstract this paper explores the problem of quantized fuzzy adaptive tracking control for a class of time delayed uncertain nonlinear systems with communication constraint the control signal is first quantized in a newly proposed asymmetric hysteresis type quantizer before it is transmitted over the networks with limited bandwidth then one of major difficulties that block the controller design is that the real control signal is hidden in the coupling dynamics between nonaffine system nonlinearity and rate dependent hysteretic quantizer to remove this obstacle a control separation method established mainly on a new nonlinear decomposition of quantizer is proposed unlike previous linear decomposition of quantizer the nonlinear one does not recourse to some conservative assumptions either on control input or system nonlinearities in combination with fuzzy backstepping technique and lyapunov krasovskii functional an adaptive fuzzy controller is developed to guarantee the boundedness of all closed loop signals and the asymptotic convergence of tracking error to an adjustable region of zero finally two simulations associated with practical control systems are conducted to verify the effectiveness and applicability of the proposed control protocol

operator identities representations of algebras and the problem of normal ordering families of operator identities related to certain powers of positive root generators of super lie algebras of first order differential operators and q deformed algebras of first order finite difference operators are presented it is shown that those identities once rewritten in terms of creation annihilation operators lead to a simplification of the problem of the normal ordering in the second quantization method

braided momentum in the q poincare group the q poincare group of m schlieker et al z phys c 53 79 1992 is shown to have the structure of a semidirect product and coproduct b soq 1 3 where b is a braided quantum group structure on the q minkowski space of four momentum with braided coproduct p p 1 1 p here the necessary b is not a usual kind of quantum group but one with braid statistics similar braided vectors and covectors v r v r exist for a general r matrix the abstract structure of the q lorentz group is also studied

study of quommutators of quantum variables and generalized derivatives a general deformation of the heisenberg algebra is introduced with two deformed operators instead of just one this is generalized to many variables and permits the simultaneous existence of coherent states and the transposition of creation operators

block marching in time with dq discretization an efficient method for time dependent problems abstract in this paper an efficient method is presented to solve time dependent problems the proposed method marches in the time direction block by block in each block there are several time levels and the numerical results at these time levels are obtained simultaneously the global method of differential quadrature is applied in each block to discretize both the spatial and temporal derivatives the proposed method is validated by a sample problem which has an exact solution for easy comparison it was found that as compared to the conventional 4 stage runge kutta method the present method could give much higher order of accuracy for numerical results and require much less computational effort

fuzzy adaptive control of multivariable nonlinear systems abstract the robust fuzzy adaptive control scheme is developed for a class of unknown nonlinear mimo systems two types of uncertainties are considered i e the matched uncertainty and the unmatched uncertainties in the control procedure fuzzy logic systems are implemented to estimate the unknown functions and robust compensators are designed in h sense for attenuating the unmatched uncertainties it is shown that the proposed control is continuous guarantees global stability and the h performance index extensive simulations on the tracking control of a two link rigid robotics manipulator verify the effectiveness of the proposed algorithms

adaptive backstepping controller design for stochastic jump systems in this technical note we improve the results in a paper by shi et al in which problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps were considered however the system considered is switching stochastically between different subsystems the dynamics of the jump system can not stay on each sliding surface of subsystems forever therefore it is difficult to determine whether the closed loop system is stochastically stable in this technical note the backstepping techniques are adopted to overcome the problem in a paper by shi et al the resulting closed loop system is bounded in probability it has been shown that the adaptive control problem for the markovian jump systems is solvable if a set of coupled linear matrix inequalities lmis have solutions a numerical example is given to show the potential of the proposed techniques

adaptive tracking for stochastic nonlinear systems with markovian switching the problem of the adaptive tracking for a class of stochastic nonlinear systems with stationary markovian switching is considered in this note an ito formula is proposed for stochastic integral equations with an integral about martingale measure an adaptive backstepping controller is designed such that the closed loop system has a unique solution that is globally bounded in probability and l4 norm of the tracking error converges to an arbitrarily small neighborhood of zero a simulation example demonstrates the efficiency of the proposed scheme

adaptive output feedback control for a class of large scale nonlinear time delay systems this paper addresses the problem of global adaptive stabilization by output feedback for a class of large scale nonlinear time delay systems with a new lyapunov krasovskii functional a memoryless adaptive output feedback controller is developed the precise knowledge of the time varying delay is not required to be known a priori it is proved that global stability of the large scale nonlinear time delay system can be achieved by the proposed approach a numerical example is given to illustrate the effectiveness of the proposed approach

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

how to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems this paper focuses on the construction of a fuzzy adaptive output feedback control based on any observer high gain hg observer sliding mode like observer etc for a class of single input single output siso uncertain or ill defined affine nonlinear systems indeed the corrective term of the proposed observer involves a well defined design function which is shown to be satisfied by the commonly used hg based observers namely for the usual hg observers and the sliding mode observers together with their implementable versions the design of the underlying update law as well as the robust control term is based on an appropriate filtering of the output tracking error this particularly allows to overcome the output observation error filtering or the necessity of the famous strictly positive real spr condition

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

on certain quantum deformations of gl n r in this article all deformations of the general linear group subject to certain restrictions which in particular ensure a smooth passage to the lie group limit are obtained representations are given in terms of certains sets of creation and annihilation operators these creation and annihilation operators may belong to a generalization of the q quark type or q hadronic type with q boson or q fermion behavior this leads to a natural definition of q direct sums of q algebras

fuzzy adaptive quantized output feedback tracking control for switched nonlinear systems with input quantization in this paper the problem of adaptive fuzzy quantized output feedback control is investigated for a class of uncertain switched nonlinear systems in strict feedback form the considered switched systems contain unknown nonlinearities hysteretic quantized input and without requiring the system states being available for measurement fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a switched fuzzy state observer is designed to estimate the unmeasured states the hysteretic quantized input is implemented to avoid the oscillation caused by logarithmic quantizer and decomposed into two bounded nonlinear functions based on the estimated states and using the backstepping design principle an adaptive fuzzy quantized output feedback control scheme is developed it is proved that whole adaptive fuzzy quantized control scheme can guarantee that all the variables in the closed loop system are bounded under a class of switching signals with average dwell time and also that the system output can track a given reference signal as closely as possible the simulation results are given to check the effectiveness of the proposed approach

adaptive tracking for periodically time varying and nonlinearly parameterized systems using multilayer neural networks this brief addresses the problem of designing adaptive neural network tracking control for a class of strict feedback systems with unknown time varying disturbances of known periods which nonlinearly appear in unknown functions multilayer neural network mnn and fourier series expansion fse are combined into a novel approximator to model each uncertainty in systems dynamic surface control dsc approach and integral type lyapunov function ilf technique are combined to design the control algorithm the ultimate uniform boundedness of all closed loop signals is guaranteed the tracking error is proved to converge to a small residual set around the origin two simulation examples are provided to illustrate the feasibility of control scheme proposed in this brief

adaptive neural output feedback control of output constrained nonlinear systems with unknown output nonlinearity this paper addresses the problem of adaptive neural output feedback control for a class of special nonlinear systems with the hysteretic output mechanism and the unmeasured states a modified bouc wen model is first employed to capture the output hysteresis phenomenon in the design procedure for its fusion with the neural networks and the nussbaum type function two key lemmas are established using some extended properties of this model to avoid the bad system performance caused by the output nonlinearity a barrier lyapunov function technique is introduced to guarantee the prescribed constraint of the tracking error in addition a robust filtering method is designed to cancel the restriction that all the system states require to be measured based on the lyapunov synthesis a new neural adaptive controller is constructed to guarantee the prescribed convergence of the tracking error and the semiglobal uniform ultimate boundedness of all the signals in the closed loop system simulations are implemented to evaluate the performance of the proposed neural control algorithm in this paper

fuzzy adaptive observer backstepping control for mimo nonlinear systems in this paper a fuzzy adaptive backstepping output feedback control approach is developed for a class of multi input and multi output mimo nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is designed for state estimation as well as system identification combining with the backstepping design techniques a fuzzy adaptive output feedback control is constructed recursively it is proved that the proposed fuzzy adaptive control approach can guarantee the semi global uniform ultimate boundedness for all the signals and the tracking error to a small neighborhood of the origin simulation studies illustrate the effectiveness of the proposed approach

two mode indirect adaptive control approach for the synchronization of uncertain chaotic systems by the use of a hierarchical interval type 2 fuzzy neural network two mode adaptive controllers have two phases of operation a learning phase and an operation phase this paper presents a two mode indirect adaptive control approach for the synchronization of chaotic systems using a hierarchical interval type 2 fuzzy neural network ht2fnn its contribution to the existing literature is the adaptation laws derived for the parameters of the membership functions based on lyapunov stability analysis since in hierarchical case each t2fnn has only two inputs the computing of the derivatives is much simpler than the case in classical interval type 2 fnn moreover a novel approach is presented for the compensation of the approximation error the tuning of the parameters of the membership functions mf and the use of an interval type 2 fnn ensures that the estimation error is very small so that it can be negligible furthermore the number of mf required is seen to be less than that needed with type 1 fuzzy sets the simulation results confirm the efficacy of the proposed scheme in the synchronization of a uncertain nonidentical chaotic systems

robust control for a class of uncertain nonlinear systems adaptive fuzzy approach based on backstepping a robust adaptive fuzzy control design approach is developed for a class of multivariable nonlinear systems with modeling uncertainties and external disturbances the controller design for the overall systems has been carried out through a number of simpler controller designs for a series of the relevant auxiliary systems based on the backstepping design technique for each auxiliary system an adaptive fuzzy logic system is introduced to learn the behavior of unknown dynamics and then a robust control algorithm is employed to efficiently compensate the approximation error and the external disturbances as well it is shown that the resulting closed loop systems guarantee a satisfactory transient and asymptotic performance a simulation example is also presented to illustrate the design procedure and controller performance

fuzzy approximation based adaptive control of strict feedback nonlinear systems with time delays this paper focuses on the problem of adaptive control for a class of nonlinear time delay systems with unknown nonlinearities and strict feedback structure based on the lyapunov krasovskii functional approach a state feedback adaptive controller is constructed by backstepping the proposed adaptive controller guarantees that the system output converges into a small neighborhood of the reference signal and all the signals of the closed loop system remain bounded compared with the results that exist the main advantage of the proposed method is that the controller design is independent of the choice of the fuzzy membership functions therefore a priori knowledge of fuzzy approximators is not necessary for control design and the proposed approach requires only one adaptive law for an nth order system two numerical examples are used to illustrate the effectiveness of the proposed approach

adaptive fuzzy control for a class of unknown nonlinear dynamical systems in this study we investigate an adaptive fuzzy controller design for a class of nonlinear multi input multi output mimo systems in interconnected form the systems considered comprise n subsystems and an unknown interconnection term is included in every equation for each subsystem the interconnection term is a function of all the states from the first to the n 1 th subsystems moreover the effects of dead zone models are considered in each subsystem of the systems these properties of the systems cause the difficulties and add further complexity to the design in order to overcome these difficulties we use the following methods 1 the fuzzy logic systems are employed to approximate the appropriate unknown functions of the systems 2 a novel backstepping design procedure is constructively designed and 3 compensative adaptation laws are provided to compensate for the effects of the dead zone inputs we show that all the signals in the closed loop system are bounded and that the outputs converge to a compact set by using the lyapunov analysis theorem simulated examples are presented that validate the effectiveness of the approach

example of infinite statistics i give a second quantized example of infinite statistics in which any representation of the symmetric group can occur for identical particles and discuss the properties of the example

adaptive fuzzy control for a class of nonlinear discrete time systems with backlash an adaptive fuzzy controller design is studied for uncertain nonlinear systems in this paper the considered systems are of the discrete time form in a triangular structure and include the backlash and the external disturbance by using the prediction function of future states the systems are transformed into an n step ahead predictor the fuzzy logic systems flss are used to approximate the unknown functions unknown backlash and backlash inversion respectively a discrete time tuning algorithm is developed to estimate the optimal fuzzy parameters compared with the previous works for the discrete time systems with backlash the main contributions of the paper are that 1 the rigorous restriction for the functional estimation error is removed and 2 the external disturbance is bounded but the bound is not required to be known a novel controller and the adaptation laws are constructed by using the discrete taylor series expansion and the difference lyapunov analysis and thus those limitations in the previous works are overcome it is proven that all the signals in the closed loop system are bounded and that the system output can be to follow the reference signal to a bounded compact set a simulation example is provided to illustrate the effectiveness of the proposed approach

relative degrees and adaptive feedback linearization control of t s fuzzy systems this paper presents a new study on the relative degrees of single input and single output t s fuzzy systems in general noncanonical forms and proposes a feedback linearization based control design method for such systems the study extends the system relative degree concepts commonly used for the control of nonlinear systems to general t s fuzzy systems derives various relative degree conditions for general t s fuzzy systems and establishes the relative degree dependent normal forms a feedback linearization based control design framework is developed for general t s fuzzy systems using its normal form to achieve closed loop stability and asymptotic output tracking under relaxed design conditions a new adaptive feedback linearization based control scheme for t s fuzzy systems in general noncanonical forms with parameter uncertainties is designed and analyzed some extensions of relative degrees and their possible application to robust adaptive control for noncanonical form t s fuzzy systems are also demonstrated an illustrative example is presented with simulation results to demonstrate the control system design procedure and to show the effectiveness of the proposed control scheme

a unifying framework for global regulation via nonlinear output feedback from iss to iiss this paper presents a unifying framework for the problem of robust global regulation via output feedback for nonlinear systems with integral input to state stable inverse dynamics subject to possibly unknown control direction the contribution of the paper is two fold firstly we consider the problem of global regulation instead of global asymptotic stabilization gas for systems with generalized dynamic uncertainties it is shown by an elementary example that gas is not solvable using conventional smooth output feedback secondly we reduce the stability requirements for the disturbance and demand relaxed assumptions for the system using our framework most of the known classes of output feedback form systems are broadened in several directions unmeasured states and unknown parameters can appear nonlinearly restrictive matching and growth assumptions are removed the dynamic uncertainty satisfies the weaker condition of sontag s integral input to state stability and the sign of high frequency gain may be unknown a constructive strategy is proposed to design a dynamic output feedback control law that drives the state to the origin while keeping all other closed loop signals bounded

alternative hamiltonian quantization the authors take a standard hamiltonian quadratic in a set of creation and annihilation operators and demonstrate an alternative quantization by quommutators i e a set of rules for transposition of these operators different from the those of the usual canonical commutation relations which yields a new spectrum of a type reminiscent of logarithmic trajectories

adaptive dynamic surface control a simplified algorithm for adaptive backstepping control of nonlinear systems in this paper we propose a new algorithm for adaptive backstepping control of non linear uncertain systems current backstepping algorithms require repeated differentiations of the modelled non linearities the addition of n first order low pass filters allows the algorithms to be implemented without differentiating any model non linearities the uncertainties are assumed to be linear in the unknown constant parameters the combined adaptive backstepping first order filter system is proven to be semi globally stable for sufficiently fast filters by a singular perturbation approach