a dsc approach to adaptive neural network tracking control for pure feedback nonlinear systems in this paper by incorporating the dynamic surface control technique into a neural network based adaptive control design framework we develop a backstepping based adaptive control design approach for uncertain non affine pure feedback nonlinear systems by using the dynamic surface control technique the problem of explosion of complexity inherent in existing methods are eliminated effectively stability analysis shows that the uniform ultimate boundedness of all the signals in the closed loop system can be guaranteed and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters simulation results demonstrate the effectiveness of the proposed scheme

chebyshev pseudospectral solution of second order elliptic equations with finite element preconditioning abstract a new chebyshev pseudospectral algorithm for second order elliptic equations using finite element preconditioning is proposed and tested on various problems bilinear and biquadratic lagrange elements are considered as well as bicubic hermite elements the numerical results show that bilinear elements produce spectral accuracy with the minimum computational work l shaped regions are treated by a subdomain approach

modeling identification and control of a class of nonlinear systems in this paper we propose a new fuzzy hyperbolic model for a class of complex systems which is difficult to model the fuzzy hyperbolic model is a nonlinear model in nature and can be easily derived from a set of fuzzy rules it can also be seen as a feedforward neural network model and so we can identify the model parameters by bp algorithm we prove that the stable controller can be designed based on linear system theory two methods of designing the controller for the fuzzy hyperbolic model are proposed the results of simulation support the effectiveness of the model and the control scheme

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

adaptive neural control for a class of strict feedback nonlinear systems with state time delays this brief proposes a simple control approach for a class of uncertain nonlinear systems with unknown time delays in strict feedback form that is the dynamic surface control technique which can solve the ldquoexplosion of complexityrdquo problem in the backstepping design procedure is extended to nonlinear systems with unknown time delays the unknown time delay effects are removed by using appropriate lyapunov krasovskii functionals and the uncertain nonlinear terms generated by this procedure as well as model uncertainties are approximated by the function approximation technique using neural networks in addition the bounds of external disturbances are estimated by the adaptive technique from the lyapunov stability theorem we prove that all signals in the closed loop system are semiglobally uniformly bounded finally we present simulation results to validate the effectiveness of the proposed approach

existence and uniqueness of pseudo almost periodic solutions of recurrent neural networks with time varying coefficients and mixed delays this paper is concerned with the existence and uniqueness of pseudo almost periodic solutions to recurrent delayed neural networks several conditions guaranteeing the existence and uniqueness of such solutions are obtained in a suitable convex domain furthermore several methods are applied to establish sufficient criteria for the globally exponential stability of this system the approaches are based on constructing suitable lyapunov functionals and the well known banach contraction mapping principle moreover the attractivity and exponential stability of the pseudo almost periodic solution are also considered for the system a numerical example is given to illustrate the effectiveness of our results

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

global asymptotic stability of recurrent neural networks with multiple time varying delays in this paper several sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time varying delays the lyapunov krasovskii stability theory for functional differential equations and the linear matrix inequality lmi approach are employed in our investigation the results are shown to be generalizations of some previously published results and are less conservative than existing results the present results are also applied to recurrent neural networks with constant time delays

adaptive tracking control of uncertain mimo nonlinear systems based on generalized fuzzy hyperbolic model this paper is concerned with the problem of adaptive tracking control for a class of multi input and multi output mimo strict feedback nonlinear systems with unknown disturbances in the controller design process all the nonlinear unknown functions are accumulated to the last step in each subsystem and the final nonlinear unknown accumulation is approximated by using generalized fuzzy hyperbolic model gfhm only the actual controller and one adaptive law are needed in each subsystem so the controllers design is much simple and the amount of calculation is greatly reduces comparing with the existing control methods it is shown that the proposed control law can guarantee that all the signals in the closed loop system are uniformly ultimately bounded and the tracking errors converge to a small neighborhood the simulation results show the effectiveness and superiority of control method in this paper

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

observer based event driven fault tolerant control for a class of system with state dependent uncertainties abstractthe method of designing an event driven observer based fault tolerant controller is addressed for a state dependent system with external disturbance and fault in this paper an event driven criterion is proposed to determine the updating of the controller based on the state of the luenberger type state dependent observer as a result communication resources can be saved significantly while the desired h performance is preserved the observer error closed loop system is rewritten as a time varying delay system by employing a state dependent integral function to be a lyapunov function candidate the error system is proved to be asymptotically stable the observer gain the controller gain and the event parameters in the event condition can be co designed and obtained in terms of solution to a set of linear matrix inequalities lmis finally a numerical example and the tunnel diode circuit model are shown that the proposed method is effective and the simulation results can reflect that the even

exponential stability of impulsive high order hopfield type neural networks with time varying delays this paper considers the problems of global exponential stability and exponential convergence rate for impulsive high order hopfield type neural networks with time varying delays by using the method of lyapunov functions some sufficient conditions for ensuring global exponential stability of these networks are derived and the estimated exponential convergence rate is also obtained as an illustration an numerical example is worked out using the results obtained

adaptive fuzzy control via observer design for uncertain nonlinear systems with unmodeled dynamics in this paper the problems of stability and tracking control for a class of large scale nonlinear systems with unmodeled dynamics are addressed by designing the decentralized adaptive fuzzy output feedback approach because the dynamic surface control technique is introduced the designed controllers can avoid the issue of explosion of complexity which comes from the traditional backstepping design procedure that deals with large scale nonlinear systems with unmodeled dynamics in addition a reduced order observer is designed to estimate those immeasurable states based on the lyapunov stability method it is proven that all the signals in the closed loop system are bounded and the system outputs track the reference signals to a small neighborhood of the origin by choosing the design parameters appropriately the simulation examples are given to verify the effectiveness of the proposed techniques

stability analysis for neural networks with time varying interval delay this letter is concerned with the stability analysis of neural networks nns with time varying interval delay the relationship between the time varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of lyapunov functional as a result some improved delay interval dependent stability criteria for nns with time varying interval delay are proposed numerical examples are given to demonstrate the effectiveness and the merits of the proposed method

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

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

exponential stability analysis for delayed neural networks with switching parameters average dwell time approach this paper is concerned with the problem of exponential stability analysis of continuous time switched delayed neural networks by using the average dwell time approach together with the piecewise lyapunov function technique and by combining a novel lyapunov krasovskii functional which benefits from the delay partitioning method with the free weighting matrix technique sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with constant and time varying delays respectively moreover the decay estimates are explicitly given the results reported in this paper not only depend upon the delay but also depend upon the partitioning which aims at reducing the conservatism numerical examples are presented to demonstrate the usefulness of the derived theoretical results

stability analysis for neural networks with time varying delay based on quadratic convex combination in this paper a novel method is developed for the stability problem of a class of neural networks with time varying delay new delay dependent stability criteria in terms of linear matrix inequalities for recurrent neural networks with time varying delay are derived by the newly proposed augmented simple lyapunov krasovski functional different from previous results by using the first order convex combination property our derivation applies the idea of second order convex combination and the property of quadratic convex function which is given in the form of a lemma without resorting to jensen s inequality a numerical example is provided to verify the effectiveness and superiority of the presented results

composite learning from adaptive dynamic surface control in the conventional adaptive control a stringent condition named persistent excitation pe must be satisfied to guarantee parameter convergence this technical note focuses on adaptive dynamic surface control for a class of strict feedback nonlinear systems with parametric uncertainties where a novel technique coined composite learning is developed to guarantee parameter convergence without the pe condition in the composite learning online recorded data together with instantaneous data are applied to generate prediction errors and both tracking errors and prediction errors are utilized to update parametric estimates the proposed approach is also extended to an output feedback case by using a nonlinear separation principle the distinctive feature of the composite learning is that parameter convergence can be guaranteed by an interval excitation condition which is much weaker than the pe condition such that the control performance can be improved from practical asymptotic stability to practical exponential stability an illustrative example is used for verifying effectiveness of the proposed approach

weakly non local solutions for capillary gravity waves fifth degree korteweg de vries equation hunter and scheurle have shown that capillary gravity water waves in the vicinity of bond number bo l 3 are consistently modelled by the korteweg de vries equation with the addition of a fifth derivative term this wave equation does not have strict soliton solutions for bo l 3 because the near solitons have oscillatory wings that extend indefinitely from the core of the wave however these solutions are arbitrarily small perturbations of solitary waves because the amplitude of the wings is exponentially small in the amplitude 6 of the core pomeau ramani and grammaticos have calculated the amplitude of the wings by applying matched asymptotics in the complex plane in the limit e 0 in this article we describe a mixed chebyshev radiation function pseudospectral method which is able to calculate the weakly non local solitons for all e we show that for fixed phase speed the solitons form a three parameter family because the linearized wave equation has three eigensolutions we also show that one may repeat the soliton with even spacing to create a three parameter of periodic solutions which we also compute because the amplitude of the wings is exponentially small these non local capillary gravity solitons are as interesting as the classical localized solitons that solve the korteweg de vries equation

event triggered fuzzy adaptive compensation control for uncertain stochastic nonlinear systems with given transient specification and actuator failures abstract in this paper an event triggered fuzzy adaptive compensation controller is constructed for uncertain stochastic nonlinear systems with given transient specification and actuator failures the main characteristics of the systems are that they take into account the effect of actuator failures and given transient specification system communication resource limitation simultaneously it is still an arduous task and challenge to design for uncertain stochastic nonlinear system specially to stabilize the uncertain nonlinear stochastic systems the fuzzy logic systems are used to approximate the unknown functions an event triggered control mechanism is established to save the system communication resource and a transformed system control mechanism is developed to satisfy the given transient specification all the time in normal mode or faulty mode based on the lyapunov approach it is proved that all the signals of the closed loop system are bounded and the tracking error is limited to a given transient specification the simulation results illustrates the effectiveness of the proposed control approach

technical communique improved delay range dependent stability criteria for linear systems with time varying delays this paper is concerned with the stability analysis of linear systems with time varying delays in a given range a new type of augmented lyapunov functional is proposed which contains some triple integral terms in the proposed lyapunov functional the information on the lower bound of the delay is fully exploited some new stability criteria are derived in terms of linear matrix inequalities without introducing any free weighting matrices numerical examples are given to illustrate the effectiveness of the proposed method

single parameter learning based fuzzy fault tolerant output feedback dynamic surface control of constrained input nonlinear systems abstract this paper addresses the problem of adaptive fuzzy fault tolerant dynamic surface control for a class of constrained input nonlinear systems to resolve this problem the design of an observer based single parameter learning spl control method using output feedback is proposed the takagi sugeno t s fuzzy system is used to identify and approximate online the uncertain nonlinear dynamics requiring no knowledge the barriers that restrict the applications of the traditional backstepping and approximation based approach including the explosion of complexity and the dimension curse problems are circumvented via dynamic surface control and spl techniques the merit of the proposed method lies in that only one parameter in the entire control scheme requires online adjustment regardless of the number of parameters in the t s fuzzy system that characterizes the fuzzy rules the calculation burden in this sense is reduced to the extent of the minimum value the truncated adaptation method is used to avoid the chattering and instability caused by constrained input it is shown with rigorous proof using the lyapunov and invariant set theorems that all the closed loop signals are guaranteed semi globally uniformly ultimately bounded the output tracking error is adjustable by means of design parameters in an explicit form and can be adjusted to an arbitrarily small value around zero by appropriately chosen control parameters even under faulty and constrained actuators simulation and comparative results are provided to demonstrate the effectiveness of the proposed control approach

stable inversion for nonlinear systems abstract there have been two recent major developments in output tracking for nonlinear systems and our first main contribution is to relate these under appropriate assumptions we show that the bounded solution of the partial differential equation of isidori and byrnes for each trajectory of an exosystem must be given by an integral representation formula of devasia chen and paden under restrictive hypotheses devasia chen and paden develop a picard process that converges to the solution of the integral equation this solution to the integral equation is also a bounded solution to a dynamical equation driven by the desired outputs in aircraft applications our nonlinear systems are perturbations of pure feedback systems with outputs and we find a solution to the stable inversion problem i e finding bounded controls and bounded state trajectories in response to bounded output signals in two steps the first step ignores the perturbation error and computes the major part of the desired control and corresponding state trajectory the second step computes the remaining control and states by finding a noncausal and stable solution to an error driven dynamical equation in other words the method of devasia chen and paden is applied to an error system and not to the full system this two step procedure is the second main contribution of this paper throughout this paper it is assumed that our nonlinear systems have vector relative degree

stability analysis of markovian jumping stochastic cohen grossberg neural networks with mixed time delays in this letter the global asymptotical stability analysis problem is considered for a class of markovian jumping stochastic cohen grossberg neural networks cgnns with mixed delays including discrete delays and distributed delays an alternative delay dependent stability analysis result is established based on the linear matrix inequality lmi technique which can easily be checked by utilizing the numerically efficient matlab lmi toolbox neither system transformation nor free weight matrix via newton leibniz formula is required two numerical examples are included to show the effectiveness of the result

a novel two loop large offset tracking control of an uncertain nonlinear system with input constraints abstract under a large deviation between the initial state and the desired trajectory the traditional single loop control method usually fails to solve the output tracking of siso nonlinear systems due to the inherent uncertainties input saturation and unmeasurable states in this work a novel tracking control system is proposed in the framework of two loop control system to achieve high accurate tracking performance and reconcile the contradiction between the system s available regulating capacity and the required tracking capacity specifically an observer and command filtered based adaptive fuzzy controller are synthesized in the inner loop to guarantee a satisfying tracking accuracy and remain robust to uncertainties a simplified fuzzy approximator is utilized to estimate the uncertainties with a single adaptive parameter then a replanned reference trajectory is generated in the outer loop by online optimization to minimize the transient performance over the predictive horizon moreover a tracking governor of reference trajectory is proposed to obtain an adaptive convergence rate with respect to the desired trajectory while only satisfying relatively loose constraints simulation results prove that the proposed two loop scheme can not only improve the tracking accuracy but also has the adaptability to fulfill the particular engineering problems that have a large difference between the initial condition and the desired trajectory

decentralized adaptive output feedback control for a class of nonlinear large scale systems with unknown time varying delayed interactions in this paper the authors investigate a decentralized adaptive output feedback controller design for large scale nonlinear systems with input saturations and time delayed interconnections unmatched in control inputs the interaction terms with unknown time varying delays are bounded by unknown nonlinear bounding functions including all states of subsystems this point is a main contribution of this paper compared with previous output feedback control approaches which assume that the time delayed bounding functions only depend on measurable output variables the bounding functions are compensated by using appropriate lyapunov krasovskii functionals and the function approximation technique based on neural networks the observer dynamic surface design technique is employed to design the proposed memoryless local controller for each subsystem in addition we prove that all signals in the closed loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin finally an example is provided to illustrate the effectiveness of the proposed control system

robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects this paper focuses on the hybrid effects of parameter uncertainty stochastic perturbation and impulses on global stability of delayed neural networks by using the ito formula lyapunov function and halanay inequality we established several mean square stability criteria from which we can estimate the feasible bounds of impulses provided that parameter uncertainty and stochastic perturbations are well constrained moreover the present method can also be applied to general differential systems with stochastic perturbation and impulses

stabilization of multi group models with multiple dispersal and stochastic perturbation via feedback control based on discrete time state observations abstract this paper focuses on the multi group models with multiple dispersal and stochastic perturbation mgmds the effect of both multiple dispersal among groups and stochastic perturbation are taken into consideration the stabilization of mgmds is investigated via feedback control based on the discrete time state observations in addition a systematic method is given to construct a global lyapunov function for mgmds by means of graph theory and lyapunov method some sufficient conditions are obtained to ensure the stabilization in the sense of mean square asymptotical stability an upper bound of the duration between two consecutive state observations is estimated moreover to show the applicability of our results the main theory is employed to a stochastic coupled oscillators finally a numerical example is given to illustrate the effectiveness and feasibility of the theoretical results

delay slope dependent stability results of recurrent neural networks by using the fact that the neuron activation functions are sector bounded and nondecreasing this brief presents a new method named the delay slope dependent method for stability analysis of a class of recurrent neural networks with time varying delays this method includes more information on the slope of neuron activation functions and fewer matrix variables in the constructed lyapunov krasovskii functional then some improved delay dependent stability criteria with less computational burden and conservatism are obtained numerical examples are given to illustrate the effectiveness and the benefits of the proposed method

generalized halanay inequalities and their applications to neural networks with unbounded time varying delays in this brief we discuss some variants of generalized halanay inequalities that are useful in the discussion of dissipativity and stability of delayed neural networks integro differential systems and volterra functional differential equations we provide some generalizations of the halanay inequality which is more accurate than the existing results as applications we discuss invariant set dissipative synchronization and global asymptotic stability for the hopfield neural networks with infinite delays we also prove that the dynamical systems with unbounded time varying delays are globally asymptotically stable

novel stability analysis for recurrent neural networks with multiple delays via line integral type l k functional this paper studies the stability problem of a class of recurrent neural networks rnns with multiple delays by using an augmented matrix vector transformation for delays and a novel line integral type lyapunov krasovskii functional a less conservative delay dependent global asymptotical stability criterion is first proposed for rnns with multiple delays the obtained stability result is easy to check and improve upon the existing ones then two numerical examples are given to verify the effectiveness of the proposed criterion

neural network based near optimal control for a class of discrete time affine nonlinear systems with control constraints in this paper the near optimal control problem for a class of nonlinear discrete time systems with control constraints is solved by iterative adaptive dynamic programming algorithm first a novel nonquadratic performance functional is introduced to overcome the control constraints and then an iterative adaptive dynamic programming algorithm is developed to solve the optimal feedback control problem of the original constrained system with convergence analysis in the present control scheme there are three neural networks used as parametric structures for facilitating the implementation of the iterative algorithm two examples are given to demonstrate the convergence and feasibility of the proposed optimal control scheme

analysis on robust h performance and stability for linear systems with interval time varying state delays via some new augmented lyapunov krasovskii functional in this paper the problem of h performance and stability analysis for linear systems with interval time varying delays is considered first by constructing a newly augmented lyapunov krasovskii functional which has not been proposed yet an improved h performance criterion with the framework of linear matrix inequalities lmis is introduced next the result and method are extended to the problem of a delay dependent stability criterion finally numerical examples are given to show the superiority of proposed method

dynamic surface control using neural networks for a class of uncertain nonlinear systems with input saturation in this paper a dynamic surface control dsc scheme is proposed for a class of uncertain strict feedback nonlinear systems in the presence of input saturation and unknown external disturbance the radial basis function neural network rbfnn is employed to approximate the unknown system function to efficiently tackle the unknown external disturbance a nonlinear disturbance observer ndo is developed the developed ndo can relax the known boundary requirement of the unknown disturbance and can guarantee the disturbance estimation error converge to a bounded compact set using ndo and rbfnn the dsc scheme is developed for uncertain nonlinear systems based on a backstepping method using a dsc technique the problem of explosion of complexity inherent in the conventional backstepping method is avoided which is specially important for designs using neural network approximations under the proposed dsc scheme the ultimately bounded convergence of all closed loop signals is guaranteed via lyapunov analysis simulation results are given to show the effectiveness of the proposed dsc design using ndo and rbfnn

robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances in recent years the global stability of recurrent neural networks rnns has been investigated extensively it is well known that time delays and external disturbances can derail the stability of rnns in this paper we analyze the robustness of global stability of rnns subject to time delays and random disturbances given a globally exponentially stable neural network the problem to be addressed here is how much time delay and noise the rnn can withstand to be globally exponentially stable in the presence of delay and noise the upper bounds of the time delay and noise intensity are characterized by using transcendental equations for the rnns to sustain global exponential stability moreover we prove theoretically that for any globally exponentially stable rnns if additive noises and time delays are smaller than the derived lower bounds arrived at here then the perturbed rnns are guaranteed to also be globally exponentially stable three numerical examples are provided to substantiate the theoretical results

new delay dependent stability results for neural networks with time varying delay this paper studies the problem of stability analysis for neural networks nns with a time varying delay unlike the previous works the activation functions are assumed to be neither monotonic nor differentiable nor bounded by defining a more general type of lyapunov functionals some new less conservative delay dependent stability criteria are established in terms of linear matrix inequalities lmis meanwhile the computational complexity of the newly obtained stability conditions is reduced because less variables are involved numerical examples are given to illustrate the effectiveness and the benefits of the proposed method

asymptotics beyond all orders asymptotology and borel summation asymptotics superasymptotics hyperasymptotics m berry the geometric model of crystal growth numerical analysis of the geometric model of crystal growth j m hammersley dendritic crystal growth an experimental assessment of continuum models of dendritic growth j p gollub directional solidification of solids directional growth of dilute mixtures and lamellar eutectics k kassner et al flow in a hele shaw cell viscous displacement in a hele shaw cell s tanveer the rapidly forced pendulum exponentially small estimate for separatrix splittings j scheurle et al ordinary differential equations singular perturbations of solitons y pomeau solitary water waves in the presence of small surface tension solitary waves with ripples beyond all orders j t beale problems in optics potpourri 23 additional articles index

relaxed stability criteria for neural networks with time varying delay using extended secondary delay partitioning and equivalent reciprocal convex combination techniques this article investigates global asymptotic stability for neural networks nns with time varying delay which is differentiable and uniformly bounded and the delay derivative exists and is upper bounded first we propose the extended secondary delay partitioning technique to construct the novel lyapunov krasovskii functional where both single integral and double integral state variables are considered while the single integral ones are only solved by the traditional secondary delay partitioning second a novel free weight matrix equality fwme is presented to resolve the reciprocal convex combination problem equivalently and directly without schur complement which eliminates the need of positive definite matrices and is less conservative and restrictive compared with various improved reciprocal convex inequalities furthermore by the present extended secondary delay partitioning equivalent reciprocal convex combination technique and bessel legendre inequality two different relaxed sufficient conditions ensuring global asymptotic stability for nns are obtained for time varying delays respectively with unknown and known lower bounds of the delay derivative finally two examples are given to illustrate the superiority and effectiveness of the presented method

a one layer recurrent neural network with a discontinuous hard limiting activation function for quadratic programming in this paper a one layer recurrent neural network with a discontinuous hard limiting activation function is proposed for quadratic programming this neural network is capable of solving a large class of quadratic programming problems the state variables of the neural network are proven to be globally stable and the output variables are proven to be convergent to optimal solutions as long as the objective function is strictly convex on a set defined by the equality constraints in addition a sequential quadratic programming approach based on the proposed recurrent neural network is developed for general nonlinear programming simulation results on numerical examples and support vector machine svm learning show the effectiveness and performance of the neural network

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

adaptive fuzzy terminal sliding mode control for a class of mimo uncertain nonlinear systems this paper presents a new adaptive terminal sliding mode tracking control design for a class of nonlinear systems using fuzzy logic system the terminal sliding mode control tsm was developed to provide faster convergence and higher precision control than the linear hyperplane based sliding control however the original tsm encountered singularity problem with discontinuous control action moreover a prior knowledge about the plant to be controlled is required the proposed controller combines a continuous non singular tsm with an adaptive learning algorithm and fuzzy logic system to estimate the dynamics of the controlled plant so that closed loop stability and finite time convergence of tracking errors can be guaranteed the performance of the proposed control strategy is evaluated through the control of a two link rigid robotic manipulator finally the effectiveness of the proposed scheme is demonstrated through the control of the ankle and knee movements in paraplegic subjects using functional electrical stimulation simulation and experimental results verify that the proposed control strategy can achieve favorable control performance with regard to system parameter variations and external disturbances 2011 elsevier b v all rights reserved

new results on stability analysis for delayed markovian generalized neural networks with partly unknown transition rates the stability of delayed markovian generalized neural networks is studied where the transition rates of the modes are partly unknown the partly unknown transition rates generalize the traditional works that are with all known transition rates then a lyapunov krasovskii functional lkf with a delay product type dpt term is constructed the dpt term is not only simple but also fully utilizes the information of time delay based on the new dpt lkf stability criteria are presented which are with lower computational complexity and less conservative in the end the validity and superiorities of the analytical results are verified by several examples

pseudospectral delves freeman computations of the radiation coefficient for weakly nonlocal solitary waves of the third order nonlinear schroedinger equation and their relation to hyperasymptotic perturbation theory we revive a strategy of delves to precondition a spectral calculation using an almost diagonal galerkin matrix we also show that hyperasymptotic singular perturbation theory is a specialization of the delves freeman iteration to a single step with a diagonal galerkin matrix we calculate the first three orders in the hyperasymptotic expansion of the radiation coefficient of the weakly nonlocal envelope solitary waves of the third order nonlinear schroedinger tnls equation which is important in fiber optics telecommunications and water waves in a long appendix it was necessary to develop some non numerical but numerically essential additions to the theory of the tnls equation good numerics often requires a much deeper understanding of a problem than the generation of a string of power series coefficients

hierarchical stability conditions for a class of generalized neural networks with multiple discrete and distributed delays this brief investigates the analysis issue for global asymptotic stability of a class of generalized neural networks with multiple discrete and distributed delays to tackle delays arising in different neuron activation functions we employ a generalized model with multiple discrete and distributed delays which covers various existing neural networks we then generalize the bessel legendre inequalities to deal with integral terms with any linearly independent functions and nonlinear function of states based on these inequalities we design the lyapunov krasovskii functional and derive hierarchical linear matrix inequality stability conditions finally three numerical examples are provided to demonstrate that the proposed method is less conservative with a reasonable numerical burden than the existing results

adaptive neural dynamic surface control of strict feedback nonlinear systems with full state constraints and unmodeled dynamics abstract in this paper the problem of adaptive neural network nn dynamic surface control dsc is discussed for a class of strict feedback nonlinear systems with full state constraints and unmodeled dynamics by introducing a one to one nonlinear mapping the strict feedback system with full state constraints is transformed into a novel pure feedback system without state constraints radial basis function rbf neural networks nns are used to approximate unknown nonlinear continuous functions unmodeled dynamics is dealt with by introducing a dynamical signal using modified dsc and introducing integral type lyapunov function adaptive nn dsc is developed using young s inequality only one parameter is adjusted at each recursive step in the design it is shown that all the signals in the closed loop system are semi global uniform ultimate boundedness sguub and the full state constraints are not violated simulation results are provided to verify the effectiveness of the proposed approach

observer based decentralized fuzzy neural sliding mode control for interconnected unknown chaotic systems via network structure adaptation in this paper an observer based fuzzy neural sliding mode control ofnsmc scheme for interconnected unknown chaotic systems is developed the ofnsmc system is composed of a computation controller and a robust controller the computation controller containing a self structuring fuzzy neural network sfnn identifier is the principle controller and the robust controller is designed to achieve l 2 tracking performance the sfnn identifier uses the structure and parameter learning phases to perform the estimation of the interconnected unknown chaotic system dynamics the structure learning phase consists of the growing of membership functions the splitting of fuzzy rules and the pruning of fuzzy rules and thus the sfnn identifier can avoid the time consuming trial and error tuning procedure for determining the network structure of fuzzy neural network the total states of the interconnected chaotic systems are not assumed to be available for measurement also the unknown nonlinearities of the interconnected chaotic systems are not restricted to the systems output only to demonstrate the effectiveness of the proposed method simulation results are illustrated in this paper

brief paper markovian jump delayed hopfield networks with multiplicative noise a non symmetric version of hopfield networks subject to state multiplicative noise pure time delay and markov jumps is considered such networks arise in the context of visuo motor control loops and may therefore be used to mimic their complex behavior in this paper we adopt the lur e postnikov systems approach to analyze the stochastic stability and the l 2 gain of generalized hopfield networks including these effects

hybrid fuzzy adaptive fault tolerant control for a class of uncertain nonlinear systems with unmeasured states in this paper a hybrid adaptive output feedback fault tolerant control is investigated for a class of uncertain nonlinear systems with unmeasured states the generalized fuzzy hyperbolic model is used to approximate the unknown nonlinear functions and the fuzzy state estimator fse is established for estimating the unmeasured states based on the backstepping and dynamic surface control technique a novel adaptive control method is proposed by introducing the prediction errors between fse and serial parallel estimation model it is proved that all the variables of the closed loop systems are semi globally uniformly ultimately bounded by lyapunov approach and the tracking errors can converge to a small neighborhood two simulation examples are used to illustrate the effectiveness of the proposed control method

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

a new criterion of delay dependent asymptotic stability for hopfield neural networks with time delay in this brief the problem of global asymptotic stability for delayed hopfield neural networks hnns is investigated a new criterion of asymptotic stability is derived by introducing a new kind of lyapunov krasovskii functional and is formulated in terms of a linear matrix inequality lmi which can be readily solved via standard software this new criterion based on a delay fractioning approach proves to be much less conservative and the conservatism could be notably reduced by thinning the delay fractioning an example is provided to show the effectiveness and the advantage of the proposed result

prescribed performance adaptive fuzzy output feedback dynamic surface control for nonlinear large scale systems with time delays the adaptive fuzzy decentralized output feedback control method is proposed for a class of nonlinear large scale systems the considered nonlinear systems contain unstructured uncertainties unknown time varying delays and immeasurable states fuzzy logic systems are used to approximate the unstructured uncertainties and a fuzzy state observer is designed to estimate the unmeasured states based on the backstepping recursive design technique and the prescribed performance technique a new adaptive fuzzy output feedback control method is developed in order to overcome the problem of explosion of complexity inherent in the backstepping control design the dynamic surface control dsc technique is introduced into the control scheme based on lyapunov krasovskii functional it is proved that all the signals in the closed loop system are bounded and the tracking errors remain an adjustable neighborhood of the origin with the prescribed performance bounds the simulation examples and comparison with the previous control methods are provided to show the effectiveness of the proposed control approach

exponential stability and stabilization of delayed memristive neural networks based on quadratic convex combination method this paper is concerned with the exponential stability and stabilization of memristive neural networks mnns with delays first we present some generalized double integral inequalities which include some existing inequalities as their special cases second combining with quadratic convex combination method these double integral inequalities are employed to formulate a delay dependent stability condition for mnns with delays third a state dependent switching control law is obtained for mnns with delays based on the proposed stability conditions the desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities finally the feasibility and effectiveness of the proposed results are tested by two numerical examples

recurrent fuzzy wavelet neural network variable impedance control of robotic manipulators with fuzzy gain dynamic surface in an unknown varied environment abstract in this paper an intelligent variable impedance control combined with a fuzzy gain dynamic surface is proposed to improve the interaction of the robot manipulator with an unknown varied environment the parameters of the proposed variable impedance are adapted by optimization an introduced cost function using a recurrent fuzzy wavelet network the stability conditions for the varying inertial stiffness and damping are presented to guarantee the stability of the variable impedance additionally a fuzzy dynamic surface method is developed to tune the gains of the dynamic surface as a robust controller the proposed fuzzy gain dynamic surface is used to force the end effector of the manipulator to track the desired impedance profile in the presence of large disturbances using lyapunov s method the stability of the mentioned closed loop system is proved finally by using a designed simulator for irb120 abb robot several simulations are carried out to verify the performance of the proposed method for the execution of various tasks in an unknown varied environment in the presence of large disturbances

a hyperasymptotic perturbative method for computing the radiation coefficient for weakly nonlocal solitary waves we offer a new computational method to calculate the radiation coefficient of a weakly nonlocal solitary wave in the limit that the amplitude e of the core of the structure tends to zero a weakly nonlocal solitary wave is a finite amplitude nondissipative wave which decays to a sinusoidal oscillation of amplitude at large distance from the core the multiple scales series for the solitary wave in powers of e is asymptotic but divergent when truncated at optimal order superasymptotic approximation the series gives no information about the radiation coefficient except order of magnitude because the absolute error is o we describe two hyperasymptotic approximations which add a second different asymptotic series to the multiple scales expansion so as to compute itself the zeroth order hyperasymptotic approximation has a relative error of o e in the sequence of approximations may be extrapolated to give the proportionality constant in the limiting asymptotic expression for as e 0 the first order hyperasymptotic approximation has a relative error of only o e2 its extrapolation gives the o e correction to the limit as e 0

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

weakly nonlocal solitary waves in a singularly perturbed korteweg de vries equation a fifth order korteweg de vries equation is considered where the fifth order derivative term is multiplied by a small parameter it is known that solitary wave solutions of this model equation are nonlocal in that the central core of the wave is accompanied by copropagating trailing oscillations here using the techniques of exponential asymptotics these solutions are reexamined and it is established that they form a one parameter family characterized by the phase shift of the trailing oscillations explicit asymptotic formula relating the oscillation amplitude to the phase shift are obtained

note on stability of linear systems with time varying delay this note considers the stability of linear systems with a time varying delay we are interested in a simple lyapunov krasovskii functional lkf approach without delay decomposition in this category all recent tractable results had a fixed bound on the allowable maximum size of the delay for years we propose a new simple lkf including the cross terms of variables and quadratic terms multiplied by a higher degree scalar function and present a new result expressed in the form of lmis we show by two well known examples that our result overcomes the previous allowable maximum size of delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time delay

adaptive control for a class of uncertain strict feedback nonlinear systems based on a generalized fuzzy hyperbolic model in this study we propose an effective method for designing an adaptive controller for a class of uncertain strict feedback nonlinear systems with unknown bounded disturbances during the controller design process all of the unknown functions are accumulated at the intermediate steps to approximate the last step in addition only one generalized fuzzy hyperbolic model is used to approximate the total unknown functions for the system thus only the actual control law needs to be implemented and one adaptive law is proposed for the overall controller design process as a result the controller design is much simpler and the computational burden is reduced greatly using lyapunov techniques we obtain the uniformly ultimately bounded stability of all the signals for the closed loop system our simulation results verified the theoretical analysis and they illustrated the superior performance of the method proposed in this study

exact tracking using backstepping control design and high order sliding modes in this technical note a controller ensuring exponential exact tracking in the presence of matched and unmatched disturbances for the nonlinear systems in the block controllable form is proposed the controller is designed using the backstepping procedure and combines the feedback linearization technique with the high order sliding modes the matched and unmatched disturbances are compensated by the injection of a continuous term generated by the robust exact high order sliding modes differentiator the obtained control law is differentiable and can be applied directly to the system simulations verify the performance of the proposed controller

multivariable adaptive dynamic surface control based on norm estimation of unknown parameter matrices in this article a novel output feedback adaptive dynamic surface control scheme is proposed for linear time invariant multivariable plants based on the norm estimation of unknown parameter matrices besides avoiding the explosion of complexity problem in traditional multivariable backstepping design the proposed scheme has the following features 1 only one parameter needs to be updated on line regardless of the plant order and input output dimension 2 only the hurwitz condition is required for the high frequency gain matrix and 3 the performance of the tracking error can be guaranteed it is shown that all signals of the closed loop system are semi globally uniformly bounded simulation results are given to illustrate the effectiveness of the proposed scheme

global stability analysis of neural networks with multiple time varying delays in this note we study the equilibrium and stability properties of neural networks with time varying delays our main results give sufficient conditions for the existence uniqueness and global asymptotic stability of the equilibrium point the proposed conditions establish the relationships between network parameters of the neural systems and the delay parameters the obtained results are applicable to all continuous nonmonotonic neuron activation functions and do not require the interconnection matrices to be symmetric some examples are also presented to compare our results with the previous results derived in the literature

an improved result on dissipativity and passivity analysis of markovian jump stochastic neural networks with two delay components in this paper we investigate the dissipativity and passivity of markovian jump stochastic neural networks involving two additive time varying delays using a lyapunov krasovskii functional with triple and quadruple integral terms we obtain delay dependent passivity and dissipativity criteria for the system using a generalized finsler lemma gfl a set of slack variables with special structure are introduced to reduce design conservatism the dissipativity and passivity criteria depend on the upper bounds of the discrete time varying delay and its derivative are given in terms of linear matrix inequalities which can be efficiently solved through the standard numerical software finally our illustrative examples show that the proposed method performs well and is successful in problems where existing methods fail

global stability of complex valued recurrent neural networks with time delays since the last decade several complex valued neural networks have been developed and applied in various research areas as an extension of real valued recurrent neural networks complex valued recurrent neural networks use complex valued states connection weights or activation functions with much more complicated properties than real valued ones this paper presents several sufficient conditions derived to ascertain the existence of unique equilibrium global asymptotic stability and global exponential stability of delayed complex valued recurrent neural networks with two classes of complex valued activation functions simulation results of three numerical examples are also delineated to substantiate the effectiveness of the theoretical results

fuzzy dynamic surface control for uncertain nonlinear systems under input saturation via truncated adaptation approach in this paper a fuzzy control scheme is presented for uncertain nonlinear systems with input saturation and external disturbance using truncated adaptation and dynamic surface control technique fuzzy logic systems are used in the online approximating of uncertain system dynamics and adaptation laws used to online adjust weights of fuzzy logic system are designed auxiliary system is constructed and used to truncate the adaptation laws of fuzzy logic system and disturbance attenuator to prevent aggressive action when input saturation happens dynamic surface control technique is incorporated into traditional backstepping design to circumvent the problem of explosion of complexity caused by differentiating the so called virtual controllers during the recursive procedures it is proved that the proposed controller guarantees the uniformly ultimately boundedness of all signals in the closed loop system the steady tracking error and transient tracking error can be adjusted to arbitrarily small by choosing proper design parameters in spite of uncertain dynamics external disturbance and input saturation numerical simulations are presented to demonstrate the effectiveness of the proposed controller

further results on delay dependent stability criteria of neural networks with time varying delays in this brief paper an augmented lyapunov functional which takes an integral term of state vector into account is introduced owing to the functional an improved delay dependent asymptotic stability criterion for delayed neural networks nns is derived in term of linear matrix inequalities lmis it is shown that the obtained criterion can provide less conservative result than some existing ones when linear fractional uncertainties appear in nns a new robust delay dependent stability condition is also given numerical examples are given to demonstrate the applicability of the proposed approach