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

approximation based adaptive fuzzy tracking control for a class of nonstrict feedback stochastic nonlinear time delay systems this paper focuses on the problem of approximation based adaptive fuzzy tracking control for a class of stochastic nonlinear time delay systems with a nonstrict feedback structure a variable separation approach is introduced to overcome the design difficulty from the nonstrict feedback structure mamdani type fuzzy logic systems are utilized to model the unknown nonlinear functions in the process of controller design and an adaptive fuzzy tracking controller is systematically designed by using a backstepping technique it is shown that the proposed controller guarantees that all signals in the closed loop system are fourth moment semiglobally uniformly ultimately bounded and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value simulation results are provided to demonstrate the effectiveness of our results further developments will consider how to generalize the proposed strategy to nonstrict feedback nonlinear systems with input nonlinearities

resonances of third order differential operators abstract we consider resonances for third order ordinary differential operators with compactly supported coefficients on the real line resonance are defined as zeros of a fredholm determinant on a non physical sheet of three sheeted riemann surface we determine upper bounds of the number of resonances in complex discs at large radius we express the trace formula in terms of resonances only

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

robust backstepping control for a class of time delayed systems in this note the problem of robust output feedback control for a class of nonlinear time delayed systems is considered the systems considered are in strict feedback form state observer is first designed then based on the observed states the controller is designed via backstepping method both the designed observer and controller are independent of the time delays based on lyapunov stability theory we prove that the constructed controller can render the closed loop system asymptotically stable simulation results further verify the effectiveness of the proposed approach

a numerical algorithm to find all feedback nash equilibria in scalar affine quadratic differential games this note deals with solving scalar coupled algebraic riccati equations these equations arise in finding linear feedback nash equilibria of the scalar n player affine quadratic differential game a numerical procedure is provided to compute all the stabilizing solutions the main idea is to reformulate the riccati equations into an extended eigenvalue eigenvector problem for a specific parametrized matrix u in i r 2 n times 2 n since the size of u increases exponentially on n the algorithm only applies for games where the number of players is not too large

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

adaptive consensus control for a class of nonlinear multiagent time delay systems using neural networks because of the complicity of consensus control of nonlinear multiagent systems in state time delay most of previous works focused only on linear systems with input time delay an adaptive neural network nn consensus control method for a class of nonlinear multiagent systems with state time delay is proposed in this paper the approximation property of radial basis function neural networks rbfnns is used to neutralize the uncertain nonlinear dynamics in agents an appropriate lyapunov krasovskii functional which is obtained from the derivative of an appropriate lyapunov function is used to compensate the uncertainties of unknown time delays it is proved that our proposed approach guarantees the convergence on the basis of lyapunov stability theory the simulation results of a nonlinear multiagent time delay system and a multiple collaborative manipulators system show the effectiveness of the proposed consensus control algorithm

technical communique feedback nash equilibria in the scalar infinite horizon lq game in this note we consider linear stationary feedback nash equilibria of the scalar linear quadratic differential game the planning horizon considered is assumed to be infinite we present both necessary and sufficient conditions on the system parameters for the existence of a unique solution of the associated algebraic riccati equations are that stabilizes the closed loop system for the case of more solutions singleton valued refinements of the equilibrium concept are studied

resonances for euler bernoulli operator on the half line abstract we consider resonances for fourth order differential operators on the half line with compactly supported coefficients we determine asymptotics of a counting function of resonances in complex discs at large radius describe the forbidden domain for resonances and obtain trace formulas in terms of resonances we apply these results to the euler bernoulli operator on the half line the coefficients of this operator are positive and constants outside a finite interval we show that this operator does not have any eigenvalues and resonances iff its coefficients are constants on the whole half line

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

adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances a novel function approximator is constructed by combining a fuzzy logic system with a fourier series expansion in order to model unknown periodically disturbed system functions then an adaptive backstepping tracking control scheme is developed where the dynamic surface control approach is used to solve the problem of explosion of complexity in the backstepping design procedure and the time varying parameter dependent integral lyapunov function is used to analyze the stability of the closed loop system the semiglobal uniform ultimate boundedness of all closed loop signals is guaranteed and the tracking error is proved to converge to a small residual set around the origin two simulation examples are provided to illustrate the effectiveness of the control scheme designed in this paper

the inverse sturm liouville problem ii soit q q 0 2 l r 2 0 1 le probleme de sturm liouville y q x y y 0 x 1 y 0 cos y 0 sin 0 y 1 cos y 1 sin 0 a un spectre discret de valeurs propres simples 0 q 1 q avec des fonctions propres h 0 x q h 1 x q on fixe p dans 0 2 l r 2 0 1 et soit m p q 0 2 l r 2 0 1 n q n p n 0 l espace de tous les points q de meme spectre que p on etudie m p comme une sous variete de 0 2 l r 2 0 1

coupled matrix riccati equations in minimal cost variance control problems we present an algorithm for the solution of a nontrivial coupled system of algebraic riccati equations appearing in risk sensitive control problems moreover we use comparison methods to derive non blowup conditions for the solutions of a corresponding terminal value problem for coupled systems of riccati differential equations

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

adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems an adaptive fuzzy control approach is proposed for a class of multiple input multiple output mimo nonlinear systems with completely unknown nonaffine functions the mimo systems are composed of n subsystems and each of subsystems is in the nested lower triangular form it is difficult and complicated to control this class of systems due to the existence of unknown nonaffine functions and the couplings among the nested subsystems this difficulty is overcome by introducing some special type lyapunov functions and taking advantage of the mean value theorem the backstepping design method and the approximation property of the fuzzy systems the proposed control approach can guarantee that all the signals in the closed loop system are bounded a simulation experiment is utilized to verify the feasibility of the proposed approach

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

robust adaptive fuzzy fault tolerant control for a class of non lower triangular nonlinear systems with actuator failures in this paper the problem of adaptive fuzzy fault tolerant tracking control is studied for a class of non lower triangular nonlinear systems with actuator failures according to the same structure of virtual control inputs and the monotonously increasing property of the bounding functions a variable separation approach is proposed by applying the backstepping technique an adaptive fuzzy control approach is presented which can guarantee the semi global boundedness of all signals within the closed loop system the tracking error using the proposed control scheme eventually converges to a small neighborhood of the origin

adaptive control for nonlinear mimo time delay systems based on fuzzy approximation this paper focuses on the problem of adaptive control for a class of nonlinear multi input and multi output mimo systems with time delays a state feedback adaptive controller is constructed by backstepping technique fuzzy logic systems are used to approximate unknown nonlinear functions in the process of the controller design the main advantages of the proposed approach are twofold 1 the controller design is independent of the knowledge of the basis functions of fuzzy logic systems and 2 the suggested approach requires only m adaptive laws to control a nonlinear time delay system with m inputs simulation results illustrate the effectiveness of the proposed approach

an inverse scattering formalism for higher order differential operators abstract an inverse scattering formalism is presented for certain linear ordinary differential operators of arbitrary even order n which generalizes the gel fand levitan theory for sturm liouville operators under suitable hypotheses it is proved that for given n 2 the coefficients in these operators are uniquely determined by a single spectral matrix our proof makes use of a transformation due to m k fage which generalizes the povzner levitan transformation for sturm liouville operators

on polynomial feedback nash equilibria for two player scalar differential games in this paper two player scalar differential games are thoroughly studied in the presence of polynomial dynamics and focusing on the notion of solution provided by polynomial feedback nash equilibria it is well known that such strategies are related to the solution of coupled partial differential equations namely the so called hamilton jacobi isaacs equations herein we firstly prove a somewhat negative result stating that for a generic choice of the parameters two player scalar polynomial differential games do not admit polynomial nash equilibria then we focus on the class of linear quadratic lq games and we propose an algorithm that by borrowing techniques from algebraic geometry allows to recast the problem of computing all stabilizing nash feedback strategies into that of finding the zero of a single polynomial function in a scalar variable this permits a comprehensive characterization in terms of number and values of the set of solutions to the associated game

factorization and the dressing method for the gel fand dikii hierarchy abstract the isospectral flows of an n th order linear scalar differential operator l under the hypothesis that it possesses a baker akhiezer function were originally investigated by segal and wilson from the point of view of infinite dimensional grassmanians and the reduction of the kp hierarchy to the gel fand dikii hierarchy the associated first order systems and their formal asymptotic solutions have a rich lie algebraic structure which was investigated by drinfeld and sokolov we investigate the matrix riemann hilbert factorizations for these systems and show that different factorizations lead respectively to the potential modified and ordinary gel fand dikii flows lie algebra decompositions the adler kostant symes method are obtained for the modified and potential flows for n 3 the appropriate factorization for the gel fand dikii flows is not a group factorization as would be expected yet a modification of the dressing method still works a direct proof based on a fredholm determinant associated with the factorization problem is given that the potentials are meromorphic in x and in the time variables potentials with baker akhiezer functions include the multisoliton and rational solutions as well as potentials in the scattering class with compactly supported scattering data the latter are dense in the scattering class

state and output feedback control of interval type 2 fuzzy systems with mismatched membership functions this paper is concerned with the problems of state and output feedback control for interval type 2 it2 fuzzy systems with mismatched membership functions the it2 fuzzy model and the it2 state and output feedback controllers do not share the same membership functions a novel performance index which is expressed as an extended dissipativity performance is introduced to be a generalization of h infty l 2 l infty passive and dissipativity performances indexes first the it2 takagi sugeno fuzzy model and the controllers are constructed by considering the mismatched membership functions second on the basis of lyapunov stability theory the it2 fuzzy state and output feedback controllers are designed respectively to guarantee that the closed loop system is asymptotically stable with extended dissipativity performance the existence conditions of the two kinds of controllers are obtained in terms of convex optimization problems which can be solved by standard software finally simulation results are provided to illustrate the effectiveness of the proposed methods

adaptive fuzzy control for full states constrained systems with nonstrict feedback form and unknown nonlinear dead zone this paper addresses the problem of direct adaptive fuzzy tracking control design for a class of uncertain nonstrict feedback systems with nonlinear dead zone and full state constraints fuzzy logic systems are used to approximate some unknown nonlinear functions and less adjustable parameters are adopted in each backstepping design process this advantage is first to take into account the full state constrained nonstrict feedback systems with input dead zone nonlinearity to guarantee that the full state constraints are not violated a novel adaptive fuzzy controller is developed by introducing barrier lyapunov function with the error variables furthermore it is proved that all the closed loop signals remain semi globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin two simulation examples are provided to verify the effectiveness of the proposed control method

constructive epsilon nash equilibria for nonzero sum differential games in this paper a class of infinite horizon nonzero sum differential games and their nash equilibria are studied and the notion of epsilon alpha nash equilibrium strategies is introduced dynamic strategies satisfying partial differential inequalities in place of the hamilton jacobi isaacs partial differential equations associated with the differential games are constructed these strategies constitute local epsilon alpha nash equilibrium strategies for the differential game the proposed methods are illustrated on a differential game for which the nash equilibrium strategies are known and on a lotka volterra model with two competing species simulations indicate that both dynamic strategies yield better performance than the strategies resulting from the solution of the linear quadratic approximation of the problem

model approximation for fuzzy switched systems with stochastic perturbation in this paper the model approximation problem is investigated for a takagi sugeno fuzzy switched system with stochastic disturbance for a high order considered system our attention is focused on the construction of a reduced order model which not only approximates the original system well with a hankel norm performance but translates it into a lower dimensional fuzzy switched system as well by using the average dwell time approach and the piecewise lyapunov function technique a sufficient condition is first proposed to guarantee the mean square exponential stability with a hankel norm error performance for the error system the model approximation is then converted into a convex optimization problem by using a linearization procedure finally simulations are provided to illustrate the effectiveness of the proposed theory

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

a novel approach to output feedback control of fuzzy stochastic systems this paper investigates the problem of hankel norm output feedback controller design for a class of t s fuzzy stochastic systems the full order output feedback controller design technique with the hankel norm performance is proposed by the fuzzy basis dependent lyapunov function approach and the conversion on the hankel norm controller parameters sufficient conditions are established to design the controllers such that the resulting closed loop system is stochastically stable and satisfies a prescribed performance the desired output feedback controller can be obtained by solving a convex optimization problem which can be efficiently solved by standard numerical algorithms finally a henon map system is used to illustrate the effectiveness of the proposed techniques

combined partial bar and riemann hilbert inverse methods for integrable non linear evolution equations in 2 1 dimensions the authors give a natural combination of partial bar and riemann hilbert problem inverse methods for an n th order scalar spectral problem which solves a number of integrable non linear evolution equations in two space and one time 2 1 dimensions the theory embraces the two kadomtsev petviashvili equations 1970 and their lump solutions

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

the inverse problem for ordinary differential operators on the line on etudie le probleme inverse sur la ligne pour l operateur p d n q n 2 d n 2 q 0 d d idx pour tout ordre n 2 et sans hypothese de propriete d auto adjoint

a multiple model mrac scheme for multivariable systems with matching uncertainties this paper develops a multivariable multiple model adaptive control scheme for adaptive state feedback state tracking control of systems whose plant model matching conditions are uncertain and parameters are unknown to deal with the uncertainty of plant model matching conditions needed for adaptive control multiple reference model systems are employed to generate multiple parameter estimation and feedback control signals from which a most suitable control input is selected by a control switching mechanism designed using multiple estimation errors such a new multiple model control design is based on an expanded control system parametrization which has the capacity to cover system structural uncertainties stability analysis and simulation results ensure and verify the desired adaptive control system stability and tracking performance

open loop nash equilibrium in polynomial differential games via state dependent riccati equation this paper studies finite as well as infinite time horizon nonzero sum polynomial differential games in both cases we explore the so called state dependent riccati equations to find a set of strategies that guarantee an open loop nash equilibrium for this particular class of nonlinear games such a method presents advantages in simplicity of the design of equilibrium strategies and yields computationally effective solution algorithms we demonstrate that this solution leads the game to an e or quasi equilibrium and provide an upper bound for this e quantity the proposed solution is given as a set of n coupled polynomial riccati like state dependent differential equations where each equation includes a p linear form tensor representation for its polynomial part we provide an algorithm for finding the solution of the state dependent algebraic equation in the infinite time case based on a hamiltonian approach and give conditions on the existence of such stabilizing solutions for a third order polynomial a numerical example is presented to illustrate effectiveness of the approach

model reduction for interval type 2 takagi sugeno fuzzy systems this paper investigates the problem of model reduction for interval type 2 it2 fuzzy systems subject to d stability constraints the membership functions and the number of rules can be freely chosen and they are different between the original system and the reduced order system by introducing some slack matrices and utilizing lyapunov stability theory the existence condition of model reduction is obtained to guarantee that the reduced order model can approximate the original system with an h performance the parameters of the reduced order system in the condition can be obtained by standard software finally some simulation results are provided to demonstrate the effectiveness of the proposed results