h control of uncertain fuzzy continuous time systems a new kind of dynamical fuzzy model is proposed to represent the continuous time complex system which includes both linguistic information and system uncertainties a new stability analysis and control system design approach is developed for this kind of dynamical fuzzy model since the fuzzy model considers the norm bounded disturbance the controller design problem becomes a h control problem a constructive algorithm is developed to obtain the h feedback control law finally an example is given to illustrate the application of the method

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

design of fuzzy control systems with guaranteed stability abstract this paper addresses the analysis and design of fuzzy control systems the fuzzy systems are represented by a family of local state space models with aggregation the controller is designed by considering each local state feedback controller and a compensating controller the compensating controller is based on the well known variable structure control theory it is shown that this controller guarantees global stability of the closed loop fuzzy system the issues of a state observer for the fuzzy system is also addressed a numerical example and an example of nonlinear system control are given for demonstration of the performance of the method

distributed memoryless detection and accommodation of unknown time delayed interaction faults in a class of interconnected nonlinear systems this paper addresses a memoryless design problem for the distributed fault detection and accommodation fda of a class of large scale nonlinear systems in the presence of nonlinear interaction faults with unknown time delays existing works designed distributed fda schemes without considering interaction delays however we consider these delays design distributed memoryless detection estimators and time varying thresholds for detecting unknown time delayed interaction faults and analyze the distributed fault detectability then an approximation based distributed fault accommodation scheme which is independent of time delays is constructed via lyapunov stability theorem thus it is shown that all signals of the total controlled closed loop system are uniformly ultimately bounded and tracking errors of subsystems converge to an adjustable neighborhood of the origin finally a simulation example is presented to show the effectiveness of the proposed methodology

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

adaptive fuzzy control of nonlinear systems in pure feedback form based on input to state stability using mean value theorem and backstepping technique a robust adaptive fuzzy control scheme is proposed for a class of pure feedback nonlinear systems with unknown dead zone and disturbances via input to state stability takagi sugeno t s type fuzzy logic systems are used to approximate the uncertain nonlinear functions and fewer learning parameters need to be adjusted online based on small gain theorem the closed loop control system is proven to be semiglobally uniformly ultimately bounded and the tracking error converges to a neighborhood of zero by choosing appropriate parameters simulation results demonstrate the effectiveness of the control scheme

direct adaptive controller for nonaffine nonlinear systems using self structuring neural networks a direct adaptive state feedback controller is proposed for highly nonlinear systems we consider uncertain or ill defined nonaffine nonlinear systems and employ a neural network nn with flexible structure i e an online variation of the number of neurons the nn approximates and adaptively cancels an unknown plant nonlinearity a control law and adaptive laws for the weights in the hidden layer and output layer of the nn are established so that the whole closed loop system is stable in the sense of lyapunov moreover the tracking error is guaranteed to be uniformly asymptotically stable uas rather than uniformly ultimately bounded uub with the aid of an additional robustifying control term the proposed control algorithm is relatively simple and requires no restrictive conditions on the design constants for the stability the efficiency of the proposed scheme is shown through the simulation of a simple nonaffine nonlinear system

regularity properties of solutions to linear quadratic optimal control problems with state constraints abstract we establish regularity properties of solutions of linear quadratic optimal control problems involving state inequality constraints under simply stated and directly verifiable hypotheses on the data it is shown that if the state constraint has index k 0 then the optimal control u is k times differentiable the k th derivative may be discontinuous but it is a function of bounded variation and consequently it has left and right limits at each point in its domain if on the other hand the state constraint has index k 0 then the optimal control is continuous the latter property is perhaps surprising because it implies that for the class of problems considered optimal state trajectories cannot abruptly change direction when they strike the boundary of the state constraint region these findings are significant because they justify assumptions which underlie analysis of junction conditions i e properties of state trajectories at contact points with the boundary of the state constraint set provided elsewhere in the literature

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

frequency weighted spl lscr sub spl infin norm and optimal hankel norm model reduction a new relative error model reduction method is proposed using frequency weighted balanced realization and explicit spl lscr sub spl infin norm error bounds are also derived for the relative error and multiplicative error the method only needs to solve two lyapunov equations it is further shown that this method is equivalent to the balanced stochastic truncation if the plant is square and minimum phase this paper also gives a complete solution to the frequency weighted hankel norm approximation with antistable weighting these results are then applied to spl lscr sub spl infin norm model reduction and several numerically effective algorithms are proposed it is shown through many numerical examples that these algorithms work very well and in many cases produce almost optimal solutions

tracking control for nonaffine systems a self organizing approximation approach this paper considers tracking control for single input single output nonaffine dynamic systems a performance dependent self organizing approximation based approach is proposed the designer specifies a positive tracking error criterion the self organizing approximation based controller then monitors the tracking performance and adds basis elements only as needed to achieve the tracking specification even though the system is not affine the approach is defined such that the approximated function is independent of the control variable u stability is proved and the self organization is derived in a lyapunov based methodology to illustrate certain novel aspects of the proposed controller a numerical example is included

fault detection and accommodation of a class of nonlinear systems with unknown multiple time delayed faults this paper investigates a fault detection and accommodation fda problem of a class of nonlinear time delay systems in the presence of unknown multiple time delayed faults compared with existing literature a main contribution of this paper is to design a time delay independent fda scheme namely the exact information on time delays is not required to implement the proposed fda scheme under the assumption that the magnitude and occurrence time of multiple faults are unknown we first design a delay independent fault detection scheme with a detection threshold for time delay systems and analyze the fault detectability then an approximation based fault accommodation design activated after the detection of the first fault is presented for compensating multiple faults the robustness of the fault detection scheme and asymptotic stability of the tracking error are established through lyapunov stability analysis a simulation example is used to illustrate the proposed fda scheme

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

a fuzzy disturbance observer and its application to control in this paper a fuzzy disturbance observer fdo is developed and its application to the control of a nonlinear system under the internal and external disturbances is presented to construct the fdo two parameter tuning methods are proposed and shown to be useful in adjusting the parameters of the fdo the first tuning method employs the disturbance observation error to guarantee that the fdo monitors the unknown disturbance the next one enlarges the concept of error and introduces augmented error to guarantee that the fdo monitors the disturbance and the control objective is achieved in addition the relationships between the suggested fdo based control and the conventional adaptive fuzzy controls reported in the previous literatures are discussed and it is shown in a rigorous manner that the disturbance observation error or the augmented error converges to a region of which size can be kept arbitrarily small finally some examples and computer simulation results are presented to illustrate the effectiveness and the applicability of the fdo

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

stabilization of takagi sugeno models with non measured premises input to state stability approach abstract this work deals with the observer based output stabilization problem for takagi sugeno models with non measured premises it aims at providing efficient design methods for the controller observer pair with minimal constrained hypothesis on the model non linear functions the main idea is to consider the closed loop and the error dynamic as two interacting subsystems and study them in the input to state stability framework this paper provides also some results about the existence of a stabilizing output feedback for all models of a sub class of takagi sugeno models to illustrate the efficiency of the proposed design procedures illustrative examples and a comparative study with existing results in the literature based on more restrictive hypothesis are presented

learning from iss modular adaptive nn control of nonlinear strict feedback systems this paper studies learning from adaptive neural control anc for a class of nonlinear strict feedback systems with unknown affine terms to achieve the purpose of learning a simple input to state stability iss modular anc method is first presented to ensure the boundedness of all the signals in the closed loop system and the convergence of tracking errors in finite time subsequently it is proven that learning with the proposed stable iss modular anc can be achieved the cascade structure and unknown affine terms of the considered systems make it very difficult to achieve learning using existing methods to overcome these difficulties the stable closed loop system in the control process is decomposed into a series of linear time varying ltv perturbed subsystems with the appropriate state transformation using a recursive design the partial persistent excitation condition for the radial basis function neural network nn is established which guarantees exponential stability of ltv perturbed subsystems consequently accurate approximation of the closed loop system dynamics is achieved in a local region along recurrent orbits of closed loop signals and learning is implemented during a closed loop feedback control process the learned knowledge is reused to achieve stability and an improved performance thereby avoiding the tremendous repeated training process of nns simulation studies are given to demonstrate the effectiveness of the proposed method

control of discrete time nonlinear systems with a time varying structure in this paper we present a control methodology for a class of discrete time nonlinear systems that depend on a possibly exogenous scheduling variable this class of systems consists of an interpolation of nonlinear dynamic equations in strict feedback form and it may represent systems with a time varying nonlinear structure moreover this class of systems is able to represent some cases of gain scheduling control takagi sugeno fuzzy systems as well as input output realizations of nonlinear systems which are approximated via localized linearizations we present two control theorems one using what we call a global approach akin to traditional backstepping and a local approach our main result where backstepping is again used but the control law is an interpolation of local control terms an aircraft wing rock regulation problem with varying angle of attack is used to illustrate and compare the two approaches

self organizing approximation based control for higher order systems adaptive approximation based control typically uses approximators with a predefined set of basis functions recently spatially dependent methods have defined self organizing approximators where new locally supported basis elements were incorporated when existing basis elements were insufficiently excited in this paper performance dependent self organizing approximators will be defined the designer specifies a positive tracking error criteria the self organizing approximation based controller then monitors the tracking performance and adds basis elements only as needed to achieve the tracking specification the method of this paper is applicable to general th order input state feedback linearizable systems this paper includes a complete stability analysis and a detailed simulation example

adaptive neural control for a class of stochastic nonlinear systems by backstepping approach this paper addresses adaptive neural control for a class of stochastic nonlinear systems which are not in strict feedback form based on the structural characteristics of radial basis function rbf neural networks nns a backstepping design approach is extended from stochastic strict feedback systems to a class of more general stochastic nonlinear systems in the control design procedure rbf nns are used to approximate unknown nonlinear functions and the backstepping technique is utilized to construct the desired controller the proposed adaptive neural controller guarantees that all the closed loop signals are bounded and the tracking error converges to a sufficiently small neighborhood of the origin two simulation examples are used to illustrate the effectiveness of the proposed approach

nonlinear adaptive wavelet control using constructive wavelet networks in this paper an adaptive wavelet network based control approach is proposed for highly nonlinear uncertain dynamical systems wavelet network as a kind of universal approximator has two novel properties orthonormality and multiresolution the orthonormal property ensures that adding a new resolution new wavelets does not affect the existing wavelet network that may have been well tuned in the sequel the online adjustment of the structure of the nonlinear adaptive wavelet controller awc can be done in a constructive manner by gradually increasing the network resolution the multiresolution property on the other hand assures a guaranteed improvement of the approximation precision when a new resolution is added in real life problems we are unable to know the adequate size of a network either a neural network nn or a wavelet network to produce the required approximation precision by virtue of the novel wavelet network properties a coarse or very simple structure can be selected first if the system fails to converge after the elapse of a dwell time a new wavelet resolution is considered to be necessary and added directly in this manner the awc can be easily constructed and tuned from the coarse to finer levels until the performance requirement is satisfied the trial and error way of selecting the network structure which may lead to either an inadequate or a highly redundant structure can be avoided in this paper the proposed adaptive wavelet network is applied first to a class of nonlinear dynamical systems with a partially known model and an affine in input structure then the adaptive wavelet network is applied to a class of nonlinear nonaffine dynamical systems

a new approach to lipschitz continuity in state constrained optimal control for a linear quadratic state constrained optimal control problem it is proved in 11 that under an independence condition for the active constraints the optimal control is lipschitz continuous we now give a new proof of this result based on an analysis of the euler discretization given in 9 there we exploit the lipschitz continuity of the control to estimate the error in the euler discretization here we show that the theory developed for the euler discretization can be used to derive the lipschitz continuity of the optimal control

adaptive neural control of mimo nonlinear state time varying delay systems with unknown dead zones and gain signs in this paper adaptive neural control is proposed for a class of uncertain multi input multi output mimo nonlinear state time varying delay systems in a triangular control structure with unknown nonlinear dead zones and gain signs the design is based on the principle of sliding mode control and the use of nussbaum type functions in solving the problem of the completely unknown control directions the unknown time varying delays are compensated for using appropriate lyapunov krasovskii functionals in the design the approach removes the assumption of linear functions outside the deadband as an added contribution by utilizing the integral lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead zone disturbance the closed loop control system is proved to be semi globally uniformly ultimately bounded simulation results demonstrate the effectiveness of the approach

adaptive neural output feedback controller design with reduced order observer for a class of uncertain nonlinear siso systems an adaptive output feedback control is studied for uncertain nonlinear single input single output systems with partial unmeasured states in the scheme a reduced order observer roo is designed to estimate those unmeasured states by employing radial basis function neural networks and incorporating the roo into a new backstepping design an adaptive output feedback controller is constructively developed a prominent advantage is its ability to balance the control action between the state feedback and the output feedback in addition the scheme can be still implemented when all the states are not available the stability of the closed loop system is guaranteed in the sense that all the signals are semiglobal uniformly ultimately bounded and the system output tracks the reference signal to a bounded compact set a simulation example is given to validate the effectiveness of the proposed scheme

new results on h filtering for fuzzy systems with interval time varying delays this paper investigates the problem of h filtering for continuous takagi sugeno t s fuzzy systems with an interval time varying delay in the state based on the delay partitioning idea a new approach is proposed for solving this problem which can achieve much less conservative feasibility conditions the attention is focused on the design of an h filter via the parallel distributed compensation scheme such that the filter error system is asymptotically stable and the h attenuation level from disturbance to estimation error is below a prescribed scalar the constructed lyapunov krasovskii functional by applying the delay partitioning method can potentially guarantee the obtained delay dependent conditions to be less conservative than those in the literature the obtained results are formulated in the form of linear matrix inequalities lmis which can be readily solved via standard numerical software finally an example is illustrated to show the reduction in conservatism of the proposed filter design method

stable adaptive tracking of uncertain systems using nonlinearly parametrized on line approximators the design of stable adaptive neural controllers for uncertain nonlinear dynamical systems with unknown nonlinearities is considered the lyapunov synthesis approach is used to develop state feedback adaptive control schemes based on a general class of nonlinearly parametrized on line approximation models the key assumptions are that the system uncertainty satisfies a strict feedback condition and that the network reconstruction error and higher order terms of the on line approximator with respect to the network weights satisfy certain bounding conditions an adaptive bounding design is used to show that the overall neural control system guarantees semi global uniform ultimate boundedness within a neighbourhood of zero tracking error the theoretical results are illustrated through a simulation example

a survey of the maximum principles for optimal control problems with state constraints this paper gives a survey of the various forms of pontryagin s maximum principle for optimal control problems with state variable inequality constraints the relations between the different sets of optimality conditions arising in these forms are shown furthermore the application of these maximum principle conditions is demonstrated by solving some illustrative examples

robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors this paper describes the design of the robust adaptive fuzzy controller for uncertain single input single output nonlinear dynamical systems with unknown nonlinearities these unknown nonlinearities are approximated by the fuzzy system with a set of fuzzy if then rules whose parameters are adjusted on line according to some adaptive laws for the purpose of controlling the output of the nonlinear system to track a given trajectory the lyapunov synthesis approach is used to develop a state feedback adaptive control algorithm based on the adaptive fuzzy model the key assumption is that the reconstruction errors satisfy certain bounding conditions the control law consists of two terms one is the certainty equivalent control and the other is the bounding control a bounding parameter adaptive law is used to obtain this bounding control the overall control system guarantees that the tracking error converges in the small neighborhood of zero and that all signals involved are uniformly bounded it is also shown that in the special case the tracking error exponentially converges to zero even though the approximation errors exist

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

adaptive parameter estimator based on t s fuzzy models and its applications to indirect adaptive fuzzy control design in this paper a new on line parameter estimation methodology for the general continuous time takagi sugeno t s fuzzy model whose parameters are poorly known or uncertain is presented an estimator with an appropriate adaptive law for updating the parameters is designed and analyzed based on the lyapunov theory the adaptive law is designed so that the estimation model follows the parameterized plant model by the proposed estimator the parameters of the t s fuzzy model can be estimated by observing the behavior of the system and it can be a basis for indirect adaptive fuzzy control in order to show the applicability of the proposed estimator indirect adaptive fuzzy control design examples with the proposed estimator are presented

robust stabilizability for a class of transfer functions this paper is concerned with the robust stabilizability for single input single output plants robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency dependent uncertainty band function around the transfer function of a nominal model a necessary and sufficient condition for robust stabilizability is derived based on the well known nevanlinna pick theory in classical analysis it is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model in order for the class to be robustly stabilizable a procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown

flexible stability criteria for a linguistic fuzzy dynamic system abstract this paper considers the stability problems of continuous and discrete type fuzzy control systems respectively on the basis of matrix measures and matrix norms several stability criteria for the systems are proposed some of these criteria are flexible with different chosen parameter p that means the trade off between the conservativeness and the computing convenience of the criteria depends on the chosen value of p totally

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

output feedback control of uncertain nonlinear systems using a self structuring adaptive fuzzy observer this paper describes the design of an output feedback controller based on an adaptive fuzzy observer for uncertain single input single output nonlinear dynamical systems we have focused on the realization of a minimal dynamic order for the adaptive fuzzy observer for this purpose we adopt an adaptive fuzzy observer in which no strictly positive real spr condition is needed and we combine a self structuring scheme with an on line estimation of fuzzy parameters by using this proposed scheme we can reduce the dynamic order of the adaptive output feedback fuzzy control system the lyapunov synthesis approach is used to guarantee a global uniform ultimate boundedness property of the state estimation error and tracking error as well as all other signals in the closed loop system no a priori knowledge of an upper limits on the uncertainties including optimal parameters and modeling errors is required the theoretical results are illustrated through simulation examples

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

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

structure identification of fuzzy model abstract the problems of structure identification of a fuzzy model are formulated a criterion for the verification of a structure is discussed using the criterion an algorithm for identifying a structure is suggested further a successive identification algorithm of the parameters is suggested the proposed methods are applied to an example

adaptive control for a class of nonlinear systems with a time varying structure we present a direct adaptive control method for a class of uncertain nonlinear systems with a time varying structure we view the nonlinear systems as composed of a finite number of pieces which are interpolated by functions that depend on a possibly exogenous scheduling variable we assume that each piece is in strict feedback form and show that the method yields stability of all signals in the closed loop as well as convergence of the state vector to a residual set around the equilibrium whose size can be set by the choice of several design parameters the class of systems considered is a generalization of the class of strict feedback systems traditionally considered in the backstepping literature we also provide design guidelines based on l sub 2 bounds on the transient

approaches to quadratic stability conditions and h sub spl infin control designs for t s fuzzy systems in this paper the problems of quadratic stability conditions and h sub spl infin control designs for takagi sugeno t s fuzzy systems have been studied first a new quadratic stability condition which is more simple than that in a previous paper has been proposed second two new sufficient conditions in the terms of linear matrix inequalities lmis which guarantee the existence of the state feedback h sub spl infin control for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally based on the lmis the h sub spl infin controller designing methods for the t s fuzzy systems have been given

adaptive neural control for a class of nonlinearly parametric time delay systems in this paper an adaptive neural controller for a class of time delay nonlinear systems with unknown nonlinearities is proposed based on a wavelet neural network wnn online approximation model a state feedback adaptive controller is obtained by constructing a novel integral type lyapunov krasovskii functional which also efficiently overcomes the controller singularity problem it is shown that the proposed method guarantees the semiglobal boundedness of all signals in the adaptive closed loop systems an example is provided to illustrate the application of the approach

stable and optimal adaptive fuzzy control of complex systems using fuzzy dynamic model a design method is presented for the stabilization of multivariable complex nonlinear systems which can be represented by fuzzy dynamic model firstly an adaptive fuzzy control law is addressed then the closed loop fuzzy system is robustly stabilized under some bounded perturbations and disturbances by adding a supervising controller based on the variable structure control theory of uncertain systems a sufficient condition for the stability of the closed loop fuzzy system is also derived using the concept of connective stability in decentralized control of large scale systems under this condition an optimal fuzzy controller is designed with genetic algorithms two examples are given to illustrate the application of the method

stability analysis and design of takagi sugeno fuzzy systems this work presents stable composite control criteria for multivariable takagi sugeno t s fuzzy systems on the basis of the linear matrix inequality lmi control strategy and parametric optimization the composite fuzzy control algorithms are derived unlike earlier studies of fuzzy control systems on an lmi framework this investigation develops a supervisory control approach such that a fuzzy controller can be synthesized more efficiently moreover a robust control scheme is applied to the t s fuzzy model with parametric uncertainties the sufficient conditions are deduced in the form of reduced lmis and adaptive tuning rules finally numeric simulations are given to validate the proposed approach

a new neuro fds definition for indirect adaptive control of unknown nonlinear systems using a method of parameter hopping the indirect adaptive regulation of unknown nonlinear dynamical systems is considered in this paper the method is based on a new neuro fuzzy dynamical system neuro fds definition which uses the concept of adaptive fuzzy systems afss operating in conjunction with high order neural network functions fhonnfs since the plant is considered unknown we first propose its approximation by a special form of an fds and then the fuzzy rules are approximated by appropriate honnfs thus the identification scheme leads up to a recurrent high order neural network rhonn which however takes into account the fuzzy output partitions of the initial fds the proposed scheme does not require a priori experts information on the number and type of input variable membership functions making it less vulnerable to initial design assumptions once the system is identified around an operation point it is regulated to zero adaptively weight updating laws for the involved honnfs are provided which guarantee that both the identification error and the system states reach zero exponentially fast while keeping all signals in the closed loop bounded the existence of the control signal is always assured by introducing a novel method of parameter hopping which is incorporated in the weight updating law simulations illustrate the potency of the method and comparisons with conventional approaches on benchmarking systems are given also the applicability of the method is tested on a direct current dc motor system where it is shown that by following the proposed procedure one can obtain asymptotic regulation

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

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

lmi based design of stabilizing fuzzy controllers for nonlinear systems described by takagi sugeno fuzzy model abstract there have been several recent studies concerning the stability of fuzzy control systems and the synthesis of stabilizing fuzzy controllers this paper reports on a related study of the takagi sugeno ts fuzzy systems and it is shown that the controller synthesis problems for the nonlinear systems described by the ts fuzzy model can be reduced to convex problems involving linear matrix inequalities lmis after classifying the ts fuzzy systems into three families based on how diverse their input matrices are a unique controller synthesis procedure is given for each of the families a numerical example is presented to illustrate the synthesis procedures developed in this paper

nn based adaptive tracking control of uncertain nonlinear systems disturbed by unknown covariance noise a class of uncertain nonlinear systems that are additionally driven by unknown covariance noise is considered based on the backstepping technique adaptive neural control schemes are developed to solve the output tracking control problem of such systems as it is proven by stability analysis the proposed controller guarantees that all the error variables are bounded with desired probability in a compact set while the tracking error is mean square semiglobally uniformly ultimately bounded m sguub the tracking performance and the effectiveness of the proposed design are evaluated by simulation results

sampled data adaptive nn tracking control of uncertain nonlinear systems in this paper for a class of single input single output siso uncertain nonlinear systems adaptive neural tracking controllers designed for digital computer implementation are proposed the overall scheme can be considered as a sampled data adaptive neural control system as an intermediate result it is proven that for a sufficiently small sampling period the emulated adaptive neural controller i e the discrete implementation of the continuous time adaptive neural network controller ensures semiglobal uniformly ultimate boundedness of the closed loop system then based on the exact discrete time model a controller redesign is proposed that performs efficiently for sampling periods for which the emulation controller fails the redesigned controller consists of two terms the emulated control law and an extra robustness term designed to increase the order of the perturbation with respect to the sampling period in the lyapunov difference in all cases high order neural networks are employed to approximate the unknown nonlinearities using lyapunov techniques it is proven that for a sufficiently small sampling period the proposed redesigned controller ensures the semiglobal boundedness of all the signals in the closed loop while the output of the system converges to a small neighborhood of the desired trajectory simulation results illustrate the superiority of the proposed scheme with respect to the emulation controller and verify the theoretical analysis

locally weighted online approximation based control for nonaffine systems this paper is concerned with tracking control problems for nonlinear systems that are not affine in the control signal and that contain unknown nonlinearities in the system dynamic equations this paper develops a piecewise linear approximation to the unknown functions during the system operation new control and parameter adaptation algorithms are designed and analyzed using lyapunov like methods the objectives are to achieve semiglobal stability of the state accurate tracking of bounded reference signals contained within a known domain and at least boundedness of the function approximator parameter estimates numerical simulations are included to illustrate the effectiveness of the learning algorithm

adaptive tracking control for stochastic uncertain non linear systems satisfying short and long term cost criteria the tracking control problem for a class of stochastic and uncertain non linear systems is addressed the proposed controller uses suitable radial basis function neural network designs for the approximation of the unknown non linearities while it is arbitrarily regulated in order to effectively penalize the tracking error this regulation is implemented through a risk sensitivity parameter a stability analysis based on lyapunov functions obtained by the backstepping technique proves that all the error variables are bounded in probability simultaneously for any given risk sensitivity parameter the system performance is regulated with respect to both a desired small average tracking error and low long term average cost in accordance to a risk sensitive cost criterion moreover the larger this parameter is the mean square tracking error becomes semiglobally uniformly ultimately bounded in a smaller area while a lower level of a long term average cost is achieved the effectiveness of the design approac

takagi sugeno fuzzy model based indirect adaptive fuzzy observer and controller design this paper proposes the design scheme of the alternative adaptive observer and controller based on the takagi sugeno t s fuzzy model the t s fuzzy modeling and the state feedback control technique are adopted for the simple structure the proposed method maintains consistent performance in the presence of parameter uncertainties and incorporates linguistic fuzzy information from human operators in addition with the simple adaptive state feedback controller it solves the singularity problem which occurs in the inverse dynamics based on the feedback linearization method using lyapunov theory and lipschitz condition the stability analysis is conducted and the adaptive law is derived the proposed method is applied to the stabilization problem of a flexible joint manipulator in order to guarantee its performance

globally stable adaptive backstepping neural network control for uncertain strict feedback systems with tracking accuracy known a priori this paper addresses the problem of globally stable direct adaptive backstepping neural network nn tracking control design for a class of uncertain strict feedback systems under the assumption that the accuracy of the ultimate tracking error is given a priori in contrast to the classical adaptive backstepping nn control schemes this paper analyzes the convergence of the tracking error using barbalat s lemma via some nonnegative functions rather than the positive definite lyapunov functions thus the accuracy of the ultimate tracking error can be determined and adjusted accurately a priori and the closed loop system is guaranteed to be globally uniformly ultimately bounded the main technical novelty is to construct three new n th order continuously differentiable functions which are used to design the control law the virtual control variables and the adaptive laws finally two simulation examples are given to illustrate the effectiveness and advantages of the proposed control method

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

distributed consensus tracking for multiple uncertain nonlinear strict feedback systems under a directed graph in this brief we study the distributed consensus tracking control problem for multiple strict feedback systems with unknown nonlinearities under a directed graph topology it is assumed that the leader s output is time varying and has been accessed by only a small fraction of followers in a group the distributed dynamic surface design approach is proposed to design local consensus controllers in order to guarantee the consensus tracking between the followers and the leader the function approximation technique using neural networks is employed to compensate unknown nonlinear terms induced from the controller design procedure from the lyapunov stability theorem it is shown that the consensus errors are cooperatively semiglobally uniformly ultimately bounded and converge to an adjustable neighborhood of the origin

stabilization of uncertain dynamic systems including state delay the authors consider a class of time varying systems with time varying state delay and uncertain input and parameters they present sufficient conditions on the open loop to obtain an arbitrary degree closed loop stability they construct a min max controller from knowledge of the upper bound of the delay

a global exponential fuzzy observer design for time delay takagi sugeno uncertain discrete fuzzy bilinear systems with disturbance a robust h fuzzy observer is proposed for a class of time delay takagi sugeno t s uncertain discrete fuzzy bilinear systems with disturbance utilizing the lipschitz conditions and some variable transformations a linear matrix inequality lmi approach is developed and a sufficient condition is obtained to design the robust h fuzzy observer the robust h fuzzy observer for time delay t s uncertain discrete fuzzy bilinear systems with disturbance can be obtained directly through the lmis with no preassigned matrices the convergent rate of the error state can be estimated from the initial conditions and the delay time of t s uncertain discrete fuzzy bilinear systems the designed robust h fuzzy observer can guarantee the dynamics of the observer error to be globally exponentially stable and has a prescribed h performance a numerical example is given to demonstrate the feasibility and effectiveness of the proposed observer design method

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

dynamic optimization problems with free time and active state constraints free time dynamic optimization problems are treated with state constraints in which the data is permitted to be measurable with respect to the time variable necessary conditions for such problems have previously been derived only under the assumption that the state constraint is inactive at the optimal endtimes a more detailed analysis than has yet been undertaken of the interaction between the optimal free endtimes and the state constraint permits the removal of this assumption an example clarifies the nature of the new necessary condition

adaptive control for output feedback nonlinear systems in the presence of modeling errors the paper is extending output feedback nonlinear control and backstepping approaches to a class of systems approximately diffeomorphic to output feedback systems that include unknown functions the unknown functions are addressed via online function approximation which results in two types of uncertainty parametric uncertainty due to online function approximation and non parametric uncertainty the non parametric uncertainty results from the inability of any function approximator to perfectly model an unknown function and from terms unmodeled by the output feedback form the non parametric terms are assumed to be bounded by unknown constants the backstepping procedure is applied to adapt with respect to both parametric uncertainties and the upper bound on the non parametric uncertainties

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

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

adaptive fuzzy tracking control of nonlinear time delay systems with unknown virtual control coefficients in this paper a novel adaptive fuzzy control scheme is proposed for a class of uncertain single input and single output siso nonlinear time delay systems with the lower triangular form fuzzy logic systems are used to approximate unknown nonlinear functions then the adaptive fuzzy tracking controller is constructed by combining lyapunov krasovskii functionals and the backstepping approach the proposed controller guarantees uniform ultimate boundedness of all the signals in the closed loop system while the tracking error converges to a small neighborhood of the origin an advantage of the proposed control scheme lies in that the number of adaptive parameters is not more than the order of the systems under consideration finally simulation studies are given to demonstrate the effectiveness of the proposed design scheme

learning from neural control of nonlinear systems in normal form a deterministic learning theory was recently proposed which states that an appropriately designed adaptive neural controller can learn the system internal dynamics while attempting to control a class of simple nonlinear systems in this paper we investigate deterministic learning from adaptive neural control anc of a class of nonlinear systems in normal form with unknown affine terms the existence of the unknown affine terms makes it difficult to achieve learning by using previous methods to overcome the difficulties firstly an extension of a recent result is presented on stability analysis of linear time varying ltv systems then with a state transformation the closed loop control system is transformed into a ltv form for which exponential stability can be guaranteed when a partial persistent excitation pe condition is satisfied accurate approximation of the closed loop control system dynamics is achieved in a local region along a recurrent orbit of closed loop signals consequently learning of control system dynamics i e closed loop identification from adaptive neural control of nonlinear systems with unknown affine terms is implemented

distributed adaptive containment control of uncertain nonlinear multi agent systems in strict feedback form abstract this paper presents a distributed containment control approach for uncertain nonlinear strict feedback systems with multiple dynamic leaders under a directed graph topology where the leaders are neighbors of only a subset of the followers the strict feedback followers with nonparametric uncertainties are considered and the local adaptive dynamic surface controller for each follower is designed using only neighbors information to guarantee that all followers converge to the dynamic convex hull spanned by the dynamic leaders where the derivatives of leader signals are not available to implement controllers i e the position information of leaders is only required the function approximation technique using neural networks is employed to estimate nonlinear uncertainty terms derived from the controller design procedure for the followers it is shown that the containment control errors converge to an adjustable neighborhood of the origin

hybrid learning mechanism for interval a2 c1 type 2 non singleton type 2 takagi sugeno kang fuzzy logic systems a proposed learning methodology based on a hybrid mechanism for training interval a2 c1 type 2 non singleton type 2 takagi sugeno kang fuzzy logic systems uses a recursive square root filter to tune the type 1 consequent parameters and the steepest descent method to tune the interval type 2 antecedent parameters the proposed hybrid learning algorithm changes the interval type 2 model parameters adaptively to minimize some criterion function as new information becomes available and to match desired input output data pairs its antecedent sets are type 2 fuzzy sets its consequent sets are type 1 fuzzy sets and its inputs are interval type 2 non singleton fuzzy numbers with uncertain standard deviations as reported in the literature the performance indices of hybrid models have proved to be better than those of the individual training mechanisms used alone comparison with non hybrid interval a2 c1 type 2 takagi sugeno kang fuzzy logic systems and with non hybrid a1 c0 type 1 takagi sugeno kang fuzzy logic systems shows that the proposed hybrid mechanism is a well performing non linear adaptive method that enables the interval type 2 fuzzy model to match an unknown non linear mapping and to converge very fast experiments were carried out involving the application of the hybrid interval a2 c1 type 2 non singleton type 2 takagi sugeno kang fuzzy logic systems for modeling and prediction of the scale breaker entry temperature in a hot strip mill for three different types of coils the results demonstrate how the interval type 2 fuzzy system learns from selected input output data pairs and improves its performance as hybrid training progresses

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

adaptive fuzzy tracking control for a class of perturbed strict feedback nonlinear time delay systems this paper is concerned with the problem of adaptive fuzzy output tracking for a class of perturbed strict feedback nonlinear systems with time delays and unknown virtual control coefficients fuzzy logic systems in mamdani type are used to approximate the unknown nonlinear functions then the adaptive fuzzy tracking controller is designed by using the backstepping technique and lyapunov krasovskii functionals the proposed adaptive fuzzy controller guarantees that all the signals in the closed loop system are bounded and the system output eventually converges to a small neighborhood of the desired reference signal an advantage of the proposed control scheme lies in that the number of the online adaptive parameters is not more than the order of the original system finally two examples are used to demonstrate the effectiveness of our results proposed in this paper

direct adaptive self structuring fuzzy controller for nonaffine nonlinear system a direct adaptive state feedback controller for highly nonlinear systems is proposed this paper considers uncertain or ill defined nonaffine nonlinear systems and employ a static fuzzy logic system fls with an on line structuring algorithm the fls approximates and adaptively cancels an unknown plant nonlinearity a control law and adaptive laws for unknown fuzzy parameters and bounding constant are established so that the whole closed loop system is stable in the sense of lyapunov the tracking error is guaranteed to be uniformly asymptotically stable rather than uniformly ultimately bounded with the aid of an additional robustifying control term no a priori knowledge of an upper bound on an lumped uncertainty is required

local analysis of continuous time takagi sugeno fuzzy system with disturbances bounded by magnitude or energy a lagrange multiplier method abstract this paper is concerned with the problem of computing the bounds of disturbances for continuous time takagi sugeno fuzzy model two kinds of disturbances are investigated by applying the non parallel distributed compensation non pdc law non quadratic lyapunov function and lagrange multiplier method one is bounded by magnitude the other is bounded by energy if the exogenous disturbances are bounded by magnitude the maximal value of the magnitude under which the closed loop system can be controlled is obtained by solving an optimization problem on the other hand if the disturbances are bounded by energy except for the maximal bound some conditions are derived to get two local regions a smaller and a bigger such that all the trajectories starting from the smaller region will remain in the bigger one which is required to be contained in a specific compact set where the original system can be represented as t s model exactly in the end the effectiveness of the proposed results is demonstrated by two examples

adaptive neural control for strict feedback nonlinear systems without backstepping in this brief a new adaptive neurocontrol algorithm for a single input single output siso strict feedback nonlinear system is proposed most of the previous adaptive neural control algorithms for strict feedback nonlinear systems were based on the backstepping scheme which makes the control law and stability analysis very complicated the main contribution of the proposed method is that it demonstrates that the state feedback control of the strict feedback system can be viewed as the output feedback control problem of the system in the normal form as a result the proposed control algorithm is considerably simpler than the previous ones based on backstepping depending heavily on the universal approximation property of the neural network nn only one nn is employed to approximate the lumped uncertain system nonlinearity the lyapunov stability of the nn weights and filtered tracking error is guaranteed in the semiglobal sense

optimal l2 approximation with fixed poles a simplified version of the optimal l 2 approximation of stable transfer function matrices is considered where the poles of the approximant are fixed the optimality condition is represented as an interpolation condition which is further reduced to a linear equation with a positive definite coefficient matrix some distinctive characteristics of the optimal approximation are derived a simple and explicit representation for the minimum approximation error is given as a function of poles