output feedback nn control for two classes of discrete time systems with unknown control directions in a unified approach in this paper output feedback adaptive neural network nn controls are investigated for two classes of nonlinear discrete time systems with unknown control directions 1 nonlinear pure feedback systems and 2 nonlinear autoregressive moving average with exogenous inputs narmax systems to overcome the noncausal problem which has been known to be a major obstacle in the discrete time control design both systems are transformed to a predictor for output feedback control design implicit function theorem is used to overcome the difficulty of the nonaffine appearance of the control input the problem of lacking a priori knowledge on the control directions is solved by using discrete nussbaum gain the high order neural network honn is employed to approximate the unknown control the closed loop system achieves semiglobal uniformly ultimately bounded sguub stability and the output tracking error is made within a neighborhood around zero simulation results are presented to demonstrate the effectiveness of the proposed control

universal neural network control of mimo uncertain nonlinear systems in this brief a continuous tracking control law is proposed for a class of high order multi input multi output uncertain nonlinear dynamic systems with external disturbance and unknown varying control direction matrix the proposed controller consists of high gain feedback nussbaum gain matrix selector online approximator ola model and a robust term the ola model is represented by a two layer neural network the continuousness of the control signal is guaranteed to relax the requirement for the actuator bandwidth and avoid the incurred chattering effect asymptotic tracking performance is achieved theoretically by standard lyapunov analysis the control feasibility is also verified in simulation environment

brief paper adaptive optimal control for continuous time linear systems based on policy iteration in this paper we propose a new scheme based on adaptive critics for finding online the state feedback infinite horizon optimal control solution of linear continuous time systems using only partial knowledge regarding the system dynamics in other words the algorithm solves online an algebraic riccati equation without knowing the internal dynamics model of the system being based on a policy iteration technique the algorithm alternates between the policy evaluation and policy update steps until an update of the control policy will no longer improve the system performance the result is a direct adaptive control algorithm which converges to the optimal control solution without using an explicit a priori obtained model of the system internal dynamics the effectiveness of the algorithm is shown while finding the optimal load frequency controller for a power system

universal approximation using radial basis function networks there have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables some of these studies deal with cases in which the hidden layer nonlinearity is not a sigmoid this was motivated by successful applications of feedforward networks with nonsigmoidal hidden layer units this paper reports on a related study of radial basis function rbf networks and it is proved that rbf networks having one hidden layer are capable of universal approximation here the emphasis is on the case of typical rbf networks and the results show that a certain class of rbf networks with the same smoothing factor in each kernel node is broad enough for universal approximation

recurrent neural network based multivariable adaptive control for a class of nonlinear dynamic systems with time varying delay at the beginning an approximate nonlinear autoregressive moving average narma model is employed to represent a class of multivariable nonlinear dynamic systems with time varying delay it is known that the disadvantages of robust control for the narma model are as follows 1 suitable control parameters for larger time delay are more sensitive to achieving desirable performance 2 it only deals with bounded uncertainty and 3 the nominal narma model must be learned in advance due to the dynamic feature of the narma model a recurrent neural network rnn is online applied to learn it however the system performance becomes deteriorated due to the poor learning of the larger variation of system vector functions in this situation a simple network is employed to compensate the upper bound of the residue caused by the linear parameterization of the approximation error of rnn an e modification learning law with a projection for weight matrix is applied to guarantee its boundedness without persistent excitation under suitable conditions the semiglobally ultimately bounded tracking with the boundedness of estimated weight matrix is obtained by the proposed rnn based multivariable adaptive control finally simulations are presented to verify the effectiveness and robustness of the proposed control

practical adaptive fuzzy tracking control for a class of perturbed nonlinear systems with backlash nonlinearity abstract this paper addresses the adaptive fuzzy tracking control problem for a class of perturbed nonlinear systems with backlash nonlinearity in the proposed control scheme fuzzy logic systems are used to approximate the unknown nonlinearity in each backstepping design and the classic adaptive technique is employed to deal with some unknown parameters the proposed fuzzy controller is developed by introducing some non negative switching functions and novel parameter adaptation learning laws are designed using the modification method it is emphasized that with the help of novel parameter adaptation laws the high gain phenomenon in the previous work can be avoided in addition by borrowing the property of the introduced non negative functions and the inequality technique an adaptive technique is employed to estimate the norm of the ideal weight vector such that the number of adaptation learning parameters online is reduced by employing barbalat s lemma it can be proved that all the signals in the closed loop system remain semi globally uniformly ultimately bounded and especially that the tracking error converges to an accuracy predefined a priori two simulation examples are provided to verify the effectiveness of the proposed control scheme

nearly optimal control laws for nonlinear systems with saturating actuators using a neural network hjb approach the hamilton jacobi bellman hjb equation corresponding to constrained control is formulated using a suitable nonquadratic functional it is shown that the constrained optimal control law has the largest region of asymptotic stability ras the value function of this hjb equation is solved for by solving for a sequence of cost functions satisfying a sequence of lyapunov equations le a neural network is used to approximate the cost function associated with each le using the method of least squares on a well defined region of attraction of an initial stabilizing controller as the order of the neural network is increased the least squares solution of the hjb equation converges uniformly to the exact solution of the inherently nonlinear hjb equation associated with the saturating control inputs the result is a nearly optimal constrained state feedback controller that has been tuned a priori off line

on nash approximation of complex analytic sets in runge domains abstract we prove that every complex analytic set x in a runge domain can be approximated by nash sets on any relatively compact subdomain 0 of moreover for every nash subset y of with y x the approximating sets can be chosen so that they contain y 0 as a consequence we derive a necessary and sufficient condition for a complex analytic set x to admit a nash approximation which coincides with x along its arbitrary given subset

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

multi step heuristic dynamic programming for optimal control of nonlinear discrete time systems abstract policy iteration and value iteration are two main iterative adaptive dynamic programming frameworks for solving optimal control problems policy iteration converges fast while requiring an initial stabilizing control policy which is a strict constraint in practice value iteration avoids the requirement of initial admissible control policy while converging much slowly this paper tries to utilize the advantages of policy iteration and value iteration and avoids their drawbacks at the same time therefore a multi step heuristic dynamic programming mshdp method is developed for solving the optimal control problem of nonlinear discrete time systems mshdp speeds up value iteration and avoids the requirement of initial admissible control policy in policy iteration at the same time the convergence theory of mshdp is established by proving that it converges to the solution of the bellman equation for implementation purpose the actor critic neural network nn structure is developed the critic nn is employed to estimate the value function and its nn weight vector is computed with a least square scheme the actor nn is used to estimate the control policy and a gradient descent method is proposed for updating its nn weight vector according to the comparative simulation studies on two examples the effectiveness and advantages of mshdp are verified

adaptive dynamic programming for finite horizon optimal control of discrete time nonlinear systems with varepsilon error bound in this paper we study the finite horizon optimal control problem for discrete time nonlinear systems using the adaptive dynamic programming adp approach the idea is to use an iterative adp algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an error bound the optimal number of control steps can also be obtained by the proposed adp algorithms a convergence analysis of the proposed adp algorithms in terms of performance index function and control policy is made in order to facilitate the implementation of the iterative adp algorithms neural networks are used for approximating the performance index function computing the optimal control policy and modeling the nonlinear system finally two simulation examples are employed to illustrate the applicability of the proposed method

online adaptive optimal control for continuous time nonlinear systems with completely unknown dynamics an online adaptive optimal control is proposed for continuous time nonlinear systems with completely unknown dynamics which is achieved by developing a novel identifier critic based approximate dynamic programming algorithm with a dual neural network nn approximation structure first an adaptive nn identifier is designed to obviate the requirement of complete knowledge of system dynamics and a critic nn is employed to approximate the optimal value function then the optimal control law is computed based on the information from the identifier nn and the critic nn so that the actor nn is not needed in particular a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier nn and critic nn simultaneously which converge to small neighbourhoods around their ideal values the closed loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the lyapunov theory the proposed ada

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

fuzzy tracking adaptive control of discrete time switched nonlinear systems this paper is concerned with the problem of fuzzy tracking adaptive control for a class of discrete time switched uncertain nonlinear systems with arbitrary switching based on the common lyapunov function method and by utilizing the fuzzy logic systems to approximate the unknown nonlinear functions an adaptive fuzzy controller is firstly constructed for a class of uncertain nonlinear discrete time switched systems meanwhile the proposed adaptive control algorithm reduces the amount of online adjustable parameters based on the above techniques the constructed fuzzy controllers and the adaptive law can guarantee that all the signals are bounded and the system output can converge to a small neighborhood of the reference signal in the closed loop system an illustrative example is provided to demonstrate the effectiveness of the proposed approaches

neural network observer based optimal control for unknown nonlinear systems using adaptive dynamic programming in this paper an observer based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming adp algorithm first a neural network nn observer is designed to estimate system states then based on the observed states a neuro controller is constructed via adp method to obtain the optimal control in this design two nn structures are used a three layer nn is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics and a critic nn is employed to approximate the value function the optimal control law is computed using the critic nn and the observer nn uniform ultimate boundedness of the closed loop system is guaranteed the actor critic and observer structures are all implemented in real time continuously and simultaneously finally simulation results are presented to demonstrate the effectiveness of the proposed control scheme

exact boundary controllability for 1 d quasilinear wave equations in this paper we present a unified constructive method to establish the local exact boundary controllability for 1 d quasilinear wave equations with boundary conditions of various types

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

reinforcement learning design based adaptive tracking control with less learning parameters for nonlinear discrete time mimo systems based on the neural network nn approximator an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output mimo nonlinear discrete time systems with unknown functions and disturbances in the design procedure two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function an optimal control signal and adaptation laws can be generated based on two nns in the previous approaches the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design consequently compared with the existing results the main contributions of this paper are 1 only two parameters are needed to be adjusted and thus the number of the adaptation laws is smaller than the previous results and 2 the updating parameters do not depend on the number of the subsystems for mimo systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks it is proven that the tracking errors the adaptation laws and the control inputs are uniformly bounded using lyapunov analysis method the simulation examples are employed to illustrate the effectiveness of the proposed algorithm

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

adaptive fuzzy control for synchronization of nonlinear teleoperators with stochastic time varying communication delays in this paper adaptive fuzzy control is investigated for nonlinear teleoperators with time delays which ensures synchronization of positions and velocities of the master and slave manipulators and does not rely on the use of the scattering transformation compared with the previous passivity framework the communication delays are assumed to be stochastic time varying by feedback linearization the nonlinear dynamics of the teleoperation system is transformed into two subsystems local master slave position control with unmodeled dynamics and delayed motion synchronization then based on linear matrix inequalities lmi and markov jump linear systems adaptive fuzzy control strategies are developed for the nonlinear teleoperators with modeling uncertainties and external disturbances by using the approximation property of the fuzzy logic systems it is proven that the master slave teleoperation system is stochastically stable in mean square under specific lmi conditions and all the signals of the resulting closed loop system are uniformly bounded finally the extensive simulations are performed to show the effectiveness of the proposed method

robust adaptive neural network control for a class of uncertain mimo nonlinear systems with input nonlinearities in this paper robust adaptive neural network nn control is investigated for a general class of uncertain multiple input multiple output mimo nonlinear systems with unknown control coefficient matrices and input nonlinearities for nonsymmetric input nonlinearities of saturation and deadzone variable structure control vsc in combination with backstepping and lyapunov synthesis is proposed for adaptive nn control design with guaranteed stability in the proposed adaptive nn control the usual assumption on nonsingularity of nn approximation for unknown control coefficient matrices and boundary assumption between nn approximation error and control input have been eliminated command filters are presented to implement physical constraints on the virtual control laws then the tedious analytic computations of time derivatives of virtual control laws are canceled it is proved that the proposed robust backstepping control is able to guarantee semiglobal uniform ultimate boundedness of all signals in the closed loop system finally simulation results are presented to illustrate the effectiveness of the proposed adaptive nn control

kernel based least squares policy iteration for reinforcement learning in this paper we present a kernel based least squares policy iteration klspi algorithm for reinforcement learning rl in large or continuous state spaces which can be used to realize adaptive feedback control of uncertain dynamic systems by using klspi near optimal control policies can be obtained without much a priori knowledge on dynamic models of control plants in klspi mercer kernels are used in the policy evaluation of a policy iteration process where a new kernel based least squares temporal difference algorithm called klstd q is proposed for efficient policy evaluation to keep the sparsity and improve the generalization ability of klstd q solutions a kernel sparsification procedure based on approximate linear dependency ald is performed compared to the previous works on approximate rl methods klspi makes two progresses to eliminate the main difficulties of existing results one is the better convergence and near optimality guarantee by using the klstd q algorithm for policy evaluation with high precision the other is the automatic feature selection using the ald based kernel sparsification therefore the klspi algorithm provides a general rl method with generalization performance and convergence guarantee for large scale markov decision problems mdps experimental results on a typical rl task for a stochastic chain problem demonstrate that klspi can consistently achieve better learning efficiency and policy quality than the previous least squares policy iteration lspi algorithm furthermore the klspi method was also evaluated on two nonlinear feedback control problems including a ship heading control problem and the swing up control of a double link underactuated pendulum called acrobot simulation results illustrate that the proposed method can optimize controller performance using little a priori information of uncertain dynamic systems it is also demonstrated that klspi can be applied to online learning control by incorporating an initial controller to ensure online performance

adaptive fuzzy control for a class of stochastic pure feedback nonlinear systems with unknown hysteresis this paper addresses the problem of adaptive fuzzy control for a class of stochastic pure feedback nonlinear systems with unknown direction hysteresis compared with the existing researches on hysteresis problem the stochastic disturbances and the unknown hysteresis are simultaneously considered in the pure feedback systems in addition the hysteresis parameters as well as the direction of hysteresis are unknown by introducing an auxiliary virtual controller and employing the new properties of nussbaum function the major technique difficulty arising from the unknown direction hysteresis is overcome based on the fuzzy logic system s online approximation capability a novel adaptive fuzzy control scheme is presented via the backstepping technique it is shown that the proposed control scheme guarantees that all the signals of the closed loop system are semiglobally uniformly bounded in probability and the tracking error converges to a neighborhood of the origin in the sense of mean quantic value finally simulation results further demonstrate the effectiveness of the proposed control scheme

model free optimal tracking control via critic only q learning model free control is an important and promising topic in control fields which has attracted extensive attention in the past few years in this paper we aim to solve the model free optimal tracking control problem of nonaffine nonlinear discrete time systems a critic only q learning coql method is developed which learns the optimal tracking control from real system data and thus avoids solving the tracking hamilton jacobi bellman equation first the q learning algorithm is proposed based on the augmented system and its convergence is established using only one neural network for approximating the q function the coql method is developed to implement the q learning algorithm furthermore the convergence of the coql method is proved with the consideration of neural network approximation error with the convergent q function obtained from the coql method the adaptive optimal tracking control is designed based on the gradient descent scheme finally the effectiveness of the developed coql method is demonstrated through simulation studies the developed coql method learns with off policy data and implements with a critic only structure thus it is easy to realize and overcome the inadequate exploration problem

discrete time neural net controller for a class of nonlinear dynamical systems a family of two layer discrete time neural net nn controllers is presented for the control of a class of mnth order mimo dynamical system no initial learning phase is needed so that the control action is immediate in other words the neural network nn controller exhibits a learning while functioning feature instead of a learning then control feature a two layer nn is used which is linear in the tunable weights the structure of the neural net controller is derived using a filtered error approach it is indicated that delta rule based tuning when employed for closed loop control can yield unbounded nn weights if 1 the net cannot exactly reconstruct a certain required function or 2 there are bounded unknown disturbances acting on the dynamical system certainty equivalence is not used overcoming a major problem in discrete time adaptive control in this paper new online tuning algorithms for discrete time systems are derived which are similar to spl epsiv modification for the case of continuous time systems that include a modification to the learning rate parameter and a correction term to the standard delta rule

neural network control based adaptive learning design for nonlinear systems with full state constraints in order to stabilize a class of uncertain nonlinear strict feedback systems with full state constraints an adaptive neural network control method is investigated in this paper the state constraints are frequently emerged in the real life plants and how to avoid the violation of state constraints is an important task by introducing a barrier lyapunov function blf to every step in a backstepping procedure a novel adaptive backstepping design is well developed to ensure that the full state constraints are not violated at the same time one remarkable feature is that the minimal learning parameters are employed in blf backstepping design by making use of lyapunov analysis we can prove that all the signals in the closed loop system are semiglobal uniformly ultimately bounded and the output is well driven to follow the desired output finally a simulation is given to verify the effectiveness of the method

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

adaptive output feedback fuzzy tracking control for a class of nonlinear systems this paper is concerned with the problem of adaptive fuzzy tracking control via output feedback for a class of uncertain single input single output siso strict feedback nonlinear systems the dynamic feedback strategy begins with an input driven filter by utilizing fuzzy logic systems to approximate unknown and desired control input signals directly instead of the unknown nonlinear functions an output feedback fuzzy tracking controller is designed via a backstepping approach it is shown that the proposed fuzzy adaptive output controller can guarantee that all the signals remain bounded and that the tracking error converges to a small neighborhood of the origin simulations results are presented to demonstrate the effectiveness of the proposed methods

trajectory priming with dynamic fuzzy networks in nonlinear optimal control fuzzy logic systems have been recognized as a robust and attractive alternative to some classical control methods the application of classical fuzzy logic fl technology to dynamic system control has been constrained by the nondynamic nature of popular fl architectures many difficulties include large rule bases i e curse of dimensionality long training times etc these problems can be overcome with a dynamic fuzzy network dfn a network with unconstrained connectivity and dynamic fuzzy processing units called feurons in this study dfn as an optimal control trajectory priming system is considered as a nonlinear optimization with dynamic equality constraints the overall algorithm operates as an autotrainer for dfn a self learning structure and generates optimal feed forward control trajectories in a significantly smaller number of iterations for this dfn encapsulates and generalizes the optimal control trajectories by the algorithm the time varying optimal feedback gains are also generated along the trajectory as byproducts this structure assists the speeding up of trajectory calculations for intelligent nonlinear optimal control for this purpose the direct descent curvature algorithm is used with some modifications called modified descend controller mdc algorithm for the nonlinear optimal control computations the algorithm has numerically generated robust solutions with respect to conjugate points the minimization of an integral quadratic cost functional subject to dynamic equality constraints which is dfn is considered for trajectory obtained by mdc tracking applications the adjoint theory whose computational complexity is significantly less than direct method has been used in the training of dfn which is as a quasilinear dynamic system the updating of weights identification of dfn parameters are based on broyden fletcher goldfarb shanno bfgs method simulation results are given for controlling a difficult nonlinear second order system using fully connected three feuron dfn

oka s principle for holomorphic sections of elliptic bundles 2 the h principle for locally trivial fibrations 2 1 the h principle over small subsets 2 2 the h principle over totally real submanifolds 2 3 local extension of the h principle 2 4 localizable extensions 2 5 the h principle for cm bundles 2 6 manifolds with totally real souls 2 7 totally real extensions 2 8 nicely localizable extensions 2 9 the basic h principle for z x 2 10 homomorphisms and holomorphic maps of rank r

adaptive neural output feedback tracking control for a class of uncertain discrete time nonlinear systems this brief studies an adaptive neural output feedback tracking control of uncertain nonlinear multi input multi output mimo systems in the discrete time form the considered mimo systems are composed of n subsystems with the couplings of inputs and states among subsystems in order to solve the noncausal problem and decouple the couplings it needs to transform the systems into a predictor form the higher order neural networks are utilized to approximate the desired controllers by using lyapunov analysis it is proven that all the signals in the closed loop system is the semi globally uniformly ultimately bounded and the output errors converge to a compact set in contrast to the existing results the advantage of the scheme is that the number of the adjustable parameters is highly reduced the effectiveness of the scheme is verified by a simulation example

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

discrete time l and l2 norm vanishment and low gain feedback with their applications in constrained control the existing low gain feedback which is a parameterized family of stabilizing state feedback gains whose magnitudes approach zero as the parameter decreases to zero has been designed in very specific ways in this paper by recognizing the l and l 2 slow peaking phenomenon that exists in discrete time systems under low gain feedback more general notions of l and l 2 norm vanishment are considered so as to provide a full characterization of the nonexistence of slow peaking phenomenon in some measured signals low gain feedback that does not lead to l and l 2 slow peaking in the control input are respectively referred to as l and l 2 low gain feedback based on the notions of l and l 2 vanishment not only can the existing low gain feedback be recognized as an l low gain feedback but also a new design approach referred to as the l 2 low gain feedback approach is developed for discrete time linear systems parallel to the effectiveness of l low gain feedback in magnitude constrained control the l 2 low gain feedback is instrumental in the control of discrete time systems with control energy constraints the notions of l and l 2 vanishment also result in a systematic approach to the design of l and l 2 low gain feedback by providing a family of solutions including those resulting from the existing design methods

data based robust adaptive control for a class of unknown nonlinear constrained input systems via integral reinforcement learning this paper presents a data based robust adaptive control methodology for a class of nonlinear constrained input systems with completely unknown dynamics by introducing a value function for the nominal system the robust control problem is transformed into a constrained optimal control problem due to the unavailability of system dynamics a data based integral reinforcement learning rl algorithm is developed to solve the constrained optimal control problem based on the present algorithm the value function and the control policy can be updated simultaneously using only system data the convergence of the developed algorithm is proved via an established equivalence relationship to implement the integral rl algorithm an actor neural network nn and a critic nn are separately utilized to approximate the control policy and the value function and the least squares method is employed to estimate the unknown parameters by using lyapunov s direct method the obtained approximate optimal control is verified to guarantee the unknown nonlinear system to be stable in the sense of uniform ultimate boundedness two examples are provided to demonstrate the effectiveness and applicability of the theoretical results

sufficient condition for the existence of the compact set in the rbf neural network control in this brief sufficient conditions are proposed for the existence of the compact sets in the neural network controls first we point out that the existence of the compact set in a classical neural network control scheme is unsolved and its result is incomplete next as a simple case we derive the sufficient condition of the existence of the compact set for the neural network control of first order systems finally we propose the sufficient condition of the existence of the compact set for the neural network based backstepping control of high order nonlinear systems the theoretic result is illustrated through a simulation example

policy iteration adaptive dynamic programming algorithm for discrete time nonlinear systems this paper is concerned with a new discrete time policy iteration adaptive dynamic programming adp method for solving the infinite horizon optimal control problem of nonlinear systems the idea is to use an iterative adp technique to obtain the iterative control law which optimizes the iterative performance index function the main contribution of this paper is to analyze the convergence and stability properties of policy iteration method for discrete time nonlinear systems for the first time it shows that the iterative performance index function is nonincreasingly convergent to the optimal solution of the hamilton jacobi bellman equation it is also proven that any of the iterative control laws can stabilize the nonlinear systems neural networks are used to approximate the performance index function and compute the optimal control law respectively for facilitating the implementation of the iterative adp algorithm where the convergence of the weight matrices is analyzed finally the numerical results and analysis are presented to illustrate the performance of the developed method

adaptive fuzzy robust tracking controller design via small gain approach and its application an adaptive fuzzy robust tracking control afrtc algorithm is proposed for a class of nonlinear systems with the uncertain system function and uncertain gain function which are all the unstructured or nonrepeatable state dependent unknown nonlinear functions arising from modeling errors and external disturbances the takagi sugeno type fuzzy logic systems are used to approximate unknown uncertain functions and the afrtc algorithm is designed by use of the input to state stability approach and small gain theorem the algorithm is highlighted by three advantages 1 the uniform ultimate boundedness of the closed loop adaptive systems in the presence of nonrepeatable uncertainties can be guaranteed 2 the possible controller singularity problem in some of the existing adaptive control schemes met with feedback linearization techniques can be removed and 3 the adaptive mechanism with minimal learning parameterizations can be obtained the performance and limitations of the proposed method are discussed the uses of the afrtc for the tracking control design of a pole balancing robot system and a ship autopilot system to maintain the ship on a predetermined heading are demonstrated through two numerical examples simulation results show the effectiveness of the control scheme