adaptive predefined performance control for mimo systems with unknown direction via generalized fuzzy hyperbolic model an adaptive predefined performance control problem is investigated for a class of multiple input multiple output systems with unknown control direction and unknown backlash like hysteresis nonlinearities by using generalized fuzzy hyperbolic model gfhm compared with the existing methods the main features are as follows the prediction error is introduced to construct the adaptive laws which means that the approximate accuracy of the gfhm is solved the nussbaum type gain is utilized to deal with the unknown control direction which avoids the requirement of direction a priori and by transforming the tracking errors into new error variables the prescribed steady state and transient performance can be ensured it is shown that the proposed control approach can guarantee that all the signals of the resulting closed loop systems are bounded and the output tracks a desired trajectory while the tracking errors are confined all times within the prescribed bounds finally two simulation results and some comparisons are provided to verify the effectiveness of the proposed approach since the proposed control strategy is only implemented in a healthy case how to extend the strategy to a faulty case will be a further topic

direct model reference takagi sugeno fuzzy control of siso nonlinear systems this study presents a novel direct model reference fuzzy controller it relaxes the special conditions on the reference model that is required by some of the approaches described in the literature as well as covering a more general class of takagi sugeno t s systems the stability of the proposed method is proved using a proper lyapunov function in addition the effects of modeling errors on the proposed controller are considered and a robust modification algorithm to alleviate this problem is introduced and analyzed the proposed method is then simulated on a flexible joint robot in a feedback linearization form and on chua s chaotic electrical circuit finally it is implemented and tested on a nonlinear dc motor with nonlinear state dependent disturbance

asymptotic fuzzy tracking control for a class of stochastic strict feedback systems this paper presents an asymptotic tracking control design method for stochastic strict feedback systems via fuzzy logic systems in the existing results stochastic controls are usually limited to be bounded in probability however how to realize the asymptotic tracking control for stochastic strict feedback systems remains a control dilemma this paper achieves the asymptotic tracking control by proposing a novel gain suppressing inequality approach specifically the three part construction is performed to achieve such control objective for stochastic systems first the novel gain suppressing inequality technique is developed to lay the foundation for carrying out the lyapunov stability analysis second the developed inequality technique is integrated with each step of the backstepping based adaptive control design procedure third analyses are provided to realize the asymptotic tracking control of stochastic strict feedback systems

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

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

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

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

time average control of martingale problems a linear programming formulation one studies the average cost for controlled systems given as solutions of the martingale problem for their generator the control problem is reformulated as a linear programming problem and conditions are given for the existence of an optimal solution it is further shown that the optimal control can be taken to depend only on the history of the system and that this cost remains optimal for systems with different initial distributions

lmi based stability analysis for fuzzy model based control systems using artificial t s fuzzy model this paper investigates the stability of fuzzy model based fmb control systems an alternative stability analysis approach using an artificial fuzzy system based on the lyapunov stability theory is proposed to facilitate the stability analysis the continuous membership functions of the takagi sugeno t s fuzzy model are represented by the staircase ones with the nice property of the staircase membership functions it turns the set of infinite number of linear matrix inequality lmi based stability conditions into a finite one furthermore the staircase membership functions carrying system information can be brought to the stability conditions to relax the stability conditions the stability of the original fmb control systems is guaranteed by the satisfaction of the lmi based stability conditions the proposed stability analysis is applied to the fmb control systems of which the t s fuzzy model and fuzzy controller do not share the same premise membership functions and thus is able to enhance the design flexibility of the fuzzy controller a simulation example is given to illustrate the merits of the proposed approach

model approximation for discrete time state delay systems in the t s fuzzy framework this paper is concerned with the problem of h model approximation for discrete time takagi sugeno t s fuzzy time delay systems for a given stable t s fuzzy system our attention is focused on the construction of a reduced order model which not only approximates the original system well in an h performance but is also translated into a linear lower dimensional system by applying the delay partitioning approach a delay dependent sufficient condition is proposed for the asymptotic stability with an h error performance for the error system then the h model approximation problem is solved by using the projection approach which casts the model approximation into a sequential minimization problem subject to linear matrix inequality lmi constraints by employing the cone complementary linearization algorithm moreover by further extending the results h model approximation with special structures is obtained i e delay free model and zero order model finally two numerical examples are provided to illustrate the effectiveness of the proposed methods

nonlinear optimal control via occupation measures and lmi relaxations we consider the class of nonlinear optimal control problems ocps with polynomial data i e the differential equation state and control constraints and cost are all described by polynomials and more generally for ocps with smooth data in addition state constraints as well as state and or action constraints are allowed we provide a simple hierarchy of lmi linear matrix inequality relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value under some convexity assumptions the sequence converges to the optimal value of the ocp preliminary results show that good approximations are obtained with few moments

a novel robust adaptive fuzzy tracking control for a class of nonlinearmulti input multi output systems robust adaptive fuzzy tracking control of a class of uncertain multi input multi output nonlinear systems with coupled interconnections is considered in this paper takagi sugeno t s fuzzy systems are used to approximate the unknown system functions a novel adaptive control scheme is developed on the basis of the so called dynamic surface control and minimal learning parameters techniques the proposed scheme has following two key features first the number of parameters updated online for each subsystem is reduced to one and both problems of curse of dimension for high dimensional systems and explosion of complexity inherent in the conventional backstepping methods are circumvented second the potential controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques is overcome it is shown via lyapunov theory that all the signals in the closed loop system are semiglobally uniformly ultimately bounded finally simulation results via two examples are presented to demonstrate the effectiveness and advantages of the proposed scheme

adaptive 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

on a representation of the limit occupational measures set of a control system with applications to singularly perturbed control systems a representation of the limit occupational measures set of a control system in terms of the vector function defining the system s dynamics is established applications in averaging of singularly perturbed control systems are demonstrated

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

fuzzy controller design for nonlinear impulsive fuzzy systems with time delay the stabilization problem is investigated for continuous time takagi sugeno t s fuzzy systems with time delay and impulsive effects in this paper some delay independent and delay dependent stabilization approaches are developed for both state feedback and observer based feedback cases which are based on the lyapunov krasovskii functional approach and a parallel distributed compensation scheme the time delay is dealt by lyapunov theory allied with the halanay lemma the restriction on the interval between each impulsive instant and output sampled instant needs not be equal to or less than a constant scalar but it only requires an inequality satisfaction when the impulsive effects vanish the results can be extended to the corresponding sufficient conditions for the cases of a nonlinear continuous time delay system with a state feedback and observer based sampled output feedback finally some examples are given to demonstrate the effectiveness of the proposed method

occupation measures for controlled markov processes characterization and optimality for controlled markov processes taking values in a polish space control problems with ergodic cost infinite horizon discounted cost and finite horizon cost are studied each is posed as a convex optimization problem wherein one tries to minimize a linear functional on a closed convex set of appropriately defined occupation measures for the problem these are characterized as solutions of a linear equation asssociated with the problem this characterization is used to establish the existence of optimal markov controls the dual convex optimization problem is also studied

h_ infty filter design for a class of networked control systems via t s fuzzy model approach this paper is concerned with h design for a class of networked control systems ncss with multiple state delays via the takagi sugeno t s fuzzy model the transfer delays and packet loss that are induced by the limited bandwidth of communication networks are considered the focus of this paper is on the analysis and design of a full order h filter such that the filtering error dynamics are stochastically stable and a prescribed h attenuation level is guaranteed sufficient conditions are established for the existence of the desired filter in terms of linear matrix inequalities lmis an example is given to illustrate the effectiveness and applicability of the proposed design method

fuzzy adaptive decentralized output feedback control for large scale nonlinear systems with dynamical uncertainties in this paper an adaptive fuzzy decentralized robust output feedback control approach is proposed for a class of large scale strict feedback nonlinear systems with the unmeasured states the large scale nonlinear systems in this paper are assumed to possess the unstructured uncertainties unmodeled dynamics and unknown high frequency gain sign fuzzy logic systems are used to approximate the unstructured uncertainties k filters are designed to estimate the unmeasured states and a dynamical signal and a special nussbaum gain function are introduced into the control design to solve the problem of unknown high frequency gain sign and dominate unmodeled uncertainties respectively based on the backstepping design and adaptive fuzzy control methods an adaptive fuzzy decentralized robust output feedback control scheme is developed it is proved that the proposed adaptive fuzzy control approach can guarantee that all the signals in the closed loop system are uniformly and ultimately bounded and the tracking errors converge to a small neighborhood of the origin the effectiveness of the proposed approach is illustrated by using simulation results

singular perturbations in infinite dimensional control systems in this paper we consider a singularly perturbed control system involving differential inclusions in banach spaces with slow and fast solutions using the averaging approach we obtain sufficient conditions for the hausdorff convergence of the set of slow solutions in the supremum norm we present applications of the theorem to prove convergence of the fast solutions in terms of invariant measures and convergence of equi lipschitz solutions

linear programming approach to deterministic long run average problems of optimal control we establish that deterministic long run average problems of optimal control are asymptotically equivalent to infinite dimensional linear programming problems lpps and we establish that these lpps can be approximated by finite dimensional lpps the solutions of which can be used for construction of the optimal controls general results are illustrated with numerical examples

noninteracting adaptive control of pmsm using interval type 2 fuzzy logic systems based on the type 2 fuzzy logic systems and adaptive control theory this paper develops a decentralized adaptive fuzzy controller for a permanent magnet synchronous motor pmsm the adaptive law is designed to compensate for the interconnection effects and the reconstruction errors using a sliding mode term the type 2 fuzzy logic systems are used to model the unknown functions based on lyapunov s stability theorem the stability of closed loop systems can be verified moreover the proposed overall control schemes guarantee that all the signals that are involved are bounded to demonstrate the effectiveness of the proposed methods simulation results are illustrated in this paper

time average control of martingale problems existence of a stationary solution one studies the average cost for controlled systems via the martingale problem for their generator the stationary distributions for these processes on the product of the state and control spaces are characterized in terms of integration of the generator and existence of a stationary solution is established the gives existence of a stationary control

decentralized adaptive neural control for high order stochastic nonlinear strongly interconnected systems with unknown system dynamics abstract this paper studies the problem of decentralized adaptive neural backstepping control for a class of high order stochastic nonlinear systems with unknown strongly interconnected nonlinearity during the control of the high order nonlinear interconnected systems only one adaptive parameter is used to overcome the over parameterization problem and radial basis function rbf neural networks are employed to tackle the difficulties brought about by completely unknown system dynamics and stochastic disturbances in addition to address the problem arising from high order strongly interconnected nonlinearities with full states of the overall system the variable separation technique is introduced based on the monotonically increasing property of the bounding functions next a decentralized adaptive neural control method is proposed based on lyapunov stability theory in which the controller is designed to decrease the number of learning parameters it is shown that the designed controller can ensure that all the signals in the closed loop system are 4 moment or 2 moment semi globally uniformly ultimately bounded sguub and the tracking error converges to a small neighborhood of the origin finally two simulation examples are offered to illustrate the effectiveness of the proposed control scheme

fuzzy wavelet neural network with an accelerated hybrid learning algorithm an accelerated hybrid learning algorithm is proposed for the training of fuzzy wavelet neural networks fwnns the algorithm gives the initial parameters by the clustering algorithm and then updates them with a combination of backpropagation and recursive least squares methods the parameters are updated in the direction of steepest descent but with a local adaptive learning rate that is different for each epoch and only depends on the sign of the gradient error function this adaptive learning rate is chosen such as to accelerate convergence the learning algorithm is inspired from the halving method to find polynomials roots even though the results are quite satisfactory the algorithm is much simpler than others that have been reported in addition it does includes no excessive terms in adapting formulation unlike much of the research in this area furthermore this algorithm somewhat increases accuracy while using far fewer parameters simulation results indicate a superior convergence speed in comparison with other training methods in fwnn

filippov s and filippov wazewski s theorems on closed domains abstract the celebrated filippov s theorem implies that given a trajectory x1 0 r n of a differential inclusion x f t x with the set valued map f measurable in t and k lipschitz in x for any initial condition x2 0 r n there exists a trajectory x2 starting from x2 0 such that x1 t x2 t ekt x1 0 x2 0 filippov wazewski s theorem establishes the possibility of approximating any trajectory of the convexified differential inclusion x co f t x by a trajectory of the original inclusion x f t x starting from the same initial condition in the present paper we extend both theorems to the case when the state variable x is constrained to the closure of an open subset r n the latter is allowed to be non smooth we impose a generalized soner type condition on f and yielding extensions of the above classical results to infinite horizon constrained problems applications to the study of regularity of value functions of optimal control problems with state constraints are discussed as well

sofmls online self organizing fuzzy modified least squares network in this paper an online self organizing fuzzy modified least square sofmls network is proposed the algorithm has the ability to reorganize the model and adapt itself to a changing environment where both the structure and learning parameters are performed simultaneously the network generates a new rule if the smallest distance between the new data and all the existing rules the winner rule is more than a prespecified radius the major contributions of this paper are as follows 1 a new network is proposed in which unidimensional membership functions are used and only two parameters for each rule are employed thus reducing the number of parameters the network avoids the singularity produced by the widths in the antecedent part for online learning 2 a new pruning algorithm based on the density is proposed where the density is the number of times each rule is used in the algorithm the rule that has the smallest density the looser rule in a selected number of iterations is pruned if the value of its density is smaller than a prespecified threshold and 3 the stability of the proposed algorithm is proven and the bound for the average of the identification error is found the condition that led the algorithm to avoid the local minimum is found and it is proven that the parameter error is bounded by the initial parameter error three simulations give the effectiveness of the suggested algorithm

computing the effective hamiltonian using a variational approach a numerical method for homogenization of hamilton jacobi equations is presented and implemented as an l infty calculus of variations problem solutions are found by solving a nonlinear convex optimization problem the numerical method is shown to be convergent and error estimates are provided one and two dimensional examples are worked in detail comparing known results with the numerical ones and computing new examples the cases of nonstrictly convex hamiltonians and hamiltonians for which the cell problem has no solution are treated

fuzzy approximation based adaptive control of nonlinear delayed systems with unknown dead zone this paper focuses on the problem of adaptive fuzzy control for a class of nonlinear systems without a strict feedback form a new adaptive fuzzy control scheme is proposed for nonlinear delayed systems with unknown dead zone nonlinearity control design is achieved by introducing a variable separation approach and employing the unique structural property of fuzzy logic systems the proposed adaptive fuzzy controller guarantees that all the closed loop signals are semiglobally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin two simulation examples illustrate the effectiveness of the proposed approach

approximation and regularization of lipschitz functions convergence of the gradients we examine the possible extensions to the lipschitzian setting of the classical result on c 1 convergence first approximation if a sequence f n of functions of class c 1 from r n to r converges uniformly to a function f of class c 1 then the gradient of f is a limit of gradients of f n in the sense that graph f c lim inf n graph f n second regularization the functions f n can be chosen to be of class c and c 1 converging to f in the sense that lim n f n f f n f 0 in other words the space of c functions is dense in the space of c 1 functions endowed with the c 1 pseudo norm we first deepen the properties of warga s counterexample 1981 for the extension of the approximation part to the lipschitzian setting this part cannot be extended even if one restricts the approximation schemes to the classical convolution and the lasry lions regularization we thus make more precise various results in the literature on the convergence of sub differentials we then show that the regularization part can be extended to the lipschitzian setting namely if f r n r is a locally lipschitz function we build a sequence of smooth functions f n n n such that 0 in other words the space of c functions is dense in the space of locally lipschitz functions endowed with an appropriate lipschitz pseudo distance up to now rockafellar and wets 1998 have shown that the convolution procedure permits us to have the equality lim sup n graph f n graph f which cannot provide the exactness of our result as a consequence we obtain a similar result on the regularization of epi lipschitz sets with both functional and set parts we improve previous results in the literature on the regularization of functions and sets

on sets of occupational measures generated by a deterministic control system on an infinite time horizon abstract we give a representation for the closed convex hull of the set of discounted occupational measures generated by control state trajectories of a deterministic control system we also investigate the limit behavior of the latter when the discount factor tends to zero and compare it with the limit behavior of the long run time average occupational measures set the novelty of our results is in that we allow the control set dependence on the state variables that make the results to be applicable to differential inclusions

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

adaptive fuzzy output feedback tracking backstepping control of strict feedback nonlinear systems with unknown dead zones in this paper an adaptive fuzzy backstepping control approach is considered for a class of nonlinear strict feedback systems with unknown functions unknown dead zones and immeasurable states fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy filters state observer is designed to estimate the immeasurable states by using the adaptive backstepping recursive design technique and constructing the dead zone inverse a new adaptive fuzzy backstepping output feedback control approach is developed it is mathematically proved that all the signals of the resulting closed loop adaptive control system are semiglobally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin by appropriate choice of design parameters the proposed approach cannot only solve the problem of the dead zones but also cancel the restrictive assumption in the previous literature that the states are all available for measurement two simulation examples are provided to show the effectiveness of the proposed approach

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

adaptive fuzzy control with guaranteed convergence of optimal approximation error with no a priori knowledge of plant boundary functions a novel direct adaptive fuzzy controller afc for a class of single input single output siso uncertain affine nonlinear systems is developed in this paper based on the theory of fuzzy logic systems flss with variable universes of discourse uds sufficient conditions that guarantee that the optimal fuzzy approximation error fae is locally convergent are given by the use of the output tracking error and its derivatives as input variables and by the selection of suitable adjusting parameters a variable ud fls with an optimal fae local convergence is constructed and its parameter adaptive law is derived by virtue of the lyapunov stability theorem under the assumption that the optimal fae is bounded it is proved that the closed loop system is asymptotically stable in the sense that all variables are uniformly ultimately bounded and that the tracking errors converge to zero the proposed approach eliminates the influence of the fae on the tracking errors by means of the inherent mechanism of the variable ud fls thus it has the potential to achieve high control performance without additional compensation under only a few fuzzy rules simulation studies demonstrate the superiority of the proposed afc in terms of the settling time tracking accuracy smoothness of the control input and robustness against external disturbances and parameter variations

convex duality approach to the optimal control of diffusions an alternative to the usual dynamic programming approach to the optimal control of markov processes is considered it is based on duality of convex analysis the control problem is embedded in a convex mathematical programming problem on a space of measures the dual problem is to find the supremum of smooth subsolutions to the hamilton jacobi bellman equation

second order sliding fuzzy interval type 2 control for an uncertain system with real application a new second order sliding mode type 2 fuzzy controller for nonlinear uncertain perturbed systems is developed in this paper to overcome the constraint on the knowledge of the system model we have used local models that are related to some operating points to synthesize a type 2 nominal fuzzy global model the control is based on the super twisting algorithm which is among second order sliding mode controls smcs moreover two adaptive fuzzy type 2 systems have been introduced to generate the two super twisting signals to avoid both the chattering and the constraint on the knowledge of disturbances and uncertainties upper bounds these adaptive fuzzy type 2 systems are adjusted online by two adaptation laws that are deduced from the stability analysis in the lyapunov sense it has only one input i e the sliding surface and one output i e the optimal values of the gains control which are hard to compute with the original algorithm many results of the one link manipulator are obtained first by the simulation in order to compare the performances of the proposed method with that given by levant and then in a real time application in order to confirm the efficiency of the proposed approach the experimentation and simulation are done for the tracking control problem

control synthesis of t s fuzzy systems based on a new control scheme this paper studies the control synthesis problem of takagi sugeno t s fuzzy systems by splitting the premise variable spaces and using the properties of fuzzy sets a new control scheme is proposed based on a new class of fuzzy lyapunov functions and a convex condition for designing fuzzy controllers is given where the new fuzzy lyapunov functions and fuzzy controllers are constructed based on the split subspaces in particular some existing fuzzy lyapunov functions and control schemes are special cases of the new lyapunov function and control scheme respectively numerical examples are given to illustrate the effectiveness of the proposed method

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

exact output regulation for nonlinear systems described by takagi sugeno fuzzy models the exact output regulation for takagi sugeno t s fuzzy models depends on two conditions 1 the local steady state zero error manifolds have to be the same for every local subsystem and 2 the local input matrices have to be the same for every local subsystem included in the t s fuzzy model these conditions are difficult to satisfy in general in this paper those conditions are relaxed by solving the fuzzy regulation problem directly on the overall t s fuzzy model instead of constructing the fuzzy regulator on the basis of linear local controllers by considering the fuzzy model as a special class of linear time varying systems existence conditions are rigorously derived these new conditions which can be solved by means of any mathematical software depend on the solution of a set of symbolic simultaneous linear equations depending on the membership values of the plant and or the exosystem two examples are given to illustrate the construction of the proposed regulator and to validate the improvement that is achieved with the proposed approach

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

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

fuzzy approximation based adaptive backstepping optimal control for a class of nonlinear discrete time systems with dead zone in this paper an adaptive fuzzy optimal control design is addressed for a class of unknown nonlinear discrete time systems the controlled systems are in a strict feedback frame and contain unknown functions and nonsymmetric dead zone for this class of systems the control objective is to design a controller which not only guarantees the stability of the systems but achieves the optimal control performance as well this immediately brings about the difficulties in the controller design to this end the fuzzy logic systems are employed to approximate the unknown functions in the systems based on the utility functions and the critic designs and by applying the backsteppping design technique a reinforcement learning algorithm is used to develop an optimal control signal the adaptation auxiliary signal for unknown dead zone parameters is established to compensate for the effect of nonsymmetric dead zone on the control performance and the updating laws are obtained based on the gradient descent rule the stability of the control systems can be proved based on the difference lyapunov function method the feasibility of the proposed control approach is further demonstrated via two simulation examples

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

applying a finite horizon numerical optimization method to a periodic optimal control problem computing a numerical solution to a periodic optimal control problem can be difficult especially when the period is unknown a method of approximating a solution to a stochastic optimal control problem using markov chains was developed in krawczyk j b 2001 a markovian approximated solution to a portfolio management problem information technology for economics and management 1 http www item woiz polsl pl issue journal1 htm this paper describes the application of that method to a periodic optimal control problem formulated in gaitsgory v rossomakhine s 2006 linear programming approach to deterministic long run average problems of optimal control siam journal on control and optimization 44 6 2006 2037 as a result approximately optimal feedback rules are computed that can control the system both on and off the optimal orbit

adaptive tracking control for discrete time switched nonlinear systems with dead zone inputs abstract this paper studies the adaptive tracking control problem of a discrete time switched nonlinear system with dead zone input under a class of switching signals with average dwell time due to the complicated structure of the discrete time switched nonlinear systems and the existence of the dead zone it makes a great obstacle for controlling such a class of systems the fuzzy logic systems are employed to approximate the unknown terms of each subsystem in addition both stable subsystems and unstable subsystems are considered the controllers of subsystems update laws and switching signals are designed such that the closed loop system is stable and all the signals are bounded finally a simulation example is employed to illustrate the effectiveness of the proposed method

existence of markov controls and characterization of optimal markov controls given a solution of a controlled martingale problem it is shown under general conditions that there exists a solution having markov controls which has the same cost as the original solution this result is then used to show that the original stochastic control problem is equivalent to a linear program over a space of measures under a variety of optimality criteria existence and characterization of optimal markov controls then follows an extension of echeverria s theorem characterizing stationary distributions for uncontrolled markov processes is obtained as a corollary in particular this extension covers diffusion processes with discontinuous drift and diffusion coefficients

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

linear programming approach to deterministic infinite horizon optimal control problems with discounting we investigate relationships between the deterministic infinite time horizon optimal control problem with discounting in which the state trajectories remain in a given compact set y and a certain infinite dimensional linear programming idlp problem we introduce the problem dual with respect to this idlp problem and obtain some duality results we construct necessary and sufficient optimality conditions for the optimal control problem under consideration and we give a characterization of the viability kernel of y we also indicate how one can use finite dimensional approximations of the idlp problem and its dual for construction of near optimal feedback controls the construction is illustrated with a numerical example

a unified approach to adaptive neural control for nonlinear discrete time systems with nonlinear dead zone input in this paper an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete time systems which contain unknown functions unknown dead zone input and unknown control direction different from linear dead zone the dead zone in this paper is a kind of nonlinear dead zone to overcome the noncausal problem which leads to the control scheme infeasible the systems can be transformed into a m step ahead predictor due to nonlinear dead zone appearance the transformed predictor still contains the nonaffine function in addition it is assumed that the gain function of dead zone input and the control direction are unknown these conditions bring about the difficulties and the complicacy in the controller design thus the implicit function theorem is applied to deal with nonaffine dead zone appearance the problem caused by the unknown control direction can be resolved through applying the discrete nussbaum gain and the neural networks are used to approximate the unknown function based on the lyapunov theory all the signals of the resulting closed loop system are proved to be semiglobal uniformly ultimately bounded moreover the tracking error is proved to be regulated to a small neighborhood around zero the feasibility of the proposed approach is demonstrated by a simulation example

the globally hyperbolic metric splitting for non smooth wave type space times abstract we investigate a generalization of the so called metric splitting of globally hyperbolic space times to non smooth lorentzian manifolds and show the existence of this metric splitting for a class of wave type space times the approach used is based on smooth approximations of non smooth space times by families or sequences of globally hyperbolic space times in the same setting we indicate as an application the extension of a previous result on the cauchy problem for the wave equation

duality in linear programming problems related to deterministic long run average problems of optimal control it has been established recently that under mild conditions deterministic long run average problems of optimal control are asymptotically equivalent to infinite dimensional linear programming problems lpps and that these lpps can be approximated by finite dimensional lpps in this paper we introduce the corresponding infinite and finite dimensional dual problems and study duality relationships we also investigate the possibility of using solutions of finite dimensional lpps and their duals for numerical construction of the optimal controls in periodic optimization problems the construction is illustrated with a numerical example

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

adaptive fuzzy asymptotic tracking control of uncertain nonaffine nonlinear systems with non symmetric dead zone nonlinearities this paper is concerned with the problem of robust adaptive fuzzy tracking controller design for a class of uncertain nonaffine nonlinear systems with external disturbances and non symmetric dead zone nonlinearities with the help of fuzzy logic systems flss to approximate the desired nonlinear functions a novel direct adaptive tracking control scheme is established first the implicit function theorem and the mean value theorem are used to deal with the nonaffine term with unknown dead zone input then based on the estimation information for the unknown upper bound of the compounded disturbance an adaptive fuzzy tracking controller with the corresponding parameter updating laws is designed to eliminate the effect of the compounded disturbance furthermore it is proved that all the resulting closed loop system signals are uniformly bounded and the tracking error can asymptotically converge to zero via the lyapunov stability analysis finally a numerical example is provided to verify the effectiveness of the proposed adaptive fuzzy asymptotic tracking design method

observer based t s fuzzy control for a class of general nonaffine nonlinear systems using generalized projection update laws in this paper we propose an online observer based takagi sugeno t s fuzzy output tracking control technique and an improved generalized projection update law for a class of general nonaffine nonlinear systems with unknown functions and external disturbances first a t s fuzzy model and a mean value estimation technique are adopted to approximate a so called virtual linearized system vls of a real system and avoiding a high order derivative problem respectively second a novel design concept combining the t s fuzzy controller observer and tuning algorithm by neural networks is proposed to improve system performance after that we also use improved generalized projection update laws which prevent parameters drift and confine adjustable parameters to the specified regions to tune adjustable parameters as a result both the stability guarantee based on strictly positive real spr lyapunov theory and barbalat s lemma and the better tracking performance are concluded to illustrate the effectiveness of the proposed t s fuzzy controller and observer design methodology numerical simulation results are given in this paper

chaos synchronization of uncertain fractional order chaotic systems with time delay based on adaptive fuzzy sliding mode control this paper proposes an adaptive fuzzy sliding mode control afsmc to synchronize two different uncertain fractional order time delay chaotic systems which are infinite dimensional in nature and time delay is a source of instability because modeling the behavior of dynamical systems by fractional order differential equations has more advantages than integer order modeling the adaptive time delay fuzzy logic system is constructed to approximate the unknown fractional order time delay system functions by using lyapunov stability criterion the free parameters of the adaptive fuzzy controller can be tuned online by output feedback control law and adaptive law the sliding mode design procedure not only guarantees the stability and robustness of the proposed afsmc but it also guarantees that the external disturbance on the synchronization error can be attenuated the simulation example is included to confirm validity and synchronization performance of the advocated design methodology

adaptive fuzzy tracking control based barrier functions of uncertain nonlinear mimo systems with full state constraints and applications to chemical process an adaptive control approach based on the fuzzy systems for a class of uncertain nonlinear multi input multi output mimo systems is presented in this paper this class of systems is in the nested multiple coupling structure and their states are constrained in the corresponding compact sets the properties of the system structure are inevitable to bring about a complicated design and a difficult task the fuzzy logic systems are employed to approximate the unknown functions of systems and the decoupling backstepping way is proposed to design the stability controller and adaptation laws barrier lyapunov functions blfs are constructed in the backstepping design to guarantee that the constraint bounds are not violated based on lyapunov analysis in barrier form we can prove the stability of the closed loop system two simulation examples are viewed to verify the feasibility of the approach

convex duality and nonlinear optimal control problems in nonlinear optimal control can be reformulated as convex optimization problems over a vector space of linear functionals in this way methods of convex analysis can be brought to bear on the task of characterizing solutions to such problems the result is a necessary and sufficient condition of optimality that generalizes well known sufficient conditions referred to as verification theorems in dynamic programming as a byproduct we obtain a representation of the minimum cost in terms of the upper envelope of subsolutions to the hamilton jacobi equation it is a striking illustration of the wide range of problems to which convex analysis and in particular convex duality is applicable the approach applied to parametric problems in the calculus of variations was pioneered by l c young lectures on the calculus of variations and optimal control theory w b saunders philadelphia pa 1969 as recent work has shown however it is equally fruitful when applied in optimal control thi

robust self organizing neural fuzzy control with uncertainty observer for mimo nonlinear systems this paper proposes a robust self organizing neural fuzzy control rsonfc scheme for a class of uncertain nonlinear multiple input multiple output mimo systems we first develop a self organizing neural fuzzy network sonfn with concurrent structure and parameter learning the fuzzy rules of sonfn are generated or pruned systematically the proposed rsonfc scheme comprises an sonfn identifier an uncertainty observer and a supervisory controller the sonfn identifier functions as the principal controller and the uncertainty observer is designed to oversee uncertainties within the compound system the supervisory controller combines sliding mode control smc and an adaptive bound estimation scheme with various weights to achieve h tracking performance with a desired level of attenuation projection type adaptation laws of network parameters developed using the lyapunov s synthesis approach guarantee the stability of the overall control system simulation studies on a single link flexible joint manipulator and a two link robot demonstrate the effectiveness of the proposed control scheme

on the relation between discounted and average optimal value functions abstract we investigate the relation between discounted and average deterministic optimal control problems for nonlinear control systems in particular we are interested in the corresponding optimal value functions using the concepts of viability chain controllability and controllability a global convergence result for vanishing discount rate is obtained basic ingredients for the analysis are an abelian type theorem controllability properties of the system and the morse decomposition of the corresponding control flow

asymptotic controllability and exponential stabilization of nonlinear control systems at singular points we discuss the relation between exponential stabilization and asymptotic controllability of nonlinear control systems with constrained control range at singular points using a discounted optimal control approach we construct discrete feedback laws minimizing the lyapunov exponent of the linearization thus we obtain an equivalence result between uniform exponential controllability and uniform exponential stabilizability by means of a discrete feedback law

a new methodology for the online adaptation of fuzzy self structuring controllers in this study a novel fuzzy controller which is able to self design from scratch while working online is proposed the controller does not use the information regarding the differential equations that govern the plant s behavior or any of their bounds the algorithm presented is able to determine the most adequate topology for the fuzzy controller based on the data obtained during the system s normal operation therefore the controller can start operating with an empty set of fuzzy rules and needs no offline training the proposed methodology comprises two phases adaptation of the consequents for every selected topology and online addition of new membership functions mfs some of the main advantages of this method are its robustness under changes on the plant s dynamics good performance in noisy situations and the ability to perform variable selection among a group of candidate variables unlike other online methods the modification of the topology is based on the analysis of the whole operating region of the plant thus providing higher robustness several simulation examples are used to show these features

hamilton jacobi equations viscosity solutions and generalized gradients this paper is devoted to the relationship between locally lipschitz continuous viscosity solutions and solutions in the sense of clarke of the hamilton jacobi equation arising in optimal control

nonquadratic stabilization of continuous t s fuzzy models lmi solution for a local approach this paper is concerned with nonquadratic stabilization design problem for continuous time nonlinear models in the takagi sugeno t s form obtained by sector nonlinearity approach most of the previous results found in the literature intended to establish global nonquadratic stabilization conditions which are hard to uphold due to the difficulty of handling time derivatives of the membership function by changing the paradigm of global stabilization for something less restrictive a local solution to overcome infeasible quadratic stabilization conditions is offered in this paper it is shown that the derived local nonquadratic conditions actually lead to reasonable advantages over the existing quadratic approach as well as some previous nonquadratic attempts moreover conditions for the solvability of state feedback controller design given here are written in the form of linear matrix inequalities lmis which can be efficiently solved by convex optimization techniques simulation examples are given to demonstrate the validity and applicability of the proposed approaches

differential inclusions and target problems where and how solutions associated to a differential inclusion can or cannot enter a given target is studied for this purpose partitions of the target boundary are associated with the dynamic of the system the behaviour of these solutions is qualitatively described in terms of viability and invariance kernels of sets these kernels determine points such that there exist respectively all solutions starting at these points remain in a given set of constraints the sets that are reached in finite time by viable solutions to the system are also studied finally some applications to control systems with one target are provided and the concept of semipermeable barriers will be generalized