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

state estimation for discrete time markov jump linear systems with time correlated measurement noise abstract in this paper the state estimation problem for discrete time markov jump linear systems affected by time correlated measurement noise is considered where the time correlated measurement noise is described by a linear system model with white noise as a result two algorithms are proposed to estimate the state of the system under consideration based on a measurement sequence the first algorithm is optimal in the sense of minimum mean square error which is obtained based on the measurement differencing method bayes rule and some results derived in this paper the second algorithm is a suboptimal algorithm obtained by using a lot of gaussian hypotheses the proposed suboptimal algorithm is finite dimensionally computable and does not increase computational and storage load with time computer simulations are carried out to evaluate the performance of the proposed suboptimal algorithm

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

online constrained optimization based adaptive robust control of a class of mimo nonlinear systems with matched uncertainties and input state constraints a performance oriented two loop control approach is proposed for a class of multiple input multiple output mimo systems with input saturation state constraints matched parametric uncertainties and input disturbances in the inner loop a constrained adaptive robust control arc law is synthesized to achieve the required robust tracking performances with respect to on line replanned trajectory in the presence of input saturation and various types of matched uncertainties in the outer loop a replanned trajectory is generated by solving a constrained optimization algorithm online to minimize the converging time of the overall system response to the desired trajectory while not violating various constraints interaction of the two loops is explicitly characterized by a set of inequalities that the design variables of each loop have to satisfy it is theoretically shown that the resulting closed loop system can track feasible desired trajectories with a guaranteed converging time and steady state tracking accuracy without violating the state constraints since the system in study is most appropriate to describe the dynamics of the robotic systems the control of a two axis planar robotic manipulator is used as an application example comparative simulation results demonstrate the advantage of the proposed approach over the traditional approaches in practical applications

distributed fusion estimation with square root array implementation for markovian jump linear systems with random parameter matrices and cross correlated noises the distributed fusion estimation is presented for markovian jump linear systems with random parameter matrices and cross correlated noises in sensor networks the lmmse estimator is derived based on gram schmidt orthogonal innovation sequence under a centralized framework the square root array implementation is further presented by recursively triangularizing the square roots of related positive semidefinite matrices in the lmmse estimator via the information filter form the distributed fusion estimation with square root array implementation is proposed incorporated with consensus strategy the convergent condition and the convergence point are also discussed with respect to consensus strategy this study presents the distributed fusion estimation of discrete time markovian jump linear systems with random parameter matrices and cross correlated noises in sensor networks the recursive linear minimum mean square error estimator is proposed based on the gram schmidt orthogonalization procedure under a centralized framework in order to avoid the loss of positive semidefiniteness and reduce dynamical range its square root array implementation is presented by recursively triangularizing the square roots of relevant positive semidefinite matrices furthermore via the information filter form the distributed fusion estimation with square root array implementation is derived from the centralized fusion structure incorporated with consensus strategy a maneuvering target tracking simulation in a sensor network validates the proposed method

adaptive tracking control of uncertain mimo nonlinear systems with input constraints in this paper adaptive tracking control is proposed for a class of uncertain multi input and multi output nonlinear systems with non symmetric input constraints the auxiliary design system is introduced to analyze the effect of input constraints and its states are used to adaptive tracking control design the spectral radius of the control coefficient matrix is used to relax the nonsingular assumption of the control coefficient matrix subsequently the constrained adaptive control is presented where command filters are adopted to implement the emulate of actuator physical constraints on the control law and virtual control laws and avoid the tedious analytic computations of time derivatives of virtual control laws in the backstepping procedure under the proposed control techniques the closed loop semi global uniformly ultimate bounded stability is achieved via lyapunov synthesis finally simulation studies are presented to illustrate the effectiveness of the proposed adaptive tracking control

a proper relaxation of controls with variable shifts abstract in a previous paper written jointly with q j zhu 1992 j math anal appl 169 546 561 we studied optimal control problems defined by functional integral equations and in particular ordinary differential equations with shifts in the controls and with the shifted controls not necessarily separated i e either additively or nonadditively coupled in that paper it was assumed that the domain of the state and control functions is a cartesian product of an interval with a compact metric space and that each shift h j j 1 k has a one dimensional component of the form t 1 d j where d 1 d k are constant possibly noncommensurate delays and advances in the present note we extend those results to the case where each d j is replaced by a function d j that may vary and take on at different times both positive and nonpositive values

on applicability of the interacting multiple model approach to state estimation for systems with sojourn time dependent markov model switching in this paper the attempt at the interacting multiple model imm method extension to the state estimation problem with semi markov sojourn time dependent markov stdm system model switching is analyzed it is demonstrated that such an stdm imm approach does not properly take into account the specific character of the stdm switching in the system and it becomes a reason for the reduction of estimation accuracy for this problem it is shown that a hypotheses merging should be restricted in such a way that not only the current system model but also the sojourn time in the model should be given in hypotheses to be tested some other aspects of bayesian estimation in a switching environment are also discussed

problems with relaxed shifted controls and the pointwise maximum principle abstract in previous work j warga a proper relaxation of controls with variable shifts j math anal appl 196 1995 783 793 it has been shown that controls with k variable and unrelated time shifts form a set whose closure in the weak star topology of l 1 t c k 1 is a convex and compact space this provides a basis for establishing the existence of an optimal solution of the shifted control problem by essentially copying the assumptions and arguments used for control problems without shifted controls similarly the necessary optimality conditions for original and relaxed minima that define an extremal previously studied for differential and functional equations apply directly to such problems with shifted controls except that the maximum principle follows directly in integral form only in the present note we first establish the form of dependence of the relaxed shifted controls on the shifts and then use the integral form of the maximum principle to derive a corresponding pointwise maximum principle for optimal ordinary or relaxed shifted controls acting through ordinary differential and certain functional differential equations

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

brief paper detection and estimation for abruptly changing systems the problem of state estimation and system structure detection for discrete stochastic dynamical systems with parameters which may switch among a finite set of values is considered the switchings are modelled by a markov chain with known transition probabilities a brief survey and a unified treatment of the existing suboptimal algorithms are provided the optimal algorithms require exponentially increasing memory and computations with time simulation results comparing the various suboptimal algorithms are presented

a new multiple model filter with switch time conditions the interacting multiple model filter has long been the method of choice for performing target tracking using multiple motion models the filter finds a suboptimal solution to a problem which has the implicit assumption that immediate model shifts have the highest probability when the sampling rate of the underlying continuous process is high compared to the target dynamics this is not a reasonable assumption instead changes in dynamics persist for some time in this paper we propose an alternative switching model which forces the dynamic models to persist for at least a model specific time the model is semi markov in nature with a sojourn time probability mass function which is zero for a model specific number of time steps and then follows a geometrical distribution through this assumption a less complex problem in terms of model hypotheses arises and to that problem we derive a state estimation algorithm that is close to optimal when the model assumptions are valid three other semi markov based multiple model filters are discussed and compared to in a qualitative sense we also derive a new aircraft motion model for start and termination of turns finally the proposed filter is evaluated on a benchmark scenario for tracking and the results show a performance increase compared to the interacting multiple model imm filter for the trajectories considered

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

adaptive tracking control for a class of uncertain switched nonlinear systems this paper is concerned with the problem of tracking control for a class of switched nonlinear systems in lower triangular form with unknown functions and arbitrary switchings two classes of state feedback controllers are constructed by adopting the adaptive backstepping technique and both of them are designed by using the common lyapunov function clf method the first controller is designed under multiple adaptive laws then the second one is designed based on constructing a maximum common adaptive parameter which can overcome the problem of over parameterization of the first controllers it is shown that the designed state feedback controllers can ensure that all the signals remain bounded and the tracking error converges to a small neighborhood of the origin finally simulation results are presented to show the effectiveness of the proposed approaches

dynamic surface control for a class of nonlinear systems a method is proposed for designing controllers with arbitrarily small tracking error for uncertain mismatched nonlinear systems in the strict feedback form this method is another synthetic input technique similar to backstepping and multiple surface control methods but with an important addition spl tau 1 low pass filters are included in the design where spl tau is the relative degree of the output to be controlled it is shown that these low pass filters allow a design where the model is not differentiated thus ending the complexity arising due to the explosion of terms that has made other methods difficult to implement in practice the backstepping approach while suffering from the problem of explosion of terms guarantees boundedness of tracking errors globally however the proposed approach while being simpler to implement can only guarantee boundedness of tracking error semiglobally when the nonlinearities in the system are non lipschitz

command filtered backstepping implementation of backstepping becomes increasingly complex as the order of the system increases this increasing complexity is mainly driven by the need to compute command derivatives at each step of the design with the ultimate step requiring derivatives of the same order as the plant this article addresses a modification that obviates the need to compute analytic derivatives by introducing command filters in the backstepping design while the concept of the command filter has previously been introduced in the literature the main contribution of this technical note is the rigorous analysis of the effect of the command filter on closed loop stability and performance and a proof of stability based on tikhonov s theorem the implementation approach includes a compensated tracking error that retains the standard stability properties of backstepping approaches

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

state estimation for systems with sojourn time dependent markov model switching a switching process in which the switching probabilities depend on a random sojourn time is a class of semi markov processes and is encountered in target tracking systems subject to failures and also in the socioeconomic environment in such a system knowledge of the sojourn time is needed for the computation of the conditional transition probabilities it is shown how one can infer the transition probabilities through the evaluation of the conditional distribution of the sojourn time subsequently a recursive state estimation for such systems is obtained using the conditional sojourn time distribution for dynamic systems with imperfect observations and changing structures models

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

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

command filter based adaptive fuzzy backstepping control for a class of switched nonlinear systems abstract this paper considers the adaptive fuzzy output feedback control design problem for a class of switched nonlinear systems the considered switched nonlinear systems contain unknown nonlinearities the switching signals with average dwell time and without requiring that state variables are available for measurement fuzzy logic systems are used to approximate the unknown nonlinearities and a fuzzy switched state observer is designed to estimate the immeasurable states in the framework of observer based output feedback control design technique and by introducing a command filter into the backstepping design algorithm a command filter based adaptive fuzzy backstepping output feedback control scheme is developed the stability of the closed loop system and the convergence of the tracking error are proved via average dwell time and multiple lyapunov function a numerical example is provided to illustrate the effectiveness of the proposed approach

a proper relaxation of shifted and delayed controls abstract we consider optimal control problems defined by functional integral equations with variable shifts in the controls and with the shifted controls nonadditively coupled as a special case we obtain differential equations with delays and or advances in both the state and the control functions we prove that if the original controls are measurable functions u with values in a compact metric space then the k 1 tuples u u u h 1 u h k of shifted controls have relaxed limits that form a compact and convex set this enables us to prove an existence theorem to approximate any relaxed solution with original solutions and to derive necessary conditions generalizeing pontryagin s maximum principle in integral form even for nonsmooth problems we also discuss the dependence on the shifts hj of the set of original controls u of the set of their relaxed limits and of the set of the corresponding solutions of the functional integral equation our results include the proof that the d model of rosenblueth and vinter is proper

relaxation procedures for time delay systems abstract despite the attention that optimal control problems involving time delays have received over the last two decades little attention has been paid to the important question of how such problems should be relaxed in order to assure existence of minimizers recently warga has proposed a relaxation procedure for fully nonlinear problems with delays in the state and control variables and showed that the resulting relaxed problem has a solution nevertheless the effect of this relaxation may reduce the infimum cost as we show through an example which belongs to a class of problems with commensurate delays i e the quotient of any two delays is rational for problems of this nature we provide a new relaxation procedure for which the extension is proper i e the infimum costs coincide we also present an abstract relaxation procedure applicable to problems with possibly noncommensurate delays

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

adaptive dynamic surface control a simplified algorithm for adaptive backstepping control of nonlinear systems in this paper we propose a new algorithm for adaptive backstepping control of non linear uncertain systems current backstepping algorithms require repeated differentiations of the modelled non linearities the addition of n first order low pass filters allows the algorithms to be implemented without differentiating any model non linearities the uncertainties are assumed to be linear in the unknown constant parameters the combined adaptive backstepping first order filter system is proven to be semi globally stable for sufficiently fast filters by a singular perturbation approach