Switched sampled output adaptive observer design for a class of switched nonlinearly parameterized systems under asynchronous switching

In this article, a switched sampled output adaptive observer for a class of switched nonlinearly parameterized systems is designed. Since the switching may occur during the sampling intervals while the sampled output only updates at sampling instants, the asynchronous switching phenomenon arises. Then, a collection of matched and mismatched corrective terms are introduced to deal with the asynchronous switching phenomenon based on sampled outputs and the designed observer. Moreover, some sufficient conditions are derived to achieve the boundedness of observation and parameter estimation errors based on an improved average dwell time method. Finally, the effectiveness of the theoretical result in this article is demonstrated through a simulation example.     

An adaptive sliding‐mode observer for a class of uncertain nonlinear systems

In this paper, the problem of simultaneous state and parameter estimation is studied for a class of uncertain nonlinear systems. A nonlinear adaptive sliding‐mode observer is proposed based on a nonlinear parameter estimation algorithm. It is shown that such a nonlinear algorithm provides a rate of convergence faster than exponential, ie, faster than the classic linear algorithm. Then, the proposed parameter estimation algorithm is included in the structure of a sliding‐mode state observer, providing an ultimate bound for the full estimation error and attenuating the effects of the external disturbances. Moreover, the synthesis of the observer is given in terms of linear matrix inequalities. The corresponding proofs of convergence are developed based on the Lyapunov function approach and input‐to‐state stability theory. Some simulation results illustrate the efficiency of the proposed adaptive sliding‐mode observer.     

Adaptive observer for a class of nonlinear systems with time‐varying delays

The adaptive observer design problems have been extensively studied in literature for both linear and nonlinear systems. Some researches have also been carried out on adaptive observer design for linear time‐delay systems, but there is no significant work on adaptive observer design for nonlinear time‐delay systems. In this work, the adaptive observer design problem for a class of nonlinear time‐delay systems is considered. The observer is designed for the nonlinear systems whose nonlinear functions satisfy Lipschitz condition. Like conventional adaptive observers for the systems without time delays, this observer also estimates both states and unknown parameters simultaneously. For this property, it will be very much useful for many real‐time systems where time delays cannot be avoided. The sufficient conditions for existence of the observer are derived using the linear matrix inequality approach. With the help of a numerical example, effectiveness of the proposed observer is demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.     

一类不确定线性离散系统有限时间观测器设计

针对一类不确定线性离散系统有限时间观测器最优设计问题,利用线性矩阵不等式方法以及有限时间有界的概念,给出了具有不确定外部扰动输入的线性离散系统有限时间有界的充分条件.对具有状态反馈和输出的线性不确定离散系统引入有限时间观测器的概念,可以保证在给定的有限时间区间内,观测误差小于一个给定的界,并给出了最优有限时间观测器的具体设计方案.此方案的有效性可以通过仿真实验得到验证.     

利用降维状态观测器离散系统的鲁棒容错控制

研究了线性离散不确定系统的鲁棒容错控制问题。针对线性离散控制系统存在不确定性和传感器失效的情况，利用降维观测器估计系统的状态，并基于估计的状态构成鲁棒容错控制律。给出了闭环系统具有鲁棒容错特性的充分条件。数值算例表明了算法的有效性。     

Immersion and invariance adaptive control for discrete‐time systems in strict‐feedback form with input delay and disturbances

This work presents a new adaptive control algorithm for a class of discrete‐time systems in strict‐feedback form with input delay and disturbances. The immersion and invariance formulation is used to estimate the disturbances and to compensate the effect of the input delay, resulting in a recursive control law. The stability of the closed‐loop system is studied using Lyapunov functions, and guidelines for tuning the controller parameters are presented. An explicit expression of the control law in the case of multiple simultaneous disturbances is provided for the tracking problem of a pneumatic drive. The effectiveness of the control algorithm is demonstrated with numerical simulations considering disturbances and input‐delay representative of the application.     

Input constrained adaptive tracking for a nonlinear distributed parameter tubular reactor

In this paper we address the problem of local λ tracking of a pre‐specified profile temperature for exothermic chemical reaction in a tubular reactor. In contrast to the various models in the literature, which are usually ordinary differential equations in finite‐dimensional spaces, we use a nonlinear distributed parameter model for both the evolution of the temperature and the reactant concentration. We show under nonrestrictive conditions that an adaptive output feedback controller achieves approximate asymptotic tracking where the pre‐specified asymptotic tracking accuracy, quantified by the design parameter λ>0, is guaranteed. Only a feasibility assumption in terms of the reference temperature and the input constraints is considered. Numerical simulations have been performed to illustrate the performance of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Distributed output estimation error observer-based adaptive fault-tolerant consensus tracking control of multi-agent systems

The purpose of this study is to discuss the fully distributed design of output estimation error observer and fault-tolerant consensus tracking control for a class of multi-agent systems with Lipschitz nonlinear dynamics and actuator faults. Firstly, based on the relative output measurements of neighboring agents, the distributed output estimation error observer is developed to adaptively estimate the state and fault information of each agent, and further overcome the difficulties of online updating the adaptive estimations of unknown hyper-parameters. Secondly, to achieve the state consensus tracking goal and compensate for the negative effects of actuator faults, the distributed fault-tolerant consensus tracking control scheme is proposed on the basis of the state estimation and adaptive fault estimation information, and has excellent robustness and consensus tracking control performance. Moreover, sufficient criteria can ensure that consensus tracking error of each agent converges to a small set near the origin. Finally, numerical simulations are provided to show the effectiveness of the proposed fully distributed algorithm.     

Robust adaptive tracking control of uncertain discrete time systems

In this paper, the problem of robust adaptive tracking for uncertain discrete‐time systems is considered from the slowly varying systems point of view. The class of uncertain discrete‐time systems considered is subjected to both 𝓁_∞ to 𝓁_∞ bounded unstructured uncertainty and external additive bounded disturbances. A priori knowledge of the dynamic model of the reference signal to be tracked is not completely known. For such problem, an indirect adaptive tracking controller is obtained by frozen‐time controllers that at each time optimally robustly stabilize the estimated models of the plant and minimize the worst‐case steady‐state absolute value of the tracking error of the estimated model over the model uncertainty. Based on 𝓁_∞ to 𝓁_∞ stability and performance of slowly varying system found in the literature, the proposed adaptive tracking scheme is shown to have good robust stability. Moreover, a computable upper bound on the size of the unstructured uncertainty permitted by the adaptive system and a computable tight upper bound on asymptotic robust steady‐state tracking performance are provided. Copyright © 2005 John Wiley & Sons, Ltd.     

An adaptive observer for joint estimation of states and parameters in both state and output equations

An adaptive observer is a recursive algorithm for joint state–parameter estimation of parameterized state‐space systems. Previous works on globally convergent adaptive observers consider unknown parameters either in state equations or in output equations, but not in both of them. In this paper, a new adaptive observer is designed for linear time‐varying systems with unknown parameters in both state and output equations. Its global convergence for simultaneous estimation of states and parameters is formally established under appropriate assumptions. A numerical example is presented to illustrate the performance of this adaptive observer. Copyright © 2011 John Wiley & Sons, Ltd.     

An adaptive switching scheme for uncertain discrete time‐delay systems

In this paper, an adaptive switching control algorithm is proposed for the stabilization of uncertain discrete‐time systems with time‐varying delay. It is assumed that the time delay is unknown and time varying, nonetheless bounded with a known bound. It is supposed that the system is highly uncertain, and that a set of controllers are designed (off‐line) to stabilize the system in the whole uncertain parameter space; subsequently, a switching scheme is developed to stabilize the uncertain time‐delay system. A thorough stability analysis for the uncertain time‐delay system under the mentioned control scheme is provided. Furthermore, an upper bound on the allowable rate of change of the system parameters and delay is obtained. Simulation results are presented to show the efficacy of the proposed switching scheme. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive neural prescribed performance output feedback control of pure feedback nonlinear systems using disturbance observer

In this study, an adaptive output feedback control with prescribed performance is proposed for unknown pure feedback nonlinear systems with external disturbances and unmeasured states. A novel prescribed performance function is developed and incorporated into an output error transformation to achieve tracking control with prescribed performance. To handle the unknown non-affine nonlinearities and avoid the algebraic loop problem, the radial basis function neural network (RBFNN) is adopted to approximate the unknown non-affine nonlinearities with the help of Butterworth low-pass filter. Based on the output of the RBFNN, the coupled design between sate observer and disturbance observer is presented to estimate the unmeasured states and compounded disturbances. Then, the adaptive output feedback control scheme is proposed for unknown pure feedback nonlinear systems, where a first-order filter is introduced to tackle with the issue of “explosion of complexity” in the traditional back-stepping approach. The boundedness and convergence of the closed-loop system are proved rigorously by utilizing the Lyapunov stability theorem. Finally, simulation studies are worked out to demonstrate the effectiveness of the proposed scheme.     

一种不确定非线性系统的滑模变结构观测器的研究

由于工程实际中大部分工业对象均为非线性系统,滑模观测器应用研究的重点已从线性系统转至不确定非线性系统。针对一类非线性满足Lipschitz条件,而不确定部分为有界函数的不确定非线性系统,提出一种滑模变结构观测器设计方案,将基于线性系统提出的Walcott-Zak观测器用于抑制非线性对系统的影响,而滑模变结构使得观测器对系统不确定性具有鲁棒性。对所设计观测器的稳定性进行了证明,并通过仿真验证了所提方法的有效性。     

Distributed adaptive state estimation and tracking by using active-passive sensor networks

Heterogeneous sensor networks (HSN) find a wide range of applications in the field of military and civilian environments, where sensor nodes are utilized to estimate the position of a target with both dynamics and control input being unknown for the purposes of tracking. In the HSN, nodes are considered active depending upon their ability to sense the target output while the others are taken passive. Accurate estimation requires local information exchange among the spatially located sensor nodes, so that the active nodes as well as the passive nodes converge simultaneously to the same value. The local information exchange among the nodes is dictated by a connected graph. By using the criterion of collective observability, a novel distributed adaptive estimation scheme is introduced via adaptive observer where the nodes are allowed to have different sensor modalities. Using the estimated information, a subset of active and passive nodes, referred to as mobile nodes, can track the moving target. By using a constant state feedback controller at each mobile node, the state and parameter estimation as well as the tracking errors are shown to be uniformly ultimately bounded. Simulation results verify theoretical claims.     

Robust adaptive tracking control for nontriangular time-delay nonlinear systems with input dead-zone and multiple uncertainties

This article studies the robust adaptive tracking control problem of nontriangular nonlinear systems that are affected by multiple state delays rather than the input-delay. Different from the related studies, the considered systems involve input dead-zone and various uncertainties arising in the control coefficients, structure parameters, time delays, and disturbances. A new adaptive control strategy is presented by introducing a dynamic-gain-based Lyapunov-Krasovskii functional and by generalizing the tuning function method in the framework of time-delay system theory. All the states of the closed-loop system are bounded and the tracking error can be adjusted sufficiently small. In the simulation, the delayed chemical system is studied to demonstrate the validity of the strategy.     

Less conservative criteria for fault accommodation of time‐varying delay systems using adaptive fault diagnosis observer

This paper studies the problem of fault accommodation of time‐varying delay systems using adaptive fault diagnosis observer. Based on the proposed fast adaptive fault estimation (FAFE) algorithm using only a measured output, a delay‐dependent criteria is first established to reduce the conservatism of the design procedure, and the FAFE algorithm can enhance the performance of fault estimation. On the basis of fault estimation, the observer‐based fault‐tolerant tracking control is then designed to guarantee tracking performance of the closed‐loop systems. Furthermore, comprehensive analysis is presented to discuss the calculation steps using linear matrix inequality technique. Finally, simulation results of a stirred tank reactor model are presented to illustrate the efficiency of the proposed techniques. Copyright © 2009 John Wiley & Sons, Ltd.     

Observer‐based adaptive optimal output containment control problem of linear heterogeneous Multiagent systems with relative output measurements

This paper develops a relative output‐feedback–based solution to the containment control of linear heterogeneous multiagent systems. A distributed optimal control protocol is presented for the followers to not only assure that their outputs fall into the convex hull of the leaders' output but also optimizes their transient performance. The proposed optimal solution is composed of a feedback part, depending of the followers' state, and a feed‐forward part, depending on the convex hull of the leaders' state. To comply with most real‐world applications, the feedback and feed‐forward states are assumed to be unavailable and are estimated using two distributed observers. That is, a distributed observer is designed to measure each agent's states using only its relative output measurements and the information that it receives by its neighbors. Another adaptive distributed observer is designed, which uses exchange of information between followers over a communication network to estimate the convex hull of the leaders' state. The proposed observer relaxes the restrictive requirement of having access to the complete knowledge of the leaders' dynamics by all the followers. An off‐policy reinforcement learning algorithm on an actor‐critic structure is next developed to solve the optimal containment control problem online, using relative output measurements and without requiring the leaders' dynamics. Finally, the theoretical results are verified by numerical simulations.     

Hybrid adaptive observers for locally Lipschitz systems

An adaptive observer design approach is proposed for the class of nonlinear locally Lipschitz systems. The case of disturbances affecting the state equations is considered. The proposed solution is applicable to the systems with bounded solutions and hyperminimum phase linear part. It is based on the logic‐based control approach. Efficiency of the proposed observer design is demonstrated through computer simulations for Duffing and satellite system. Copyright © 2010 John Wiley & Sons, Ltd.     

An adaptive robust observer for velocity estimation in an electro‐hydraulic system

This paper proposes the design of an observer to estimate the velocity of an electro‐hydraulic system by using pressure measurements only. The difficulties involved in the design of an observer for such a system include the highly nonlinear system dynamics, severe parametric uncertainties such as large variation of inertial load and unmatched model uncertainties. In order to address these issues, a nonlinear model‐based adaptive robust observer is designed to estimate the velocity. The contributions of the proposed work is twofold. First, it introduces a novel coordinate transformation to reconstruct the velocity estimate. And second, from a structural viewpoint, the design has two important features: (i) an underlying robust filter structure, which can attenuate the effect of uncertain nonlinearities such as friction and disturbances on the velocity estimation, and (ii) an adaptation mechanism to reduce the extent of parametric uncertainties. Experimental results on the swing motion control of an electro‐hydraulic robot arm demonstrate the effectiveness of the proposed observer. Copyright © 2012 John Wiley & Sons, Ltd.     

Actuator fault estimation based on generalized learning observer for quasi-linear parameter varying systems

This article presents a generalized learning observer (GLO) design for the simultaneous estimation of states and actuator faults for polytopic quasi-linear parameter varying systems. The proposed approach is based on the use of a GLO, which generalized the existing results on the proportional-integral observers. Conditions of existence and stability of the observer are given through the stability analysis in the sense of Lyapunov. Its design is obtained in terms of a set of linear matrix inequalities. The performance of the proposed method is evaluated by simulation in a one-link-flexible joint robot system.