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.     

Fault estimation and tolerant control for discrete‐time switched systems with sojourn probabilities

This paper addresses the issue of fault estimation and accommodation for a discrete‐time switched system with actuator faults. Here, we assume that the sojourn probabilities are known a priori. By using the reduced‐order observer method, the sojourn probability approach, and the Lyapunov technique, a fault estimation algorithm is obtained for the considered system. The main objective of this work is to design a dynamic output feedback fault‐tolerant controller based on the obtained fault estimation information such that the closed‐loop discrete‐time switched system with available sojourn probabilities is robustly mean‐square stable and satisfies a prescribed mixed and passivity disturbance attenuation level in the presence of actuator faults. More precisely, a dynamic output feedback fault‐tolerant controller is established in terms of linear matrix inequalities. Finally, numerical examples are provided to illustrate the usefulness and effectiveness of the proposed design technique.     

Adaptive control of discrete‐time nonlinear systems by recurrent neural networks in quasi‐sliding mode like regime

The aim of this study was to design an adaptive control strategy based on recurrent neural networks (RNNs). This neural network was designed to obtain a non‐parametric approximation (identification) of discrete‐time uncertain nonlinear systems. A discrete‐time Lyapunov candidate function was proposed to prove the convergence of the identification error. The adaptation laws to adjust the free parameters in the RNN were obtained in the same stability analysis. The control scheme used the states of the identifier, and it was developed fulfilling the necessary conditions to establish a behavior comparable with a quasi‐sliding mode regime. This controller does not use the regular form of the switching function that commonly appears in the sliding mode control designs. The Lyapunov candidate function to design the controller and the identifier simultaneously requires the existence of positive definite solutions of two different matrix inequalities. As consequence, a class of separation principle was proven when the RNN‐based identifier and the controller were designed by the same analysis. Simulations results were designed to show the behavior of the proposed controller solving the tracking problem for the trajectories of a direct current (DC) motor. The performance of the proposed controller was compared with the solution obtained when a classical proportional derivative controller and an adaptive first‐order sliding mode controller assuming poor knowledge of the plant. In both cases, the proposed controller showed superior performance when the relation between the tracking error convergence and the energy used to reach it was evaluated. Copyright © 2016 John Wiley & Sons, Ltd.     

Fault detection filter design for discrete‐time switched linear systems with mode‐dependent average dwell‐time

This paper is concerned with the problem of the fault detection (FD) filter design for discrete‐time switched linear systems with mode‐dependent average dwell‐time. The switching law is mode‐dependent and each subsystem has its own average dwell‐time. The FD filters are designed such that the augmented switched systems are asymptotically stable, and the residual signal generated by the filters achieves a weighted l₂‐gain for some disturbances and guarantees an H _? performance for the fault. By the aid of multiple Lyapunov functions combined with projection lemma, sufficient conditions for the design of the FD filters are formulated by linear matrix inequalities, furthermore, the filters gains are characterized in terms of the solution of a convex optimization problem. Finally, an application to boost convertor is given to illustrate the effectiveness and the applicability of the proposed design method. Copyright © 2013 John Wiley & Sons, Ltd.     

A small‐gain approach for adaptive output‐feedback NN control of switched pure‐feedback nonlinear systems

This paper investigates the problem of adaptive output‐feedback neural network (NN) control for a class of switched pure‐feedback uncertain nonlinear systems. A switched observer is first constructed to estimate the unmeasurable states. Next, with the help of an NN to approximate the unknown nonlinear terms, a switched small‐gain technique‐based adaptive output‐feedback NN control scheme is developed by exploiting the backstepping recursive design scheme, input‐to‐state stability analysis, the common Lyapunov function method, and the average dwell time (ADT) method. In the recursive design, the difficulty of constructing an overall Lyapunov function for the switched closed‐loop system is dealt with by decomposing the switched closed‐loop system into two interconnected switched systems and constructing two Lyapunov functions for two interconnected switched systems, respectively. The proposed controllers for individual subsystems guarantee that all signals in the closed‐loop system are semiglobally, uniformly, and ultimately bounded under a class of switching signals with ADT, and finally, two examples illustrate the effectiveness of theoretical results, which include a switched RLC circuit system.     

Sliding mode control of switched hybrid systems with time‐varying delay

This paper is concerned with the sliding mode control of a continuous‐time switched system with time‐varying delay in its state. By using the average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the exponential stability of the unforced system with the decay estimate explicitly given. A sufficient condition of the existence of a reduced‐order sliding mode dynamics is derived, and an explicit parametrization of the desired sliding surface is also given. The obtained conditions will be solved using the cone complementary linearization (CCL) method. An adaptive sliding mode controller for the reaching motion is then designed such that the trajectories of the resulting closed‐loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent times. All the conditions obtained in this paper are delay dependent. Finally, two numerical examples are given to illustrate the effectiveness of the proposed theory. Copyright © 2008 John Wiley & Sons, Ltd.     

Active fault‐tolerant control for switched systems with time delay

This paper focuses on the problem of active fault‐tolerant control for switched systems with time delay. By utilizing the fault diagnosis observer, an adaptive fault estimate algorithm is proposed, which can estimate the fault signal fast and exactly. Meanwhile, a delay‐dependent criterion is obtained with the purpose of reducing the conservatism of the adaptive observer design. Based on the fault estimation information, an observer‐based fault‐tolerant controller is designed to guarantee the stability of the closed‐loop system. In terms of linear matrix inequality, sufficient conditions are derived for the existence of the adaptive observer and fault‐tolerant controller. Finally, a numerical example is included to illustrate the efficiency of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Filter‐based fault detection and diagnosis using output PDFs for stochastic systems with time delays

In this paper, a fault detection and diagnosis (FDD) scheme is studied for general stochastic dynamic systems subjected to state time delays. Different from the formulation of classical FDD problems, it is supposed that the measured information for the FDD is the probability density function (PDF) of the system output rather than its actual value. A B‐spline expansion technique is applied so that the output PDF can be formulated in terms of the dynamic weights of the B‐spline expansion, by which a time delay model can be established between the input and the weights with non‐linearities and modelling errors. As a result, the concerned FDD problem can be transformed into a classic FDD problem subject to an uncertain non‐linear system with time delays. Feasible criteria to detect the system fault are obtained and a fault diagnosis method is further presented to estimate the fault. Simple simulations are given to demonstrate the efficiency of the proposed approach. Copyright © 2006 John Wiley & Sons, Ltd.     

Quasi‐passivity‐based adaptive stabilization for switched nonlinearly parameterized systems

This paper investigates the adaptive quasi‐passification‐based stabilization problem for a class of switched nonlinearly parameterized systems via average dwell time method. First, when all the subsystems have any same relative degree, the global practical stability is achieved by combining the recursive feedback quasi‐passification design technique with a switched adaptive control technique. The states and parameter estimation errors converge to the ball whose sizes can be reduced by choosing appropriate design parameters. Second, when the system states are unavailable for measurements, adaptive output feedback controllers are designed to stabilize the system using quasi‐passivity. The proposed output feedback controllers do not depend on any state observer. Finally, three examples show the effectiveness of the proposed methods.     

Actuator fault‐tolerant control based on set separation

In this paper, an actuator fault‐tolerant control (FTC) strategy based on set separation is presented. The proposed scheme employs a standard configuration consisting of a bank of observers which match the different fault situations that can occur in the plant. Each of these observers has an associated estimation error with a distinctive behaviour when a estimator matches the current fault situation of the plant. With this information from each observer, a fault diagnosis and isolation (FDI) module is able to reconfigure the control loop by selecting the appropriate stabilising controller from a bank of precomputed control laws, each of them related to one of the considered fault models. The control law consists of a reference feedforward term and a feedback gain multiplying the state estimate provided by the matching observer. A novel feature of the proposed scheme resides in the decision criteria of the FDI, which is based on the computation of sets towards which the output estimation errors related to each fault scenario and for each control configuration converge. Conditions for the design of the FDI module and for fault tolerant closed‐loop stability are given, and the effectiveness of the approach is illustrated by means of a numerical example. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimality for the linear quadratic non‐Gaussian problem via the asymmetric Kalman filter

In the linear non‐Gaussian case, the classical solution of the linear quadratic Gaussian (LQG) control problem is known to provide the best solution in the class of linear transformations of the plant output if optimality refers to classical least‐squares minimization criteria. In this paper, the adaptive linear quadratic control problem is solved with optimality based on asymmetric least‐squares approach, which includes least‐squares criteria as a special case. Our main result gives explicit solutions for this optimal quadratic control problem for partially observable dynamic linear systems with asymmetric observation errors. The main difficulty is to find the optimal state estimate. For this purpose, an asymmetric version of the Kalman filter based on asymmetric least‐squares estimation is used. We illustrate the applicability of our approach with numerical results. Copyright © 2004 John Wiley & Sons, Ltd.     

基于自适应广义滑模观测器的风力发电系统故障重构

针对风力发电系统的状态估计和执行器故障重构问题,提出一种自适应广义滑模观测器.通过构建一个增广系统,使得执行器故障成为系统状态的一部分.设计广义滑模观测器对增广系统进行状态估计从而获得所需的故障信息.针对实际风力发电系统中故障上界未知的问题,设计一种自适应算法来估计故障信息的上界.以5 MW的风电机组为研究对象,在Ma...     

Adaptive estimation and rejection of unknown sinusoidal disturbances through measurement feedback for a class of non‐minimum phase non‐linear MIMO systems

This paper develops an adaptive estimation method to estimate unknown disturbances in a class of non‐minimum phase non‐linear MIMO systems. The unknown disturbances are generated by an unknown linear exosystem. The frequencies, phases and amplitudes of the disturbances are unknown, the only available information of the disturbances is the number of distinctive frequencies. The system considered in this paper is a class of MIMO non‐linear systems in the output feedback form which can be non‐minimum phase. The proposed estimation algorithm provides exponentially convergent estimates of system states, unknown disturbances in the system and frequencies of the disturbances characterized by the eigenvalues of the exosystem. Moreover, based on the stabilization controller for the disturbance free system, the estimates of the disturbances are used to solve the disturbance rejection problem. The unknown disturbances are compensated completely with the stability of the whole closed‐loop system. Copyright © 2006 John Wiley & Sons, Ltd.     

Discrete‐time periodic adaptive control for parametric systems with non‐sector nonlinearities

In this paper, a periodic adaptive control approach is proposed for a class of discrete‐time parametric systems with non‐sector nonlinearities. The proposed periodic adaptive control law is characterized by either one‐period delayed parametric updating or two‐period delayed parametric updating when input gain contains periodic unknowns. Logarithmic‐type discrete Lyapunov function is employed to handle the difficulties caused by the uncertainties that do not satisfy the linear growth condition. Some extensions to nonlinear systems with multiple unknown parameters and time‐varying input gain, tracking tasks, as well as higher‐order systems in canonical form, are also discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

带有滑模观测器的永磁同步电机改进型PID控制

针对传统滑模观测器的抖振现象严重、估计精度低等问题,提出了一种带有二阶滑模观测器的内嵌式永磁同步电机改进型PID控制方案。根据Super twisting algorithm设计了二阶滑模观测器,取消了传统滑模观测器方案中的低通滤波器与位置补偿环节,有效抑制了滑模抖振,提高了估计精度。为了进一步改善系统的动态性能,基于牛顿插值法构造了一种具有滤波功能的离散微分器并利用三点离散微分器代替传统微分设计了转速环改进型PID控制器。仿真验证了该方案能够有效抑制抖振现象,估计精度高,稳态性能与动态性能较好。     

Stability of self‐tuning control based on Lyapunov function

The overall stability of a self‐tuning controller for discrete‐time systems is proved by using the Lyapunov function in this paper, for minimum and a class of non‐minimum phase systems. The self‐tuning controller utilizes a recursive estimate algorithm for the controller parameters based on the generalized minimum variance criterion. Previously, the stability had been proved in the case of minimum phase systems. A new type of self‐tuning controller for the discrete‐time system with delay in control input is also studied which is named the generalized minimum variance criterion‐β equivalent control, and its stability is proved. The simulation is done to evaluate the performance of the proposed self‐tuning controller. Copyright © 2008 John Wiley & Sons, Ltd.     

State estimation for short‐time switched linear systems under asynchronous switching

In this note, the state estimation problem for a class of short‐time switched linear systems is investigated. By incorporating the concept of finite‐time stability, an observer is designed to ensure the error dynamics finite‐time stable in the short‐time switching interval under the general asynchronous switching whereas synchronous switching mode is its special case. A numerical example is provided to illustrate the effectiveness of our study in this paper. Copyright © 2013 John Wiley & Sons, Ltd.