Reduced‐order observer‐based fault estimation and fault‐tolerant control for a class of discrete Lipschitz nonlinear systems

This paper addresses an issue on reduced‐order observer‐based robust fault estimation and fault‐tolerant control for a class of uncertain nonlinear discrete‐time systems. By introducing a nonsingular coordinate transformation, a new nonlinear reduced‐order fault estimation observer (RFEO) is proposed with a wide application range in order to achieve an accurate estimation of both states and faults. Next, an improved algorithm is given to obtain the optimal estimation by using a novel iterative linear matrix inequality technique. Furthermore, an RFEO‐based output feedback fault‐tolerant controller, which is independent of the RFEO, can maintain the stability and performance of the faulty system. Simulation results of an aircraft application show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust satisfactory fault‐tolerant control of continuous‐time interval systems with time‐varying state and input delays

With the performance constraints on exponential stability, H_∞ norm of disturbance attenuation and upper bound of quadratic cost performance, the satisfactory and passive fault‐tolerant control problem is investigated for a class of interval systems with time‐varying input and state delays in the case of possible actuator faults. The bounded‐varying dynamics of actuator faults is described by interval matrix, which is more general and can be dealt with by the interval system theory. The delay‐dependent satisfactory fault‐tolerant controller design is developed based on multi‐objective optimization strategy. The results are derived in the forms of linear matrix inequalities, which is convenient to be solved in practice. Simulative example is presented to illustrate the effectiveness and necessity of the proposed fault‐tolerant control strategy. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust disturbance attenuation for discrete‐time active fault tolerant control systems with uncertainties

The problems of stochastic stability and stochastic disturbance attenuation for a class of linear discrete‐time systems are considered in this paper. The system under study is a state space model possessing two Markovian jump parameters: one is failure process and another is failure detection and isolation scheme. A controller is designed to guarantee the stochastic stability and a disturbance attenuation level. Robustness problems for the above system with norm‐bounded parameter uncertainties are also investigated. It is shown that the uncertain system can be robustly stochastically stabilized and have a robust disturbance attenuation level for all admissible perturbations if a set of coupled Riccati inequalities has solutions. A numerical example is given to show the potential of the proposed technique. Copyright © 2003 John Wiley & Sons, Ltd.     

Robust static and fixed‐order dynamic output feedback control of discrete‐time parametric uncertain Luré systems: Sequential SDP relaxation approaches

Design methods are proposed for static and fixed‐order dynamic output feedback controllers for discrete‐time Luré systems with sector‐bounded nonlinearities in the presence of parametric uncertainties described by polytopes. The derived design conditions are represented in terms of bilinear matrix inequalities, which are nonconvex. By using convex relaxation methods, controller design equations are derived for systems with multiple states, outputs, and nonlinearities in terms of linear matrix inequalities (LMIs) and iterative LMIs, which are associated with semidefinite programs. The proposed design methods are developed from stability conditions using parameter‐dependent Lyapunov functions, and existing iterative numerical methods are adapted to solve certain classes of nonconvex optimization problems for controller design. Several numerical examples are provided to illustrate and verify the proposed design methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Set‐valued observer‐based active fault‐tolerant model predictive control

This paper proposes an integrated actuator and sensor active fault‐tolerant model predictive control scheme. In this scheme, fault detection is implemented by using a set‐valued observer, fault isolation (FI) is performed by set manipulations, and fault‐tolerant control is carried out through the design of a robust model predictive control law. In this paper, a set‐valued observer is used to passively complete the fault detection task, while FI is actively performed by making use of the constraint‐handling capability of robust model predictive control. The set‐valued observer is chosen to implement fault detection and isolation (FDI) because of its simple mathematical structure that is not affected by the type of faults such as sensor, actuator, and system‐structural faults. This means that only one set‐valued observer is needed to monitor all considered actuator and sensor statuses (health and fault) and to carry out the fault detection and isolation task instead of using a bank of observers (each observer matching a health/fault status). Furthermore, in the proposed scheme, the advantage of robust model predictive control is that it can effectively deal with system constraints, disturbances, and noises and allow to implement an active FI strategy, which can improve FI sensitivity when compared with the passive FI methods. Finally, a case study based on the well‐known two‐tank system is used to illustrate the effectiveness of the proposed fault‐tolerant model predictive control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Quantized feedback fault‐tolerant H ∞ controller design for linear systems with adaptive mechanism

This paper addresses the design problem of fault‐tolerant H _∞ controller for linear systems with state quantization. By combining linear matrix inequality technique and indirect adaptive method, a new method is proposed to design a fault‐tolerant controller against actuator faults via quantized state feedback. The controller gains are updating according to the online estimation of eventual faults, which are dependent on the quantized state signals. Meanwhile, the proposed designs conditions with variable gains can be proved to be less conservative than those of the traditional controller with fixed gains. A numerical example is presented to illustrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Receding horizon control for discrete‐time multiple input delay systems

This paper is concerned with stabilization problem for discrete‐time systems with multiple input delay. By defining a new cost function, the stabilization condition is derived based on monotonically nonincreasing of the optimal cost. It is shown that if the 2 weighting matrices in the cost function satisfy the given linear matrix inequality, receding horizon controller can stabilize the input delay systems. Moreover, the explicit stabilization controller with the new cost function is obtained by solving a finite horizon optimal control problem. A numerical example illustrates the effectiveness of the proposed method.     

Estimation and synthesis of reachable set for discrete‐time periodic systems

This paper is concerned with the problems of reachable set estimation and synthesis for discrete‐time periodic systems under bounded peak disturbances. For the reachable set estimation problem, the lifting approach and the pseudo‐periodic Lyapunov function approach are utilized to determine the bounding ellipsoids for the reachable set. By using the lifting approach, the periodic system is transformed into several time‐invariant systems; then, the bounding ellipsoids are determined through the transformed time‐invariant systems. By applying the pseudo‐periodic Lyapunov function approach, the bounding ellipsoids are determined through the original periodic system directly. Genetic algorithm is adopted in the pseudo‐periodic Lyapunov function approach to search for the optimal value of the decision variables. Moreover, based on the reachable set estimation results, state‐feedback controllers are designed for manipulating the reachable set. Finally, numerical examples are presented to verify the effectiveness of the theoretical findings. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust guaranteed cost control for time‐delay fractional‐order neural networks systems

In this paper, we investigate the problem of guaranteed cost control of uncertain fractional‐order neural networks systems with time delays. By employing the Lyapunov‐Razumikhin theorem, a sufficient condition for designing a state‐feedback controller which makes the closed‐loop system asymptotically stable and guarantees an adequate cost level of performance is derived in terms of bilinear matrix inequalities. Two numerical examples are given to show the effectiveness of the obtained results.     

A 2D‐based approach to guaranteed cost repetitive control for uncertain discrete‐time systems

This paper presents a two‐dimensional (2 D)‐based approach to the problem of guaranteed cost repetitive control for uncertain discrete‐time systems. The objective is to design a control law such that the closed‐loop repetitive control system is robustly stable and a certain bound of performance criteria is guaranteed for all admissible uncertainties. It is shown first how the proposed repetitive control scheme can be equivalently formulated in the form of a distinct class of 2 D system. Then, sufficient conditions for the existence of guaranteed cost control law are derived in terms of linear matrix inequality (LMI), and the control law matrices are characterized by the feasible solutions to this LMI. Moreover, an optimization problem is introduced to efficiently solve the optimal guaranteed cost control law by minimizing the upper bound of the cost function. The proposed approach is applicable not only to SISO systems, but also to MIMO systems. Two numerical examples are provided to demonstrate the effectiveness of the proposed controller design procedures. Copyright © 2010 John Wiley & Sons, Ltd.     

A framework of robust fault estimation observer design for continuous‐time/discrete‐time systems

A design framework of the observer‐based robust fault estimation for continuous‐time/discrete‐time systems is presented in this paper. Firstly, a multiconstrained fault estimation observer under the H_∞ performance specification with the regional pole constraint is proposed to achieve robust fault estimation. Then, the existence conditions for both continuous‐time/discrete‐time systems are derived explicitly. Furthermore, by introducing slack variables, improved results on the multiconstrained fault estimation observer design are obtained such that different Lyapunov functions can be separately designed for each constraint. Finally, simulation results of a vertical takeoff and landing aircraft are presented to illustrate our contributions. Copyright © 2012 John Wiley & Sons, Ltd.     

Improved approach for passive stability of discrete‐time Markovian jump linear systems via mode‐dependent time‐delayed controllers

In this paper, we investigate the problem of passive stability for discrete‐time Markovian jump linear systems via mode‐dependent time‐delayed controllers by employing an improved free‐weighting matrix approach. A Markov process as discrete‐time, discrete‐state Markov process is considered. First, a new result of mode‐dependent stability analysis is first established for error systems without ignoring any terms in the derivative of Lyapunov–Krasovskii function by considering the relationship between the time‐varying delay and its upper bound. Then, the delay‐dependent passivity criterion is provided and a mode‐dependent time‐delayed controller is designed in terms of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

H∞ control of switched linear discrete‐time systems with polytopic uncertainties

In this paper, the problem of designing H_∞ state‐feedback controllers for switched linear discrete‐time systems with polytopic uncertainties is investigated. Two approaches on designing robust and parameter‐dependent H_∞ controllers are proposed and the existence conditions of the desired controllers are derived and formulated in terms of a set of linear matrix inequalities. By solving the corresponding convex optimization problem, the desired controllers are obtained, respectively, and different optimal H_∞ noise‐attenuation level bounds of corresponding closed‐loop systems are given as well. The designed controllers have their own advantages and disadvantages regarding the conservatism and realization complexity. An illustrative example emerging in networked control systems (NCS) and numerical simulations are presented to show the applicability and effectiveness of the obtained theoretic results. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimal fixed‐levels control for nonlinear systems with quadratic cost‐functionals

This paper is devoted to general optimal control problems (OCPs) associated with a family of nonlinear continuous‐time switched systems in the presence of some specific control constraints. The stepwise (fixed‐level type) control restrictions we consider constitute a common class of admissible controls in many real‐world engineering systems. Moreover, these control restrictions can also be interpreted as a result of a quantization procedure appglied to the inputs of a conventional dynamic system. We study control systems with a priori given time‐driven switching mechanism in the presence of a quadratic cost functional. Our aim is to develop a practically implementable control algorithm that makes it possible to calculate approximating solutions for the class of OCPs under consideration. The paper presents a newly elaborated linear quadratic‐type optimal control scheme and also contains illustrative numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

A BMI approach to guaranteed cost control of discrete‐time uncertain system with both state and input delays

In this study, the guaranteed cost control of discrete time uncertain system with both state and input delays is considered. Sufficient conditions for the existence of a memoryless state feedback guaranteed cost control law are given in the bilinear matrix inequality form, which needs much less auxiliary matrix variables and storage space. Furthermore, the design of guaranteed cost controller is reformulated as an optimization problem with a linear objective function, bilinear, and linear matrix inequalities constraints. A nonlinear semi‐definite optimization solver—PENLAB is used as a solution technique. A numerical example is given to demonstrate the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.     

Observer‐based actuator fault estimation and proportional derivative fault tolerant control for continuous‐time singular systems

This paper focuses on designing fault estimation (FE) and fault tolerant control (FTC) schemes for continuous‐time singular systems affected by actuator fault. A novel observer called the extended proportional integral observer (PIO) is designed so that the estimations of system state and actuator fault can be obtained simultaneously. In contrast with the traditional PIO, better estimation performance can be obtained by using the designed observer. Furthermore, with the obtained FE information, a novel proportional derivative–type FTC scheme is given by means of the separation property and the free‐weighting matrix technique, which ensures that the closed‐loop system is normal and stable. All the feasible conditions are formulated in linear matrix inequality (LMI) frameworks. Finally, two examples are simulated to prove the superiority and practicability of the presented scheme.     

Finite‐horizon near optimal adaptive control of uncertain linear discrete‐time systems

In this paper, the finite‐horizon near optimal adaptive regulation of linear discrete‐time systems with unknown system dynamics is presented in a forward‐in‐time manner by using adaptive dynamic programming and Q‐learning. An adaptive estimator (AE) is introduced to relax the requirement of system dynamics, and it is tuned by using Q‐learning. The time‐varying solution to the Bellman equation in adaptive dynamic programming is handled by utilizing a time‐dependent basis function, while the terminal constraint is incorporated as part of the update law of the AE. The Kalman gain is obtained by using the AE parameters, while the control input is calculated by using AE and the system state vector. Next, to relax the need for state availability, an adaptive observer is proposed so that the linear quadratic regulator design uses the reconstructed states and outputs. For the time‐invariant linear discrete‐time systems, the closed‐loop dynamics becomes non‐autonomous and involved but verified by using standard Lyapunov and geometric sequence theory. Effectiveness of the proposed approach is verified by using simulation results. The proposed linear quadratic regulator design for the uncertain linear system requires an initial admissible control input and yields a forward‐in‐time and online solution without needing value and/or policy iterations. Copyright © 2014 John Wiley & Sons, Ltd.     

H2 filter design for discrete‐time Markov jump linear systems with partly unknown transition probabilities

The H₂ filter design problem for discrete‐time Markov jump linear systems with partly unknown transition probabilities is addressed in this paper. The so‐called partly unknown transition probabilities cover two cases: one is that some unknown elements have known lower and upper bounds, the other is that some unknown elements have no information available. By employing Finsler's lemma and linear matrix inequality (LMI) technique, sufficient conditions are developed in the LMI setting to design an H₂ filter such that the filtering error system is mean‐square stable and at the same time satisfies a prescribed H₂ performance index. Numerical examples are presented to illustrate the effectiveness of the developed theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust guaranteed cost control of discrete‐time networked control systems

This paper is concerned with the robust guaranteed cost control problem for networked control systems (NCSs). The plant considered is an uncertain linear discrete‐time system, where the communication limitations include packet‐loss and signal transmission delay. Our purpose is to design a robust state‐feedback guaranteed cost controller such that the resulting closed‐loop system is robustly stable, and a specified quadratic cost function is upper bound for all admissible uncertainties under such communication limitations. A model of NCSs is established which contains two additive delay components, one being a known constant, and the other unknown constant. By introducing a novel Lyapunov‐Krasoviskii function with the idea of delay partitioning, new sufficient conditions for the existence of guaranteed cost controllers are proposed. Numerical examples are provided to demonstrate the usefulness of the developed theory. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal control for discrete‐time singular stochastic systems with input delay

The finite‐horizon linear quadratic regulation problem is considered in this paper for the discrete‐time singular systems with multiplicative noises and time delay in the input. Firstly, the extremum principle is discussed, and a stationary condition is derived for the singular stochastic system. Then, based on the relationships established between the state and the costate variables, the stationary condition is also shown to be a sufficient criterion assuring the existence of the solution for the stochastic control problem. The optimal controller is designed as a linear function of the current state and the past inputs information, which can be recursively calculated by effective algorithms. With the designed optimal controllers, the explicit expression is also derived for the minimal value of the performance index. One numerical example is provided in the end of the paper to illustrate the effectiveness of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.