Teaching sampled‐data H∞ control theory using arm robot experiment system

This paper explains how to use an arm robot experiment system to teach sampled‐data H_∞ control theory. A design procedure is presented for a digital tracking control system for a continuous plant with structured uncertainties; the target is the positioning control of an arm robot. To guarantee the robust stability of the closed‐loop system and provide the desired closed‐loop performance, the design problem is first formulated as a sampled‐data H_∞ control problem, and is then transformed into an equivalent discrete‐time H_∞ control problem. Finally, linear matrix inequalities are used to obtain a reduced‐order output‐feedback controller and a static state‐feedback controller. In a course, the design procedure is explained and practice is provided through simulations and experiments. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Robust learning controller design for MIMO stochastic discrete‐time systems: An H∞‐based approach

This paper is devoted to designing iterative learning control (ILC) for multiple‐input multiple‐output discrete‐time systems that are subject to random disturbances varying from iteration to iteration. Using the super‐vector approach to ILC, statistical expressions are presented for both expectation and variance of the tracking error, and time‐domain conditions are developed to ensure their asymptotic stability and monotonic convergence. It shows that time‐domain conditions can be tied together with an H_∞‐based condition in the frequency domain by considering the properties of block Toeplitz matrices. This makes it possible to apply the linear matrix inequality technique to describe the convergence conditions and to obtain formulas for the control law design. Furthermore, the H_∞‐based approach is shown applicable to ILC design regardless of the system relative degree, which can also be used to address issues of model uncertainty. For a class of systems with a relative degree of one, simulation tests are provided to illustrate the effectiveness of the H_∞‐based approach to robust ILC design. Copyright © 2011 John Wiley & Sons, Ltd.     

H∞ filtering for continuous‐time singular systems with time‐varying delay

This paper focuses on H_∞ filter design for continuous‐time singular systems with time‐varying delay. A delay‐dependent H_∞ performance analysis result is first established for error systems via a novel estimation method. By combining a well‐known inequality with a delay partition technique, the upper bound of the derivative of the Lyapunov functional is estimated more tightly and expressed as a convex combination with respect to the reciprocal of the delay rather than the delay. Based on the derived H_∞ performance analysis results, a regular and impulse‐free H_∞ filter is designed in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the merits of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Neural‐network‐based finite‐time H∞ control for extended Markov jump nonlinear systems

This paper presents a neural‐network‐based finite‐time H_∞ control design technique for a class of extended Markov jump nonlinear systems. The considered stochastic character is described by a Markov process, but with only partially known transition jump rates. The sufficient conditions for the existence of the desired controller are derived in terms of linear matrix inequalities such that the closed‐loop system trajectory stays within a prescribed bound in a fixed time interval and has a guaranteed H_∞ noise attenuation performance for all admissible uncertainties and approximation errors of the neural networks. A numerical example is used to illustrate the effectiveness of the developed theoretic results. Copyright © 2009 John Wiley & Sons, Ltd.     

Adaptive robust H∞ state feedback control for linear uncertain systems with time‐varying delay

This paper considers the problem of adaptive robust H_∞ state feedback control for linear uncertain systems with time‐varying delay. The uncertainties are assumed to be time varying, unknown, but bounded. A new adaptive robust H_∞ controller is presented, whose gains are updating automatically according to the online estimates of uncertain parameters. By combining an indirect adaptive control method and a linear matrix inequality method, sufficient conditions with less conservativeness than those of the corresponding controller with fixed gains are given to guarantee robust asymptotic stability and H_∞ performance of the closed‐loop systems. A numerical example and its simulation results are given to demonstrate the effectiveness and the benefits of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Stochastic H∞ control problem with state‐dependent noise for weakly coupled large‐scale systems

In this paper, stochastic H_∞ state feedback control with state‐dependent noise for weakly coupled large‐scale systems is discussed. After establishing the asymptotic structure of the stochastic algebraic Riccati equation (SARE), a new iterative algorithm that combines the Newton's method with the fixed‐point algorithm is derived for the first time. As a result, both the quadratic convergence and the reduced‐order computation in the same dimension of the subsystems are attained. Copyright © 2007 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Stability and H∞ performance of multiple‐delay systems with successive delay components

This paper presents a new model for linear time‐delay systems with multiple delayed states where each delay contains finite number of successive components with different time‐varying properties, referred to as multiple‐delay system with successive time‐varying delay components (MDSSTDCs). General stability result and H_∞ performance conditions, under which the MDSSTDCs are asymptotically stable with certain H_∞ disturbance attenuation level, are derived by exploiting a general Lyapunov–Krasovskii functional and by making use of novel techniques for time‐delay systems. The result is applied to two special types of time‐delay systems frequently used in engineering applications and corresponding conditions for stability and H_∞ performance are obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Delay‐dependent model reduction for continuous‐time switched state‐delayed systems

This paper studies the problem of exponential H_∞ model reduction for continuous‐time switched delay system under average dwell time (ADT) switching signals. Time delay under consideration is interval time varying. Our attention is focused on the construction of the desired reduced order models, which guarantee that the resulting error systems under ADT switching signals are exponentially stable with an H_∞ norm bound. By introducing a block matrix and making use of the ADT approach, delay‐dependent sufficient conditions for the existence of reduced order models are derived and formulated in terms of strict linear matrix inequalities (LMIs). Owing to the absence of non‐convex constraints, it is tractable to construct an admissible reduced order model. The effectiveness of the proposed methods is illustrated via two numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

On robust H∞ filtering of uncertain Markovian jump time‐delay systems

This paper is concerned with the problems of stability analysis, H_∞ performance analysis, and robust H_∞ filter design for uncertain Markovian jump linear systems with time‐varying delays. The purpose is to improve the existing results on these problems. Firstly, a new delay‐dependent stability criterion is obtained on the basis of a novel mode‐dependent Lyapunov functional. Secondly, a new delay‐dependent bounded real lemma (BRL) is derived. It is shown that the presented stability criterion and the BRL are less conservative than the existing ones in the literature. Thirdly, with the new BRL, delay‐dependent conditions for the solvability of the addressed H_∞ filtering problem are given. All the results obtained in this paper are expressed by means of strict linear matrix inequalities. Three numerical examples are provided to demonstrate the utility of the proposed methods. Copyright © 2011 John Wiley & Sons, Ltd.     

Fault‐tolerant control for wireless networked control systems with an integrated scheduler

This paper addresses a study of fault‐tolerant control (FTC) for wireless networked control systems (WNCSs) in industrial automatic processes. The WNCSs is composed of many subsystems, which operate with different sampling cycles. In order to meet the real‐time requirements and ensure a deterministic data transmission, the time division multiple access (TDMA) mechanism is adopted in WNCSs. The data in WNCSs are transmitted following a TDMA‐based scheduler. According to the periodicity, WNCSs integrated with the scheduler is first formulated as discrete linear time periodic systems (LTPSs). Afterwards, a fault estimation method for LTPSs is developed under a H_∞ performance specification with a regional pole constraint. With the achieved state observer and fault estimator, an FTC strategy for LTPSs is explored. Finally, the proposed methods are verified on a physical experimental WiNC platform. Copyright © 2016 John Wiley & Sons, Ltd.     

Stabilization control for multimachine system using decentralized H∞ excitation controller realizing terminal voltage control and damping control

In this paper, to achieve both damping of power system oscillation and terminal voltage control simultaneously on a multimachine power system, we propose a decentralized H_∞ excitation controller. In the proposed method, H_∞ control via the Normalized Coprime Factorization approach is used to achieve the proposed design idea. By the Normalized Coprime Factorization approach, the weighting function in H_∞ control design is simplified, and output feedback controllers that take into account the realities and constraints of the power systems are designed. The proposed controller is subjected to model reduction of H_∞ controllers, and is transformed to a discrete system to perform digital control by computer systems in consideration of application to a real system. We verify that the proposed excitation controller can achieve both damping of power system oscillation and terminal voltage control by computer simulations of a multimachine power system. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 147(1): 33–41, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10254     

Robust H∞ filtering for uncertain Markovian jump systems with mode‐dependent distributed delays

This paper deals with the problem of robust H_∞ filter design for Markovian jump systems with norm‐bounded time‐varying parameter uncertainties and mode‐dependent distributed delays. Both the state and the measurement equations are assumed to be with distributed delays. Sufficient conditions for the existence of robust H_∞ filters are obtained. Via solving a set of linear matrix inequalities, a desired filter can be constructed. The developed theory is illustrated by a simulation example. Copyright © 2009 John Wiley & Sons, Ltd.     

Multivariable performance‐constrained sliding mode control for ship yaw‐motion systems with perturbations*

A performance‐constrained sliding mode controller will be proposed to satisfy the pole assignment, H_∞ norm, and individual variance constraints for linear perturbed MIMO systems. Application of this controller involves a simulation of the linearized perturbed ship steering yaw‐motion systems which will be provided for demonstration of the effectiveness of the present methodology. The control law developed in this paper is designed in the framework of a combination of the concept of the sliding mode control with the theory of upper bound covariance control. Copyright © 2000 John Wiley & Sons, Ltd.     

Fault detection for a class of nonlinear networked control systems

In this paper, an observer‐based fault detection (FD) method is presented for a class of nonlinear networked control systems (NCSs) with Markov transfer delays. Firstly, based on Euler approximate method, a nonlinear NCS model with uncertainty is proposed using the Takagi‐Sugeno (T‐S) fuzzy model. Some geometric conditions are given to transfer the NCS model into an output‐feedback form. Then, the H_∞ FD observer is designed such that the estimation error (residual) converges to zero, if there exist no fault and uncertainty in the system, or the residual is minimized in the sense of H_∞ norm, when system contains fault and uncertainties. Furthermore, to simplify the model, the approximate model without uncertainty is considered. Then, sufficient conditions for the existence of FD observer gain and the sampling time of NCSs are given to achieve the semiglobal practical property. An inverted pendulum example is used to illustrate the efficiency of the developed techniques. Copyright © 2009 John Wiley & Sons, Ltd.     

LMI solutions to the mixed ℋ︁−/ℋ︁∞ fault detection observer design for linear parameter‐varying systems

This paper addresses the mixed ??_?/??_∞ fault detection observer design issue for a class of linear parameter‐varying (LPV) systems. Analogous to the definition of the quadratic ??_∞ performance for LPV systems and the ??_? index for linear time invariant (LTI) systems, the quadratic ??_? index and the affine quadratic ??_? index for LPV systems are defined in terms of linear matrix inequalities (LMIs). The first algorithm for designing the mixed ??_?/H_∞ observer is proposed, which aims at minimizing the quadratic ??_∞ performance and maximizing the quadratic ??_? index of the observer error dynamic systems. To reduce the conservativeness of this algorithm, the affine quadratic ??_∞ performance and the affine ??_? index for LPV systems are utilized. The robustness conditions and affine ??_? index conditions for the underlying observer optimization issue are formulated as parameter‐dependent LMIs. The Gridding technique and multi‐convexity concept are applied, respectively, for reducing the parameter‐dependent LMIs to finite LMI constraints. Correspondingly, two iterative algorithms are proposed. Furthermore, the threshold design and the estimation of the worst undetectable fault size are investigated. An example is studied to demonstrate the effectiveness of the proposed algorithms. Copyright © 2010 John Wiley & Sons, Ltd.     

Mode‐independent H∞ filtering for discrete‐time Markov jump linear system with parametric uncertainties and quantized measurements

This paper is concerned with the problem of H_∞ filtering for discrete‐time Markov jump linear system with parametric uncertainties and quantized measurements, when the jumping mode information is not accessible. By converting the quantized errors into a sector‐bounded nonlinearity, the parametric uncertainties and measurements quantization are dealt with in a unified framework. The mode‐independent H_∞ filter is designed, and sufficient conditions are established via Lyapunov function approach, such that for all possible uncertain parameters and quantization errors, the resulting filtering error system is robustly stochastically stable and achieves a guaranteed H_∞ filtering error performance index. A numerical example is provided to demonstrate the feasibility and effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Delay‐dependent H∞ performance analysis and filtering for Markovian jump systems with interval time‐varying delays

This paper investigates the problems of H_∞ disturbance attenuation and H_∞ filtering for Markovian jump systems with interval time‐varying delays. In terms of linear matrix inequalities, a less conservative delay‐range‐dependent H_∞ performance condition for Markovian jump systems is proposed by constructing a different Lyapunov–Krasovskii functional. The resulting criterion has advantages over some previous ones in that they involve fewer matrix variables, but has less conservatism. Based on this new condition, an improved H_∞ filtering algorithm is developed. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper. Copyright © 2009 John Wiley & Sons, Ltd.     

Adaptive internal model control: the discrete‐time case

This paper considers the design and analysis of a discrete‐time H₂ optimal robust adaptive controller based on the internal model control structure. The certainty equivalence principle of adaptive control is used to combine a discrete‐time robust adaptive law with a discrete‐time H₂ internal model controller to obtain a discrete‐time adaptive H₂ internal model control scheme with provable guarantees of stability and robustness. The approach used parallels the earlier results obtained for the continuous‐time case. Nevertheless, there are some differences which, together with the widespread use of digital computers for controls applications, justifies a separate exposition. Copyright © 2001 John Wiley & Sons, Ltd.     

Output‐feedback H∞ quadratic tracking control of linear systems using reinforcement learning

This paper presents an online learning algorithm based on integral reinforcement learning (IRL) to design an output‐feedback (OPFB) H_∞ tracking controller for partially unknown linear continuous‐time systems. Although reinforcement learning techniques have been successfully applied to find optimal state‐feedback controllers, in most control applications, it is not practical to measure the full system states. Therefore, it is desired to design OPFB controllers. To this end, a general bounded L₂ ‐gain tracking problem with a discounted performance function is used for the OPFB H_∞ tracking. A tracking game algebraic Riccati equation is then developed that gives a Nash equilibrium solution to the associated min‐max optimization problem. An IRL algorithm is then developed to solve the game algebraic Riccati equation online without requiring complete knowledge of the system dynamics. The proposed IRL‐based algorithm solves an IRL Bellman equation in each iteration online in real time to evaluate an OPFB policy and updates the OPFB gain using the information given by the evaluated policy. An adaptive observer is used to provide the knowledge of the full states for the IRL Bellman equation during learning. However, the observer is not needed after the learning process is finished. A simulation example is provided to verify the convergence of the proposed algorithm to a suboptimal OPFB solution and the performance of the proposed method.     

Balancing control for dispersed generators considering torsional torque suppression and AVR performance for synchronous generators

Electric utility deregulation enabled PPSs (Power Producers and Suppliers) to enter the electricity market. PPSs are supposed to achieve 30‐minute balancing control for stable power supply of electric power. In addition, load rejection and instantaneous voltage drops greatly affect turbine shafting, that is, torsional torque oscillation. Therefore, PPSs must consider a reduction of torsional torque in order to prevent generator shaft damage. This paper proposes a control system which allows the achievement of both 30‐minute balancing control and reduction of torsional torque by using an H_∞ controller. The effectiveness of the proposed controller is validated by using MATLAB. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 170(1): 16–25, 2010; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20868