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.     

Quantized H∞ filtering for state‐delayed systems with finite frequency specifications

This paper presents a novel design approach for the finite frequency (FF) H_∞ filtering problem for discrete‐time state‐delayed systems with quantized measurements. The system state and output are assumed affected by FF external noises. Attention is focused on the design of a stable filter that guarantees the stability and a prescribed ?₂ gain performance level for the filtering error system in the FF domain of input noises. Sufficient conditions for the solvability of this problem are developed by choosing an appropriate Lyapunov‐Krasovskii functional based on the delay partitioning technique and using the FF ?₂ gain definition combined with the generalized S‐procedure. Then, by means of Finsler's lemma, the derived conditions are linearized and additional slack variables are further introduced to more flexible result. Final filter design conditions are consequently established in terms of linear matrix inequalities in three different frequency ranges, ie, low‐, middle‐ and high‐frequency range. Finally, a simulation example is presented to illustrate the effectiveness and the merits of the proposed approach.     

Robust fuzzy control and evolutionary fuzzy identification of singularly perturbed nonlinear systems with parameter uncertainty

This paper presents an H _∞ robust fuzzy control strategy which stabilizes singularly perturbed (SP) nonlinear systems with bounded uncertainties and guarantees disturbance attenuation bounds for all admissible uncertainties. The modified Takagi–Sugeno (T–S) fuzzy linear models are used to describe the SP nonlinear systems. By the proposed fuzzy control strategy, the number and type of membership functions in the fuzzy control rules are not necessarily the same as those in the fuzzy models. A sufficient condition for the existence of the H _∞ robust fuzzy controllers is then presented in terms of a novel linear matrix inequalities (LMIs) form which takes full consideration of modeling error and uncertainties in system parameters. This condition provides extra design parameters with more flexibility in control gain selection. Furthermore, we propose a compound search strategy composed of island genetic algorithms concatenated with the simplex method to identify the uncertain SP nonlinear systems for the fuzzy control design, and to solve the LMI problem. Finally, design example of the proposed H _∞ robust fuzzy controller for an uncertain SP nonlinear system is presented.     

Delay-dependent robust H ∞ controller design for a class of nonlinear uncertainty time-delay systems with input delay

Based on an appropriate Lyapunov function, this paper analyzes the design of a delay-dependent robust H _∞ state feedback control, with a focus on a class of nonlinear uncertainty linear time-delay systems with input delay using linear matrix inequalities. Under the condition that the nonlinear uncertain functions are gain bounded, a sufficient condition dependent on the delays of the state and input is presented for the existence of H _∞ controller. The proposed controller not only stabilized closed-loop uncertain systems but also guaranteed a prescribed H _∞ norm bound of closed-loop transfer matrix from the disturbance to controlled output. By solving a linear matrix inequation, we can obtain the robust H _∞ controller. An example is given to show the effectiveness of the proposed method. __________ Translated from Journal of Nanjing University of Aeronautics and Astronautics, 2007, 39(2): 159–163 [译自: 南京航空航天大学学报]     

Sampled-data filter design for large-scale interconnected systems with sensor fault and missing measurements

This article focuses on a decentralized sampled-data filter design for a class of large-scale interconnected systems. Precisely in the addressed system, the inevitable factors such as missing measurements, time-varying delays, randomly occurring uncertainties, and impulsive effects are taken into consideration. Also, we incorporated the gain perturbations and sensor faults in the proposed filter design. Furthermore, a new set of sufficient criterion has been derived by choosing an appropriate Lyapunov-Krasovskii functional that ensures the asymptotic stability of the resulting augmented filtering error system with the prescribed mixed H_∞ and passive performance index. Specifically, the corresponding filter gain matrices are derived by solving the developed sufficient criterion formulated in terms of linear matrix inequalities. The effectiveness of the proposed filter design technique are then exemplified by two numerical examples with simulations.     

Gain-scheduled H 2/ H ∞ filtering for linear discrete-time systems with polytopic uncertainties

The design of the gain-scheduled H ₂/H _∞ filter for polytopic discrete-time systems is investigated. By introducing additional slack variables, a new mixed H ₂/H _∞ performance criterion is proposed, which provides a decoupling between the Lyapunov matrix and system matrices. Based on the new performance criterion, a sufficient condition for the existence of the gain-scheduled H ₂/H _∞ filter is derived. Furthermore, the filter design problem is converted into a convex optimization problem with linear matrix inequality (LMI) constraints. Simulation results show the effectiveness of the proposed approach. __________ Translated from Control and Decision, 2007, 22(5): 540–544 [译自: 控制与决策]     

Full and reduced-order H∞ filtering of Takagi–Sugeno fuzzy time-varying delay systems: Input–output approach

This article addresses the issue of delay-dependent H_∞ filtering design for TakagiŮSugeno fuzzy time-varying delay systems using the input–output approach. A three-term approximation model has been used to transform the original system into two interconnected subsystems. Since the nonquadratic Lyapunov–Krasovskii functional requires to deal with the membership function's (MF) time derivative, upper-bound inequalities have been added to the obtained conditions. Based on the scaled small gain theorem, nonquadratic Lyapunov–Krasovskii functional approach and considering the bounds of the MF time-derivative, the H_∞ full- and reduced-order filters are designed and then formulated in terms of linear matrix inequalities. Finally, illustrative examples are presented to demonstrate the validity of the proposed methods.     

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.     

Frequency Regulation in Hybrid Power System Using Iterative Proportional-Integral-Derivative H ∞ Controller

This study considers frequency regulation in a hybrid power system consisting of conventional and distributed generation resources. The performance of two controllers—an H _∞ design via linear matrix inequalities and an iterative proportional-integral-derivative H _∞ via linear matrix inequalities—is assessed to maintain frequency deviation profile in acceptable limits. In the latter control design, the iterative linear matrix inequality approach is used to tune proportional-integral-derivative controller parameters subjected to H_∞ constraints in terms of the iterative linear matrix inequality. The efficacy of the control law and disturbance accommodation properties is shown. The robustness of these controllers is demonstrated in the hybrid power system with different load disturbance conditions, wind power, and parameter variations. Controller performance is compared with a suboptimal controller to demonstrate its superiority. It is found that the second controller design has satisfactory disturbance rejection properties and robustness against parameter variations over a wide range of conditions.     

High‐bandwidth design of hard disk control system using H∞ control with feedback‐type uncertainty

In hard disk drives, it is important to enlarge the control bandwidth in order to shorten the track pitch for larger data capacity. However, it is difficult for the H_∞ control method to increase the control bandwidth if the mechanical resonance modes have uncertainty. This is because the robustness of the H_∞ control method is assured by the small‐gain theorem for additive or multiplicative perturbation and the control bandwidth is limited by the uncertainty. In this study, we propose an H_∞ control method for high‐bandwidth design by introducing a new uncertainty model with a feedforward and a feedback path in order to reduce the conservatism of robust design. The effectiveness is shown by numerical simulations. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 173(4): 54–62, 2010; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21025     

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     

Sensitivity,robustness and efficiency of adaptation

The paper contains a brief review of some new results for the classical parametric ‘sensitivity-robustness’ problem. Some stability robustness criteria are shown and an optimal robust feedback design is presented. The main attention is paid to the performance index robustness. Sensitivity coefficients and their majorants are found for H₂- and H∞-norms of transfer functions. Analytical properties of H₂- and H∞-optimal feedback systems are investigated. In conclusion, robustification and adaptation as two competitive approaches to feedback design under parametric uncertainty are discussed.     

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.     

Youla Parameterization Robust Control Strategy Considering Power System Uncertainties

In view of the reduced low-frequency oscillation damping effect caused by inaccurate modeling of the power system due to various uncertainties, a Youla parameterization robust control strategy considering system uncertainties is proposed in this article. First, the uncertainties of the measurement error and parameter estimation are described by the perturbation matrix, and the convex polytopic model is utilized to describe uncertainties caused by variation of the operating point. Then, by solving the H₂/H_∞ inequalities, the Youla parameterization matrix is gained. Finally, the output error of the actual system to the nominal system is introduced to the output feedback control link via the Youla parameterization matrix. Thus, tracking control of the output error can be realized, as well as H₂/H_∞ robust control of the system. Simulation results show that the proposed method is immune to internal and external uncertainties. Compared with control methods without considering uncertainties, the proposed method is capable of damping low-frequency oscillation faster and more effectively with better robust performance.     

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.     

An integrated fault estimation and fault tolerant control method using H∞-based adaptive observers

An integrated fault estimation/fault-tolerant control (FTC) scheme is developed in this article for nonlinear Lipschitz systems in the presence of external disturbances and actuator failures. To address this problem, coupled uncertainties between the observer error dynamics and the control system are considered, which is conveniently ignored in control approaches based on the separation principle. An H_∞ -based adaptive observer is proposed to simultaneously estimate the system states and actuator faults without the restrictive strictly positive realness or persistent excitation conditions. The FTC is constructed by sliding mode control using the estimated states generated by the developed observer. A novel sufficient condition is derived in terms of linear matrix inequality (LMI) including both the system control dynamics and the estimation errors; then, the control parameters and observer gains are simultaneously obtained via solving the mentioned LMI based on the H_∞ optimization. Finally, a flexible joint robot is considered to illustrate the effectiveness of the developed method.     

Design of Sensitivity Function of Multirate VCM Control System

A method for designing a sensitivity function for a multiple‐input single‐output servo system is proposed. The method does not require weighting or weighting functions, unlike linear‐quadratic (LQ) or H_∞ design. First, a controller candidate is derived by taking into consideration the robustness specification for the plant system. Then, the sensitivity function is derived from the gain specification of the sensitivity function. As the design of a multirate controller can be shown to be equivalent to a multiple‐input single‐output system, the method is employed to design a multirate VCM position control system. The multirate controller is designed such that at frequencies higher than the Nyquist frequency, the desired robustness is achieved. © 2013 Wiley Periodicals, Inc. Electr Eng Jpn, 185(4): 53–59, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.22296     

H∞ filtering of discrete-time switched singular systems with time-varying delays

In this article, the analysis and design problems of H_∞ filtering for a class of discrete-time switched singular systems with time-varying delay under an arbitrary switching signal are investigated. The main attention is focused on the design of a linear mode-dependent filter guaranteeing the regularity, causality, and asymptotic stability of the resulting filtering error system with a prescribed H_∞ performance bound. By using a multiple Lyapunov-Krasovskii functional, and utilizing the linearization technique, novel sufficient conditions for the solvability of H_∞ problem are derived in terms of linear matrix inequalities. Solving that, the desired filter gains can be determined. Any model transformation of system, which often leads the large computational burden is involved. The free weighting matrix technique is introduced to provide additional degree of freedom, which improves the conservativeness of the developed method. Finally, numerical examples are given to demonstrate the effectiveness and the merit of the proposed approach and to compare the obtained results with some previous works in the literature.     

MAP moving horizon estimation for threshold measurements with application to field monitoring

This paper deals with state estimation of a spatially distributed system given noisy measurements from pointwise-in-time-and-space threshold sensors spread over the spatial domain of interest. A maximum a posteriori probability (MAP) approach is undertaken and a moving horizon (MH) approximation of the MAP cost function is adopted. It is proved that, under system linearity and log-concavity of the noise probability density functions, the proposed MH-MAP state estimator amounts to the solution, at each sampling interval, of a convex optimization problem. Moreover, a suitable centralized solution for large-scale systems is proposed with a substantial decrease of the computational complexity. The latter algorithm is shown to be feasible for the state estimation of spatially dependent dynamic fields described by partial differential equations via the use of the finite element spatial discretization method. A simulation case study concerning estimation of a diffusion field is presented in order to demonstrate the effectiveness of the proposed approach. Quite remarkably, the numerical tests exhibit a noise-assisted behavior of the proposed approach in that the estimation accuracy results optimal in the presence of measurement noise with non-null variance.