LMI-based adaptive reliable H∞ static output feedback control against switched actuator failures

This paper investigates the H_∞ static output feedback (SOF) control problem for switched linear system under arbitrary switching, where the actuator failure models are considered to depend on switching signal. An active reliable control scheme is developed by combination of linear matrix inequality (LMI) method and adaptive mechanism. First, by exploiting variable substitution and Finsler's lemma, new LMI conditions are given for designing the SOF controller. Compared to the existing results, the proposed design conditions are more relaxed and can be applied to a wider class of no-fault linear systems. Then a novel adaptive mechanism is established, where the inverses of switched failure scaling factors are estimated online to accommodate the effects of actuator failure on systems. Two main difficulties arise: first is how to design the switched adaptive laws to prevent the missing of estimating information due to switching; second is how to construct a common Lyapunov function based on a switched estimate error term. It is shown that the new method can give less conservative results than that for the traditional control design with fixed gain matrices. Finally, simulation results on the HiMAT aircraft are given to show the effectiveness of the proposed approaches.     

H ∞ control of networked control systems with state quantisation

This article addresses the problem of controller design for networked control systems over digital communication. The systems under consideration are stabilised via state feedback, where the effects of sampled signal, state quantisation, network-induced delay and packet dropout are considered. The proposed delay-dependent stability criteria are formulated in the form of a linear matrix inequality, which ensure asymptotic stability and a prescribed H _∞ performance level for networked control systems with admissible uncertainties. Maximum allowable delay bound of networked control systems is obtained by solving a convex optimisation problem. Furthermore, a numerical example is given to illustrate the effectiveness of the main result.     

Sampled-data H ∞ control for networked control systems with digital control inputs

In this article, the problem of sampled-data H _∞ control for networked control systems (NCSs) with digital control inputs is considered, where the physical plant is modelled as a continuous-time one, and the control inputs are discrete-time signals. By exploiting a novel Lyapunov–Krasovskii functional, using the Leibniz–Newton formula and a free-weighting matrix method, sufficient conditions for sampled-data H _∞ performance analysis and H _∞ controller design for such systems are given. Since the obtained conditions of H _∞ controller design are not expressed strictly in term of linear matrix inequalities, the sampled-data H _∞ controller is solved using modified cone complementary linearisation algorithm. In addition, the new sampled-data stability criteria for the NCSs is proved to be less conservative than some existing results. Numerical examples demonstrate the effectiveness of the proposed methods.     

LMI-based H ∞ synchronization of second-order neutral master-slave systems using delayed output feedback control

The H _∞ synchronization problem of the master and slave structure of a second-order neutral master-slave systems with time-varying delays is presented in this paper. Delay-dependent sufficient conditions for the design of a delayed output-feedback control are given by Lyapunov-Krasovskii method in terms of a linear matrix inequality (LMI). A controller, which guarantees H _∞ synchronization of the master and slave structure using some free weighting matrices, is then developed. A numerical example has been given to show the effectiveness of the method. The simulation results illustrate the effectiveness of the proposed methodology. Recommended by Editorial Board member Bin Jiang under the direction of Editor Jae Weon Choi. This research has been partially funded by the German Research Foundation (DFG) as part of the Collaborative Research Center 637 ‘Autonomous Cooperating Logistic Processes: A Paradigm Shift and its Limitations’ (SFB 637). This work was supported in part by the National Natural Science Foundation of China (60504008), by the Research Fund for the Doctoral Program of Higher Education of China (20070213084), by the Fok Ying Tung Education Foundation (111064). Hamid Reza Karimi born in 1976, received the B.Sc. degree in Power Systems Engineering from Sharif University of Technology in 1998 and M.Sc. and Ph.D. degrees both in Control Systems Engineering from University of Tehran in 2001 and 2005, respectively. From 2006 to 2007, he was a Post-doctoral Research Fellow of the Alexander-von-Humboldt Stiftung with both Technical University of Munich and University of Bremen in Germany. He held positions as Assistant Professor at the Department of Electrical Engineering of the University of Tehran in Iran, Senior Research Fellow in the Centre for Industrial Mathematics of the University of Bremen in Germany and Research Fellow of Juan de la Cierva program at the Department of Electronics, Informatics and Automation of the University of Girona in Spain before he was appointed as an Associate Professor in Control Systems at the Faculty of Technology and Science of the University of Agder in Norway in April 2009. His research interests are in the areas of nonlinear systems, networked control systems, robust filter design and vibration control of flexible structures with an emphasis on applications in engineering. Dr. Karimi was the recipient of the German Academic Awards (DAAD Award) from 2003 to 2005 and was a recipient of the Distinguished Researcher Award from University of Tehran in 2001 and 2005. He received the Distinguished PhD Award of the Iranian President in 2005 and the Iranian Students Book Agency’s Award for Outstanding Doctoral Thesis in 2007. He also received first rank of Juan de la Cierva research program in the field of Electrical, Electronic and Automation Engineering in Spain in 2007. Huijun Gao was born in Heilongjiang Province, China, in 1976. He received the M.S. degree in Electrical Engineering from Shenyang University of Technology, Shengyang, China, in 2001 and the Ph.D. degree in Control Science and Engineering from Harbin Institute of Technology, Harbin, China, in 2005. He was a Research Associate with the Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, from November 2003 to August 2004. From October 2005 to September 2007, he carried out his postdoctoral research with the Department of Electrical and Computer Engineering, University of Alberta, Canada, supported by an Alberta Ingenuity Fellowship and an Honorary Izaak Walton Killam Memorial Postdoctoral Fellowship. Since November 2004, he has been with Harbin Institute of Technology, where he is currently a Professor. His research interests include network-based control, robust control/filter theory, model reduction, time-delay systems, multidimensional systems, and their engineering applications. Dr. Gao is an Associate Editor for the IEEE Transactions on Systems, Man and Cybernetics Part B: Cybernetics, the Journal of Intelligent and Robotics Systems, the Circuits, System and Signal Processing etc. He serves on the Editorial Board of the International Journal of Systems Science, the Journal of the Franklin Institute etc. He was the recipient of the University of Alberta Dorothy J. Killam Memorial Postdoctoral Fellow Prize in 2005 and was a corecipient of the National Natural Science Award of China in 2008. He was a recipient of the National Outstanding Youth Science Fund in 2008 and the National Outstanding Doctoral Thesis Award in 2007. He was an outstanding reviewer for IEEE Transactions on Automatic Control and Automatica in 2008 and 2007 respectively, and an appreciated reviewer for IEEE Transactions on Signal Processing in 2006.     

H ∞ Optimal control

Our aim in this paper is to develop a new approach for solving the H ^∞ optimal control problem where the feedback arrangement takes the form of a linear fractional transformation. The paper is in two parts. In Part 1, a basic kind of model-matching problem is considered: given rational matrices M(s) and N(s), the H ^∞-norm of an error function defined as E(s)=M(s) – N(s)Q(s) is minimized (or bounded) subject to E(s) and Q(s) being stable. Closed-form state-space characterizations are obtained for both E(s) and Q(s). The results established here will be used in Part 2 of the paper (Hung 1989) to solve the H ^∞ optimal control problem.     

H2/H∞ control for stochastic systems with delay

This paper is concerned with the H₂/H_∞ control problem for stochastic linear systems with delay in state, control and external disturbance-dependent noise. A necessary and sufficient condition for the existence of a unique solution to the control problem is derived. The resulting solution is characterised by a kind of complex generalised forward–backward stochastic differential equations with stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the equivalent feedback solution via a new type of Riccati equations. To explain the theoretical results, we apply them to a population control problem.     

H ∞ control of a suspension with a magnetorheological damper

This research work presents an H _∞ controller based on a Takagi–Sugeno (T–S) fuzzy model for a two-degrees-of-freedom (2-DOF) one-quarter-vehicle semi-active suspension with a magnetorheological damper where the actuator dynamics are included in the control synthesis. These dynamics enclose nonlinear damper phenomena, avoided in many other studies, and that can improve the suspension system by means of a more accurate model. The objective is to obtain a semi-active suspension that considerably improves the passive suspension efficiency based on some frequency domain performance criteria. The advantage of having the T–S system as a reference is that each piecewise linear system can be exposed to the well-known control theory. Besides, the proposed solution is compared with the recent reported work to highlight its advantages. A case of study is included and simulation work supports the results. The methodology applied herein can be extended to a half-vehicle model, and to the four wheels to have a global chassis control in order to maximise passenger comfort and vehicle stability.     

H ∞ output-feedback LPV control for systems with input saturation

This paper investigates the problem of designing a dynamic H _∞ output-feedback controller under an L _∞ performance representing componentwise input constraints. In order to derive a less conservative stabilization condition therein, this paper introduces a Lyapunov function-based polytopic control law and proposes a method capable of applying the information on interpolation parameters appearing in the procedure of representing saturation nonlinearity as convex polytope. Through this paper, the resultant H _∞/L _∞ problem is efficiently solved based on the set invariance condition formulated in terms of linear matrix inequalities (LMIs).     

H ∞ predictive control of networked control systems

This article is concerned with the problem of H _∞ predictive control of networked control system with random network delay. A new control scheme termed networked predictive control is proposed. This scheme mainly consists of the control prediction generator and network delay compensator. While designing the predictor, the control input to the actuator may be different due to networked induced time-delay and data dropout, and two cases are considered depending on the way that the observer obtains the plant control input u _t . The necessary and sufficient conditions are given for the closed-loop networked predictive control system to be stochastically stable for different u _t and random network delays in controller to actuator channel (CAC) and sensor to controller channel (SCC). A simulation study shows the effectiveness of the proposed scheme.     

H∞ and H2 control of multi-agent systems with transient performance improvement

In this paper, the H_∞ consensus control and H₂ robust control synthesised with transient performance problems are investigated for a group of autonomous agents with linear or linearised dynamics. Based on the relative information between neighbouring agents and a subset of absolute information of the agents, distributed controllers are proposed for both H_∞ and H₂ cases. Compared with the existing protocols, the one presented in this article focuses on improving the transient performance of the consensus problem. By using the tools from matrix analysis and robust control theory, conditions for the existence of controllers to those problems under an undirected communication topology are provided. Then, it is shown that the H₂ performance limit of uncertain systems under a distributed controller equals the minimum H_∞ consensus index synthesised with transient performance of a single agent by using a state feedback controller, independent of the communication topology. Finally, a simulation example as an application in Raptor-90 helicopter is proposed to illustrate the effectiveness of the theoretical results.     

Mixed H2/H∞ robust model predictive control with saturated inputs

In this paper, we investigate the mixed H₂/H_∞ robust model predictive control (RMPC) for polytopic uncertain systems, which refers to the infinite horizon optimal guaranteed cost control (OGCC). To fully use the capability of actuators, we adopt a saturating feedback control law as the control strategy of RMPC. As the saturating feedback control law can be effectively represented by the convex hull of a group of auxiliary linear feedback laws, the auxiliary feedback laws allow us to design the actual feedback control law without consideration of the input constraints directly to achieve the improved performance. Moreover, we suggest the relative weights on the actual and auxiliary feedback laws to the RMPC, which in turn improves the closed-loop system performance. Furthermore, an off-line design of the proposed RMPC is also developed to make it more practical. Numerical studies demonstrate the effectiveness of the proposed algorithm.     

Discrete-time H ∞ and H 2 control with structured disturbances and probability-relaxed requirements

This paper presents a method that reduces the conservatism inherent in the disturbance representation in standard H _∞ theory. It addresses several discrete-time control synthesis problems where the disturbances acting on the system are structured by a convex family of linear filters (‘signal polytope’) and where the system disturbance attenuation level attained over the signal polytope is ensured to (just) a prescribed probability. This setup enables realistic multi-feature disturbance delimiting while accounting for uncertainty in the disturbance model itself by allowing probability waivers. The core of the probability aspects of the proposed solutions is the search for a truncated signal polytope which provides both the required probability and the best robust disturbance attenuation level. Many examples are given, including one of an aircraft output-feedback control with a polytope of low-pass filters representing different wind phenomena. The examples demonstrate that addressing realistic disturbances results in better control designs (hence better performance) and that a small certainty waiver can yield a large performance gain.     

Saturating composite disturbance-observer-based control and H ∞ control for discrete time-delay systems with nonlinearity

This note is concerned with a saturating composite disturbance-observer-based control (DOBC) and H _∞ control for a class of discrete time-delay systems with nonlinearity and disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other is supposed to have the bounded H ₂ norm, which can represent parametric uncertainties and external disturbance existing in the controlled object. The design approaches of reduced-order disturbance observer are presented for the estimation of the disturbance. By composite control law with saturation, the disturbances can be rejected and attenuated, simultaneously, the desired dynamic performances can be guaranteed for discrete time-delay systems with known and unknown nonlinear dynamics, respectively. Simulation for a flight control system is provided to show the effectiveness of the proposed scheme compared with the previous schemes.     

Design of H ∞ control of neural networks with time-varying delays

This paper deals with the H _∞ control problem of neural networks with time-varying delays. The system under consideration is subject to time-varying delays and various activation functions. Based on constructing some suitable Lyapunov–Krasovskii functionals, we establish new sufficient conditions for H _∞ control for two cases of time-varying delays: (1) the delays are differentiable and have an upper bound of the delay-derivatives and (2) the delays are bounded but not necessary to be differentiable. The derived conditions are formulated in terms of linear matrix inequalities, which allow simultaneous computation of two bounds that characterize the exponential stability rate of the solution. Numerical examples are given to illustrate the effectiveness of our results.

     

H∞ control of switched delayed systems with average dwell time

This paper considers the problems of stability analysis and H_∞ controller design of time-delay switched systems with average dwell time. In order to obtain less conservative results than what is seen in the literature, a tighter bound for the state delay term is estimated. Based on the scaled small gain theorem and the model transformation method, an improved exponential stability criterion for time-delay switched systems with average dwell time is formulated in the form of convex matrix inequalities. The aim of the proposed approach is to reduce the minimal average dwell time of the systems, which is made possible by a new Lyapunov–Krasovskii functional combined with the scaled small gain theorem. It is shown that this approach is able to tolerate a smaller dwell time or a larger admissible delay bound for the given conditions than most of the approaches seen in the literature. Moreover, the exponential H_∞ controller can be constructed by solving a set of conditions, which is developed on the basis of the exponential stability criterion. Simulation examples illustrate the effectiveness of the proposed method.     

H∞control of interconnected nonlinear sampled-data systems with parametric uncertainty

This paper studies the problem of robust control design for a class of interconnected uncertain systems under sampled measurements. The class of system under consideration is described by a state space model containing unknown cone bounded nonlinear interaction and time-varying norm-bounded parameter uncertainties in both state and output equations. Our attention is focused on the design of linear dynamic output feedback controllers using sampled measurements. We address the problem of robust H_∞ control in which both robust stability and a prescribed H_∞ performance are required to be achieved irrespective of the uncertainties and nonlinearities. The H_∞ performance measure involves both continuous-time and discrete-time signals. It has been shown that the above problems can be recast into H_∞ syntheses for related N decoupled linear sampled-data systems without parameter uncertainties and unknown nonlinearities, which can be solved in terms of Riccati differential equations with finite discrete jumps. A numerical example is given to show the potential of the proposed technique.