Robust H^∞fuzzy control design for dithered nonlinear large‐scale systems with multiple time delays

Abstract

A novel approach is proposed in this study to stabilize nonlinear multiple time-delay (NMTD) large-scale systems via a composite of fuzzy controllers and dithers. Moreover, a delay-dependent stability criterion is derived from Lyapunov's direct method. According to this criterion and the decentralized control scheme, a set of model-based fuzzy controllers is synthesized to stabilize the NMTD large-scale system and the H ∞ control performance is achieved at the same time. If the designed fuzzy controllers cannot stabilize the NMTD large-scale system, a set of dithers (as the auxiliaries of fuzzy controllers) is simultaneously introduced to stabilize the NMTD large-scale system. Finally, a numerical example with simulations is provided to illustrate the concepts discussed throughout this paper. KEYWORDS delay-dependent stability criterion, dither, large-scale system, T-S fuzzy models Optim Control Appl Meth. 2019;40:203-225.wileyonlinelibrary.com/journal/oca HSIAO During the last decade, fuzzy control has been successfully applied to the control design of nonlinear systems (see other works 3,[9][10][11][12][13][14][15][16][17][18][19] and the references therein). In these papers, a so-called Takagi-Sugeno (T-S) fuzzy model was employed to approximate a nonlinear plant, and then, a fuzzy controller was designed to stabilize the T-S fuzzy model. All of them, however, neglect the modeling error between nonlinear systems and fuzzy models. The existence of modeling error may be a source of instability for control designs based on the assumption that the fuzzy model exactly matches the nonlinear plant. 20 Chen et al, 21 Cao and Frank, 20 Kiriakidis, 22 and Cao and Lin 23 recently proposed novel approaches to overcome the influence of modeling errors in the field of model-based fuzzy control for nonlinear systems.Furthermore, not only the stability but also the control performance of nonlinear systems is important issue for control design. The H ∞ control problem for nonlinear systems has received considerable attention over the last few years. 1,16,20,24,25 Hence, a fuzzy control design with guaranteed H ∞ control performance has been introduced for nonlinear large-scale system in this study.On the other hand, it has been long known that the injection of a high-frequency signal, known as a dither, into a nonlinear system may improve its performance (see other works [26][27][28][29][30][31][32][33][34][35] and the references therein). Better performance is viewed as less distortion in the system output, augmented stability, and quenching of limit cycles as well as jump phenomena. 30 A rigorous analysis of stability in a general nonlinear system with a dither control was given in Steinberg and Kadushin. 27 Later, Zames and Shneydor 28,29 considered a specific configuration of a system and provided a lower bond for the dither repetition frequency. Subsequently, Mossaheb 26 pointed out that the dither of sufficiently high frequency may result in output of the relaxed system and that of the dithered system as close as desir...

A RobustH∞ Fault Tolerant Controller for Uncertain Systems Described by Linear Fractional Transformation Model

“…Nowadays, numerous robust ∞ control laws have been suggested for some classes of uncertain systems. These briefly include stochastic systems [11,12], switched systems [13][14][15], Markovian jump systems [16][17][18], implicit and fuzzy degenerate jump systems [19,20], singular systems [21][22][23], uncertain linear systems with time-varying delays [24], nonlinear systems with time-delays [25,26], networked control systems [27,28], observer-based repetitive control systems [29], Takagi-Sugeno (TS) fuzzy systems [30,31], synchronization of complex dynamical networks [32], stochastic systems [33], and so on. In these methods, the uncertainties are usually modeled as either additive or multiplicative or polytopic.…”

Delay‐dependentrobust control of stochastic systems with convex polynomial uncertainty

“…For the delay‐dependent criteria, 8‐10 a Lyapunov‐Krasovskii Function (LKF) plays a major part in discussing the control issues of time‐varying delayed systems. Furthermore, the LKF was also applied for some delayed polynomial systems such as Takagi‐Sugeno fuzzy systems, 9,11,12 Markov jump systems, 13,14 large‐scale systems, 15 multi‐agent systems, 16 and linear parameter varying (LPV) systems 6,10,17 . To reduce the conservatism, reciprocal convex lemma, 8 free matrix technique, 9 and Jensen inequality 10‐13 were proposed for the relaxed stability criteria.…”