Non-monotonic Approach to Robust H∞ Control of Multi-model Systems

By Jiwei Wen, Alireza Nasiri, Sing Kiong Nguang and Dhafer J. Almakhles

Non-monotonic Approach to Robust H8 Control of Multi-model Systems focuses on robust analysis and synthesis problems for multi-model systems based on the non-monotonic Lyapunov Functionals (LFs) approach that enlarges the stability region and improves control performance. By fully considering the diversity of switching laws, the multi-step time difference, the multi-step prediction, and the expansion of system dimension, the non-monotonic LF can be properly constructed. The focus of this book is placed on the H8 state feedback control, H8 filtering and H8 output feedback control for multi-model systems via a non-monotonic LF approach.

The book's authors provide illustrative examples to show the feasibility and efficiency of the proposed methods, along with practical examples that demonstrate the effectiveness and potential of theoretical results.

• Offers tools for the analysis and design of control processes where the process can be represented by multi-models
• Presents a comprehensive explanation of recent developments in non-monotonic approaches to robust H-infinity control of multi-model systems
• Gives numerical examples and simulation results in each chapter to demonstrate engineering potential

• Language: English
• Publisher: Academic Press
• Release date: Jun 6, 2019
• ISBN: 9780128148693

Jiwei Wen

Jiwei Wen received his Ph.D. degree in Control Science and Control Engineering from Jiangnan University, Wuxi, China, in 2011. From 2015 to 2016, he was a visiting scholar with the Department of Electrical and Computer Engineering, University of Auckland. Currently, he is an associate professor of School of Internet of Things Engineering, Jiangnan University, Wuxi, China. He is also a researcher in the Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Wuxi, China. His research interests include non-monotonic filtering and control approach, stochastic switched system, model predictive control and T-S fuzzy modelling and control. He has/had served as reviewer of a number of international journals. He is an Associate Editor of the International Journal of Sensors, Wireless Communications and Control.

Book preview

(DP170102644).

Chapter 1

Introduction

Abstract

output feedback control for multimodel systems via nonmonotonic LF approaches.

Keywords

Multimodel systems; T-S fuzzy systems; Nonhomogenous Markovian jump systems; Switched systems; Nonmonotonic Lyapunov function approach; filtering; feedback control

1.1 Nonmonotonic Approach and Multimodel System

1.1.1 Nonmonotonic Approach

Modern control theory involves many research fields with a set of rigorous analysis and synthesis methods. In control systems theory, stability analysis is the foundation of almost all approaches. By taking the system uncertainties into consideration, the so-called robust stability is also a hot research topic in the last twenty years. The concepts of the asymptotic stability [1], global uniform asymptotic stability (GUAS) [2], stochastic stability [3], etc. usually aim at the equilibrium points of the dynamical systems. The depth and breadth of their theoretical developments are far beyond solving specific problems of certain control systems. As a sufficient condition, Lyapunov stability is a simple and straightforward approach to address the stability analysis problem by properly choosing or constructing a Lyapunov function (LF). However, from an engineering point of view, it inevitably introduces conservativeness to some extent. Therefore, many research efforts are devoted to conservatism reduction problem, for example, designing parameter-dependent LF [4], discussing the necessity condition [5], etc. Some of these approaches successfully reduced the conservatism to a certain extent; other approaches got the analysis results but brought severe difficulties to the controller synthesis. However, none of these approaches fundamentally solved all the analysis and synthesis problems of the controlled systems. Generally, it is believed that if the framework of Lyapunov stability based on the equilibrium point is not breached, then the excessive search for the necessary conditions will gradually remove the research from the engineering background. As a matter of fact, many engineering problems can be solved only by sufficient conditions.

eventually; a natural question arises: Is the monotonic decreasing of V ?. Actually, some pioneering work already proposed NLFs in the continuous-time domain when Butz to obtain a sufficient condition of GUAS. The obtained condition in [6], however, cannot be transformed into a convex optimization problem. Subsequently, Yorke [7] gave convex conditions to address the Lyapunov stability, which cannot guarantee the GUAS. Based on the fundamental work of [6,7], Aeyels and Peuteman [8] developed an efficient approach, i.e., allowing the LF to occasionally increase on several small intervals. However, such an approach cannot achieve controller synthesis, and also the paper has not given detailed solutions in the discrete-time domain.

Since 2008, the NLF approach, which is aiming at the discrete-time nonlinear system, starts to penetrate into the research front line , which allowed LF to increase in several sampling periods between the sampling point k state feedback control [14], guaranteed cost control [15], and robust dynamic output feedback control [16] have been intensively studied using the general case of NLF with N-sample variations. The studies of NLF approach for T-S fuzzy model is also an important part of this book.

1.1.2 Multimodel System

The real complex system usually contains strong nonlinearities and encounters bad scenarios such as parameter mutations and working condition changes. The synthesis for the multimodel systems (MMSs) provides an effective method for the control of complex systems. The multimodel control system is typically composed of three main parts: a multimodel set, a controller set, and a control synthesis algorithm (also referred to as a switching algorithm). The system structure of MMS is shown in Fig. 1.1.

Figure 1.1 Multimodel control system.

The basic principle of these three parts in multimodel control system can be summarized as follows. A multimodel set is constructed, as a combination of simple models, to approximate the original complex system. The combination of these simple models is designed by a simple fixed mode of a nonlinear system and thereby is used to represent different working conditions, operation processes, etc. Next, a corresponding controller set is designed, as a combination of subcontrollers, to meet the requirements specification of the control system. The difference between the real system and the multimodel set is then processed by the control synthesis algorithm either to let the controller set switches between the subcontrollers when there is only a single subcontroller in control action or to compute the weighting coefficients for subcontrollers when there are more than one subcontroller in control action. As a result, a global control for the complex nonlinear systems can be achieved using MMSs. Examples of MMSs are T-S fuzzy systems, switched systems, nonhomogenous Markovian jump systems, and artificial neural