Nonlinear Control and Filtering for Stochastic Networked Systems

Lifeng Ma, Zidong Wang, Yuming Bo

• Publisher: CRC Press
• Year: 2018
• eBook ISBN: 9780429761928
• Edition: 1
• Topic: Mathematics
• Subtopic: Differential Equations
• Index: Mathematics

In this book, control and filtering problems for several classes of stochastic networked systems are discussed. In each chapter, the stability, robustness, reliability, consensus performance, and/or disturbance attenuation levels are investigated within a unified theoretical framework. The aim is to derive the sufficient conditions such that the resulting systems achieve the prescribed design requirements despite all the network-induced phenomena. Further, novel notions such as randomly occurring sensor failures and consensus in probability are discussed. Finally, the theories/techniques developed are applied to emerging research areas.

Key Features

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• Unifies existing and emerging concepts concerning stochastic control/filtering and distributed control/filtering with an emphasis on a variety of network-induced complexities

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• Includes concepts like randomly occurring sensor failures and consensus in probability (with respect to time-varying stochastic multi-agent systems)

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• Exploits the recursive linear matrix inequality approach, completing the square method, Hamilton-Jacobi inequality approach, and parameter-dependent matrix inequality approach to handle the emerging mathematical/computational challenges

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• Captures recent advances of theories, techniques, and applications of stochastic control as well as filtering from an engineering-oriented perspective

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• Gives simulation examples in each chapter to reflect the engineering practice

1

Introduction

1.1 Nonlinear Stochastic Networked Systems

The rapid development in network technologies in the past few years has led to a revolution in engineering practices [36]. Using a network as the basement of a feedback control loop is now widely applied in various types of engineering programs; this has gained a great deal of research interest [36, 165, 213, 255]. The usage of networks in control systems has many advantages such as low cost, reduced weight and simple installation, as well as some limitations including the network-induced time-delays (also called communication delays) and data package loss caused mainly by the complex working conditions and limited bandwidth. As a result, most of the literature on network systems has focused on how to eliminate or compensate for the effect caused by the communication delays [165, 196] and data package loss [116, 187]. Many researchers have studied the stability and controller design problems for networked systems in the presence of deterministic communication delays. Recently, due to the fact that such kinds of time-delays usually appear in a random and time-varying fashion, the communication delays have been modeled in various probabilistic ways, see [165, 196, 219, 236, 250], among which the binary random delay has gained particular research interest because of its simplicity and practicality in describing network-induced delays [219, 236].

As is well known, in the past few decades, there have been extensive study and application of stochastic systems because the stochastic phenomenon is inevitable and cannot be avoided in real-world systems. When modeling such kinds of systems, way neglecting the stochastic disturbances, which is a conventional technique in traditional control theory for deterministic systems, is not suitable anymore. Having realized the necessity of introducing more realistic models, today, a great number of real-world systems such as physical systems, financial systems, ecological systems as well as social systems are more suitable to be modeled by stochastic systems, and therefore the stochastic control problem, which deals with dynamical systems, described by difference or differential equations, and subject to disturbances characterized as stochastic processes, has drawn much research attention; see [7] and the references therein. It is worth mentioning that a kind of stochastic system represented as a deterministic system adding a stochastic disturbance characterized as white noise has gained special research interest and found extensive applications in engineering based on the fact that it is possible to generate stochastic processes with covariance functions belonging to a large class simply by sending white noise through a linear system. Hence a large class of problems can be reduced to the analysis of linear systems with white noise inputs; see [27, 33, 37, 87, 185] for examples.

Parallel to the control problems, the filtering and prediction theory for stochastic systems which aims to extract a signal from observations of signal and disturbances has been well studied and found widely applied in many engineering fields. It also plays a very important role in the solution of the stochastic optimal control problem. Research on the filtering problem was originated in [223], where the well-known Wiener-Kolmogorov filter has been proposed. However, the Wiener-Kolmogorov filtering theory has not been widely applied mainly because it requires the solution of an integral equation (the Wiener-Hopf equation) which is not easy to solve either analytically or numerically. In [94, 95], Kalman and Bucy gave a significant contribution to the filtering problem, by using the celebrated Kalman-Bucy filter which could solve the filtering problem recursively. The Kalman-Bucy filter (also known as the $\mathcal{H}$₂ filter) has been extensively adopted and widely used in many branches of stochastic control theory, since the fast development of digital computers recently; see [12, 74, 90, 130] and the references therein.

In real-world engineering, it is well acknowledged that almost all practical systems are time-varying. For such time-varying systems, a filter that could provide better transient performance than those traditional methods developed to achieve specified steady-state performance is more effective and applicable. Therefore, the filtering problems for time-varying systems have stirred considerable research interest in the past few years. For example, the difference Riccati equation method has been proposed in [237] to solve the robust Kalman filtering problem for uncertain time-varying systems. Recently, the recursive linear matrix inequality (RLMI) method has become another effective approach to deal with the filtering and control problems for time-varying systems. Originally proposed in [65], the RLMI method has so far been widely recognized and extensively utilized in both theoretical research and engineering applications associated with time-varying systems, see e. g. [40, 193]. However, up to now, the distributed filtering problem has not been adequately investigated yet for systems subject to time-varying parameters, especially for the case where the event triggering mechanism and sensor saturation are also involved.

A quintessential example that should be cited is that, up to now, most multi-agent systems (MASs) discussed in the literature have been assumed to be time-invariant and deterministic. This assumption is, however, very restrictive as almost all real-world engineering systems have certain parameters/structures which are indeed time-varying [11]. For such time-varying systems, a finite-horizon controller is usually desirable as it could provide better transient performance for the controlled system especially when the noise inputs are non-stationary; see [50, 65] for some recent results. However, when it comes to the consensus of multi-agent systems, the corresponding results have been scattered due mainly to the difficulty in quantifying the consensus over a finite horizon. It is notable that the consensus problem for MASs with time-varying parameters has received some initial research attention (see e.g. [92, 115, 257]). Nevertheless, the research on time-varying multi-agent systems is far from adequate and there are still many open challenging problems remaining for further investigation. On the other hand, sensor saturation is a frequently encountered phenomenon resulting from physical limitations of system components as well as the difficulties in ensuring high fidelity and timely arrival of the control and sensing signals through a possibly unreliable network of limited bandwidth. In other words, the sensor outputs are often saturated because the physical entities or processes cannot transmit energy and power with unbounded magnitude or rate. As such, it makes practical sense to take sensor saturation into account when dealing with the output-feedback control problems for time-varying MASs, which remains as an ongoing research issue.

1.2 Sliding Mode Control

Due to the advantage of strong robustness against model uncertainties, parameter variations and external disturbances, the sliding mode control (SMC) (also called variable structure control) problem of continuous-time systems has been extensively studied and widely applied in various fields; see, for example, [25, 79, 166, 167, 208, 218]. In recent years, the SMC problem for discrete-time systems has begun to receive increasing research attention simply because most control strategies are implemented in discrete time nowadays [2, 16, 24, 32, 34, 52, 69, 89, 91, 109, 212, 230, 233, 266]. In [2, 16], the integral type SMC schemes were proposed, respectively, for sample-data systems and a class of nonlinear discrete time systems. In [24, 32], adaptive laws were applied to the sliding mode control problems for discrete time systems with stochastic or deterministic disturbances. In [34], a simple methodology for designing sliding mode controllers was proposed for a class of linear multi-input discrete-time systems with matching perturbations. In [91], a discrete variable structure control method with a finite-time step to reach the switching surface was constructed by using the dead-beat control technique. In [52, 109], the discrete time SMC problems were solved via output feedback in the case when the system states are not available. It is worth mentioning that, in [212], a reaching law approach was introduced which can be conveniently used to develop the robust control law, and has therefore attracted quick attention in recent literature, see e.g. [230, 233, 266]. By employing such a reaching law and the proposed technique, in [230], the sliding mode control problem was tackled for discrete-time systems with input delays; in [266], a class of nonlinear systems was first modeled as a T-S fuzzy model and then stabilized by an SMC controller; and in [233], the SMC pro...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Acknowledgements
• Symbols
• 1 Introduction
• 2 Robust H∞ Sliding Mode Control for Nonlinear Stochastic Systems with Multiple Data Packet Losses
• 3 Sliding Mode Control for A Class of Nonlinear Discrete-Time Networked Systems with Multiple Stochastic Communication Delays
• 4 Sliding Mode Control for Nonlinear Networked Systems with Stochastic Communication Delays
• 5 Reliable H∞ Control for A Class of Nonlinear Time-Varying Stochastic Systems with Randomly Occurring Sensor Failures
• 6 Event-Triggered Mean Square Consensus Control for Time-Varying Stochastic Multi-Agent System with Sensor Saturations
• 7 Mean-Square H∞ Consensus Control for A Class of Nonlinear Time-Varying Stochastic Multi-Agent Systems: The Finite-Horizon Case
• 8 Consensus Control for Nonlinear Multi-Agent Systems Subject to Deception Attacks
• 9 Distributed Event-Based Set-Membership Filtering for A Class of Nonlinear Systems with Sensor Saturations over Sensor Networks
• 10 Variance-Constrained Distributed Filtering for Time-varying Systems with Multiplicative Noises and Deception Attacks over Sensor Networks
• 11 Conclusions and Future Topics
• Bibliography
• Index