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This monograph introduces methods for handling filtering and control problems in nonlinear stochastic systems arising from network-induced phenomena consequent on limited communication capacity. Such phenomena include communication delay, packet dropout, signal quantization or saturation, randomly occurring nonlinearities and randomly occurring uncertainties.

The text is self-contained, beginning with an introduction to nonlinear stochastic systems, network-induced phenomena and filtering and control, moving through a collection of the latest research results which focuses on the three aspects of:

· the state-of-the-art of nonlinear filtering and control;

· recent advances in recursive filtering and sliding mode control; and

· their potential for application in networked control systems, and concluding with some ideas for future research work. New concepts such as the randomly occurring uncertainty and the probability-constrained performance index are proposed to make the network models as realistic as possible. The power of combinations of such recent tools as the completing-the-square and sums-of-squares techniques, Hamilton‒Jacobi‒Isaacs matrix inequalities, difference linear matrix inequalities and parameter-dependent matrix inequalities is exploited in treating the mathematical and computational challenges arising from nonlinearity and stochasticity.

Nonlinear Stochastic Systems with Network-Induced Phenomena establishes a unified framework of control and filtering which will be of value to academic researchers in bringing structure to problems associated with an important class of networked system and offering new means of solving them. The significance of the new concepts, models and methods presented for practical control engineering and signal processing will also make it a valuable reference for engineers dealing with nonlinear control and filtering problems.



Chapter 1. Introduction

In this chapter, the research background on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena is introduced. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, randomly occurring uncertainties and randomly occurring nonlinearities, probabilistic sensor delays, sensor saturations, random parameter matrices, and time delays. With respect to these network-induced phenomena, the developments on recursive filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, the corresponding recursive filtering and sliding mode design technologies for nonlinear stochastic systems are discussed. Finally, the outline of the book is listed.
Jun Hu, Zidong Wang, Huijun Gao

Chapter 2. Recursive Filtering with Missing Measurements and Quantized Effects

In Chap. 2, the recursive filtering problems are investigated for non-linear systems with missing measurements over a finite horizon. Firstly, the EKF problem with multiple missing measurements is studied. Both deterministic and stochastic non-linearities are included in the system model. The phenomenon of measurement missing occurs in a random way, and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval [0, 1]. The aim of the addressed filtering problem was to design a filter such that, in the presence of both the stochastic non-linearities and multiple missing measurements, an upper bound is obtained for the filtering error covariance. Subsequently, such an upper bound is minimized by properly designing the filter gain at each sampling instant. Secondly, the proposed recursive filtering strategy is extended to deal with the filtering problem for systems with missing measurements, quantization effects, and multiplicative noises. A set of parallel results is obtained by using the similar techniques.
Jun Hu, Zidong Wang, Huijun Gao

Chapter 3. Recursive Filtering with Fading Measurements, Sensor Delays, and Correlated Noises

In this chapter, the recursive filtering problem is firstly investigated for a class of discrete-time non-linear stochastic systems with random parameter matrices, multiple fading measurements, and correlated noises. The phenomenon of measurement fading occurs in a random way and the fading probability for each sensor is governed by an individual random variable obeying a certain probability distribution over the known interval. The purpose of the addressed filtering problem is to design an unbiased, recursive, and optimal filter in the minimum variance sense. Intensive stochastic analysis is carried out to obtain the filter gain characterized by the solution to a recursive matrix equation. Based on the proposed filter approach, the gain-constrained recursive filtering problem is studied for a class of non-linear time-varying stochastic systems with probabilistic sensor delays and correlated noises. A new recursive filtering algorithm is developed that ensures both the local optimality and the unbiasedness of the designed filter at each sampling instant which achieving the prespecified filter gain constraint.
Jun Hu, Zidong Wang, Huijun Gao

Chapter 4. Probability-Guaranteed $$H_\infty $$ H ∞ Finite-Horizon Filtering with Sensor Saturations

In this chapter, the probability-guaranteed \(H_\infty \) finite-horizon filtering problem is investigated for a class of nonlinear time-varying systems with uncertain parameters and sensor saturations. The system matrices are functions of mutually independent stochastic variables that obey uniform distributions over known finite ranges. Attention is focused on the construction of a time-varying filter such that the prescribed \(H_\infty \) performance requirement can be guaranteed with probability constraint. By using the difference linear matrix inequalities (DLMIs) approach, sufficient conditions are established to guarantee the desired performance of the designed finite-horizon filter. The time-varying filter gains can be obtained in terms of the feasible solutions to a set of DLMIs that can be recursively solved by using the semidefinite programming method. A computational algorithm is specifically developed for the addressed probability-guaranteed \(H_\infty \) finite-horizon filtering problem.
Jun Hu, Zidong Wang, Huijun Gao

Chapter 5. $$H_\infty $$ H ∞ Sliding Mode Observer Design for Nonlinear Time Delay Systems

In this chapter, we investigate the \(H_\infty \) sliding mode observer (SMO) design problem for a class of discrete time delay nonlinear systems. The nonlinear descriptions quantify the maximum possible derivations from a linear model, and the system states are allowed to be immeasurable. A discrete-time discontinuous switched term is firstly proposed to make sure that the reaching condition holds. Then, by constructing a new Lyapunov–Krasovskii functional based on the idea of delay fractioning and introducing some appropriate free-weighting matrices, a sufficient condition is established to guarantee the desired performance of the error dynamics in the specified sliding mode surface by solving a minimization problem. This minimization problem involves linear objective and linear matrix inequalities that can be easily tested by means of standard numerical software.
Jun Hu, Zidong Wang, Huijun Gao

Chapter 6. Sliding Mode Control with Time-Varying Delays and Randomly Occurring Nonlinearities

In this chapter, the robust sliding mode control (SMC) problem is firstly investigated for a class of uncertain discrete stochastic systems with randomly occurring nonlinearities (RONs) and time delays. The RONs, which describe the phenomena of a class of nonlinear disturbances occurring in a random way, are modeled according to a Bernoulli distributed white sequence with a known conditional probability. Sufficient conditions are derived to ensure the stability of the sliding mode dynamics under the specified sliding surface. Such conditions are characterized in terms of a set of linear matrix inequalities with an equality constraint. A discrete-time SMC law is synthesized to guarantee the reaching condition of the discrete sliding mode surface. A computational algorithm is introduced to facilitate the implementation of the proposed control strategy. Moreover, the robust \(H_\infty \) SMC problem is investigated for a general class of discrete uncertain systems with stochastic nonlinearities and time-varying delays.
Jun Hu, Zidong Wang, Huijun Gao

Chapter 7. Sliding Mode Control with Randomly Occurring Uncertainties and Mixed Time Delays

In this chapter, the robust SMC problem is studied for discrete-time uncertain nonlinear stochastic systems with mixed time delays. Both the sectorlike nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties (ROUs) and RONs obey certain mutually uncorrelated Bernoulli distributed white noise sequences with known conditional probabilities. The mixed time delays consist of both the discrete and the distributed delays. Sufficient conditions are established to ensure the stability of the system dynamics in the specified sliding surface by solving certain semidefinite programming problem. Moreover, a discrete-time SMC law is proposed to make sure that the reaching condition holds. Secondly, the proposed control method is extended to address a class of uncertain discrete-time Markovian jump systems with mixed delays.
Jun Hu, Zidong Wang, Huijun Gao

Chapter 8. Conclusions and Future Work

In this chapter, conclusions on the book are given, and some possible research directions related to the work done in this book are pointed out.
Jun Hu, Zidong Wang, Huijun Gao


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