Nonlinear stochastic control and filtering with engineering-oriented complexities (Q2797110)

The book presents results of investigation of the control and filtering problems for stochastic systems with traditional and emerging engineering-oriented complexities. The content of this book may be conceptually divided into three parts. In Chapters 2--5, a series of approaches, especially robust control/ filtering methods, is described for the stochastic system control and filtering problems with traditional engineering-oriented complexities such as time-delays, Markovian jump parameters, nonlinearities, and parameter uncertainties, etc. Some sufficient conditions of existence of the desired controllers and filters are given by verifying the corresponding matrix inequalities or Hamilton-Jacobi inequalities. In Chapters 6--9, the analysis and synthesis problems are investigated for stochastic systems with random incomplete information. Mainly two types of randomly occurring incomplete information (i.e., missing measurements and randomly occurring nonlinearities) are considered. For more details about the randomly occurring incomplete information see the survey papers by \textit{H. Dong} et al. [Math. Probl. Eng. 2012, Article ID 416358, 15 p. (2012; Zbl 1264.93001)] and by \textit{B. Shen} et al. [Math. Probl. Eng. 2012, Article ID 530759, 16 p. (2012; Zbl 1264.93248)] where comprehensive discussions have been given. In the final Chapters 10--13, the theory and methodology developed in the previous parts are applied to investigation the state estimation/filtering problems for network control systems, genetic regulatory networks, and complex networks. The detailed outline of the book, described in the Introduction, is as follows.NEWLINENEWLINEIn Chapter 1, the research background, motivation and research problems are first introduced, which mainly involve the stochastic nonlinear systems, complex networks, networked control systems, parameter-varying systems, control and filtering, and gain-scheduling techniqueNEWLINENEWLINEIn Chapter 2, the robust stability and stabilization problems are investigated for a class of stochastic time-delay interval systems with nonlinear disturbances by using the delay-dependent analysis technique. Based on the Itô's differential formula and the Lyapunov stability theory, sufficient conditions for the solvability of the addressed problems are given in terms of the LMI technique.NEWLINENEWLINEIn Chapter 3, the robust stabilization and robust \(H_{\infty}\) control problems are studied for a class of time-delay uncertain stochastic systems with Markovian switching and nonlinear disturbance. Here, the nonlinear disturbances include the time-delay term and are also mode dependent, hence the description of the nonlinearities addressed in this chapter is more general than those in the literature. A state feedback controller is designed such that, for all nonlinear disturbances, Markovian switching and admissible uncertainties, the closed-loop system is stochastically stable with a prescribed disturbance attenuation level.NEWLINENEWLINEIn Chapter 4, the design problems of \(H_{\infty}\) output feedback controller and filter are addressed for time-delay stochastic systems with nonlinear disturbances, sensor nonlinearities, and Markovian jump parameters, respectively. A delay-dependent approach is developed to design the \(H_{\infty}\) controller and filter for stochastic delay jump systems, such that, for both the nonlinear disturbances and sensor nonlinearities, the augmented systems are stochastically stable with a prescribed disturbance attenuation level.NEWLINENEWLINEIn Chapter 5, the \(H_{\infty}\) analysis problem is discussed for a general class of nonlinear stochastic systems with time-delays, where the addressed systems are described by general stochastic differential equations. By using the Razumikhin-type method, we first establish sufficient conditions to guarantee the internal stability of the time-delay stochastic systems, and then deal with the \(H_{\infty}\) analysis problem in order to quantify the disturbance attenuation level of the addressed nonlinear stochastic time-delays system. General conditions are derived under which the \(L_2\) gain of the system is less than or equal to a given constant. Subsequently, some easy-to-test criteria are given that can be used to check the stability of the addressed systems.NEWLINENEWLINEIn Chapter 6, the filtering problem is addressed for a class of discrete-time stochastic nonlinear time-delay systems with missing measurements and stochastic disturbances. The sensor measurement missing is assumed to be random and different for individual sensor, which is modelled by a set of random variables satisfying certain probabilistic distributions on the interval \([0,1]\). Such probabilistic distributions could be any commonly used discrete distributions. By using the LMI method, sufficient conditions are derived to ensure the existence of the desired filters, and the filter gain is characterized in terms of the solution to a set of LMIs.NEWLINENEWLINEIn Chapter 7, by constructing the probability-dependent Lyapunov functions, the gain-scheduled control problem is investigated for a class of discrete-time stochastic delayed systems with Randomly Occurring sector-Nonlinearities (RONs). The sector-nonlinearities are assumed to occur according to a time-varying Bernoulli distribution with known conditional probability in real time. The aim of the addressed gain-scheduled control problem is to design a controller with scheduled gains such that, for all RONs, time-delays, and external noise disturbances, the closed-loop system is exponentially mean-square stable. Note that the designed gain-scheduled controller is based on the measured time-varying probability and is therefore less conservative than the conventional controllers with constant gains. It is shown that the time-varying controller gains can be derived in terms of the measurable probability by solving a convex optimization problem via the semidefinite program method.NEWLINENEWLINEIn Chapter 8, the gain-scheduled filtering problem is studied for a class of discrete-time systems with missing measurements, nonlinear disturbances, and external stochastic noises. The measurement missing phenomenon is assumed to occur in a random way, and the missing probability is time-varying with securable upper and low bounds that can be measured in real time. The aim of the addressed gain-scheduled filtering problem is to design a filter, such that, for all missing measurements, nonlinear disturbances, and external noise disturbances, the error dynamics is exponentially mean-square stable. The desired filter is equipped with time-varying gains based primarily on the time-varying missing probability and is therefore less conservative than the traditional filters with fixed gains. It is shown that the filter parameters can be derived in terms of the measurable probability via the semidefinite program method.NEWLINENEWLINEIn Chapter 9, the static output feedback control problem is studied for a class of 2-D uncertain stochastic nonlinear systems with time-delays, missing measurements, and multiplicative noises. A time-varying Bernoulli distribution model is proposed to describe the changing characteristic of the occurring probability of missing measurements, and the time-varying gains of the desired gain-scheduled controller include constant gains and time-varying probability that can adapt to the missing measurements with time-varying probability. By employing the probability-dependent gain-scheduled method, the designed static output feedback controller possesses less conservatism than the traditional one that is with constant gains only.NEWLINENEWLINEIn Chapter 10, the filtering problem is addressed for a class of discrete-time stochastic nonlinear networked systems with multiple random communication delays and random packet losses. The communication delay and packet losses, which are frequently encountered in communication net-works with limited signal transmission capacity, are modelled by a stochastic mechanism that combines a certain set of indicator functions dependent on the same stochastic variable. A linear filter is designed, such that, for all random incomplete measurement phenomenon, stochastic disturbances as well as sector nonlinearities, the filtering error dynamics is exponentially mean-square stable.NEWLINENEWLINEChapter 11 is concerned with the filtering problem for a class of nonlinear genetic regulatory networks with state-dependent stochastic disturbances and state delays. The feedback regulation is described by a sector-like nonlinear function. The true concentrations of the RNA and protein are estimated by designing a linear filter with guaranteed exponential stability of the filtering augmented systems. By using the LMI technique, sufficient conditions are first derived for ensuring the exponential mean square stability with a prescribed decay rate for the gene regulatory model, and then the filter gain is characterized in terms of the solution to an LMI, which can be easily solved by using available software packages.NEWLINENEWLINEIn Chapter 12, the \(H_{\infty}\) state estimation problem is investigated for a class of discrete-time complex networks with randomly occurring phenomena. The proposed randomly occurring phenomena include both probabilistic missing measurements and randomly occurring coupling delays, which are described by two random variables satisfying individual probability distributions. The purpose of the addressed \(H_{\infty}\) state estimation problem is to design a state estimator, such that, for all nonlinear disturbances, missing measurements as well as coupling delays, the dynamics of the augmented systems is guaranteed to be exponentially mean-square stable with a given \(H_{\infty}\) performance level. By constructing a novel Lyapunov-Krasovskii functional and utilizing convex optimization method as well as Kronecker product, sufficient conditions for the existence of the desired state estimator are derived.NEWLINENEWLINEIn Chapter 13, the \(H_{\infty}\) synchronization control problem is investigated for a class of dynamical networks with randomly varying nonlinearities. The time-varying nonlinearities of each node are modeled to be randomly switched between two different nonlinear functions by utilizing a Bernoulli distributed variable satisfying a randomly varying conditional probability distribution. A probability-dependent gain scheduling method is adopted to handle the time-varying characteristic of the switching probability. Attention is focused on the design of a sequence of gain-scheduled controllers, such that the controlled networks are exponentially mean-square stable, and the \(H_{\infty}\) synchronization performance is achieved in the simultaneous presence of randomly varying nonlinearities and external energy bounded disturbances. In view of semidefinite programming method, controller parameters are derived in terms of the solutions to a series of LMIs that can be easily solved by using the MATLAB toolbox.