Performance Analysis And Synthesis For Several Classes Of Discrete-time Stochastic Systems With Network-Enhanced Complexities

The thesis is concerned with the performance analysis and synthesis for several classes of discrete-time stochastic systems with various network-enhanced complex-ities. The complexities under consideration mainly include fading measurements, randomly occurring deception attacks, event-triggered communication mechanism, randomly occurring sensor saturations and randomly varying sensor delays. Then, the addressed systems cover general stochastic nonlinear systems and some time-varying discrete-time stochastic systems such as stochastic parameters systems, state-saturated time-varying systems, sensor networks and multi-agent systems. Further-more, some novel concepts, models of network-enhanced complexities, performance criteria in probability are proposed to account for the real-world engineering require-ments. They mainly involve the consensus in probability, the security in probability, the randomly occurring deception attacks, the discrete version of input-to-state sta-bility in probability and the envelope-constrained filtering performance.The content of the thesis can be divided into two parts. In the first part, the thesis focuses on finite horizon state estimation and control issues with network-enhanced complexities for discrete time-varying stochastic systems. Some new con-troller and estimator design schemes are developed in terms of the solutions to recur-sive matrix inequalities (RMIs) or backward recursive Riccati difference equations (RDEs). In the second part, the input-to-state stability in probability (ISSiP) is es-tablished for a general discrete-time stochastic nonlinear system. According to such a theory, the event-triggered consensus control and the security control are, respec-tively, investigated for stochastic multi-agent systems and discrete-time stochastic nonlinear systems. Some sufficient conditions are established to guarantee the pre-scribed performance requirements and obtain the desired controller parameters. In addition, the state estimation problem is discussed for a class of general discrete-time complex networks with randomly occurring sensor saturations (ROSSs) and randomly varying sensor delays (RVSDs). The estimator parameters are solved eas-ily by using the semi-definite programming method. The compendious frame and description of the thesis are given as follows.First, the finite-horizon H∞control problem is investigated for discrete time-varying nonlinear systems with simultaneous presence of fading measurements and randomly occurring nonlinearities. For the desired H∞performance, an auxiliary index is constructed and then a necessary and sufficient condition is derived to guar- antee such an auxiliary index. Furthermore, a novel H∞control scheme is proposed by utilizing model transformation techniques combined with a certain H2-type crite-rion. According to such a framework, the H∞consensus control problem for discrete time-varying multi-agent systems with both missing measurements and parameter uncertainties, and the distributed H∞state estimation problem for discrete time-varying nonlinear systems with both stochastic parameters and stochastic nonlinear-ities are discussed, respectively. For stochastic parameter systems, a necessary and sufficient condition is established to achieve the H∞performance constraint. Fur-thermore, the desired distributed controller/estimator parameters are characterized via solving coupled backward recursive RDEs.Second, a critical theoretical framework is established for analyzing the so-called input-to-state stability in probability (ISSiP) for general discrete-time non-linear stochastic systems. Based on such a framework, the event-triggered consensus control issue is investigated for a class of discrete-time stochastic multi-agent sys-tems with state-dependent noises. A novel definition of consensus in probability is proposed to better describe the dynamics of the consensus process of the addressed stochastic multi-agent systems, and an event-triggered communication mechanism is adopted with hope to reduce the communication burden and the energy consumption. By using the matrix analysis, a novel co-design scheme about the control gain and the threshold in the event-triggered control protocol is proposed to achieve the desired consensus in probability. Furthermore, the security control problem is addressed for discrete-time stochastic nonlinear systems. In the systems under consideration, a novel phenomenon, namely, the randomly occurring deception attack, is firstly taken into investigation. Attention is focused on the design of a dynamic output feedback controller such that the desired security is guaranteed and an upper bound of the given quadratic cost criterion is obtained. By utilizing the ISSiP approach, some suf-ficient conditions are established for the existence of the desired controller in virtue of the solvability of a set of matrix inequalities.Third, the dissipative control problem is considered for a class of discrete time-varying systems with simultaneous presence of state saturations, randomly occurring nonlinearities as well as multiple missing measurements. A new controller design algorithm is provided such that the desired dissipative performance requirement of the closed-loop systems can be guaranteed via introducing a free matrix with its infinity norm less than or equal to1. Furthermore, by utilizing the similar line in the dissipative control problem, the H∞filtering problem is addressed for discrete time-varying systems with state saturations, randomly occurring nonlinearities as well as successive packet dropouts. The desired filter parameters can be characterized via solving recursive matrix inequalities.Finally, the envelope-constrained H∞filtering problem is investigated for a class of discrete time-varying stochastic systems with fading measurements and randomly occurring nonlinearities. A novel envelope-constrained performance criterion is pro-posed to better quantify the transient dynamics of the filtering error process over the finite horizon. By utilizing the ellipsoid description on the estimation errors, the desired filter gains are characterized via solving recursive matrix inequalities (RMIs). On the other hand, a novel sensor model is proposed to describe randomly occurring sensor saturations (ROSSs) and randomly varying sensor delays (RVSDs) within a unified framework via two sets of Bernoulli distributed white sequences with known conditional probabilities. Furthermore, in light of such a measurement model, the H∞state estimation problem is discussed for a class of discrete time-delay nonlinear complex networks. The desired estimator parameters are characterized via solving a convex optimization problem.