Event-Triggered Control For Stochastic Systems Based On Impulsive Switching Modeling Strategy

Event-triggered control has been widely used in networked control systems due to its good control performance,the capability of effectively reducing the number of executions of measurement/control tasks,and improving the utilization efficiency of communica-tion/computing resources.The event-triggered control theory for deterministic models has been well developed.However,stochastic model integrating random noise and s-tochastic uncertainty in the modeling is one of the research hot-spots.Stochastic model not only complements the deterministic model but also accurately reflects the dynamic characteristics of natural and engineering systems.The presence of the stochastic noise changes the dynamics of the original system,degrades control performance,and even destroys the stability.This dissertation focuses on event-triggered control problems of continuous It?o stochastic systems.To explore the hybrid structural characteristics of networked control systems,develop effective mathematical methods,and further reduce the conservativeness of the results,a unified Lyapunov framework for linear impulsive and switched stochastic systems under dwell-time constraints is first proposed.Then the Lyapunov analysis framework for the impulsive switched systems is applied to event-triggered design,modeling,and stability analysis of event-triggered stochastic systems.The main research contents and results of this dissertation are summarized as follows:1.The stability and stabilization of linear impulsive stochastic systems with/without impulse-delay are investigated separately.For the delay-free case,a composite quasi-periodic polynomial and discretized Lyapunov function approaches are proposed for es-tablishing dwell-time based stability criteria in the mean square and almost sure senses,respectively.For the impulse-delay case,a switching modeling technique is proposed to model the impulse-delay system as a delay-free switched impulsive system.By devel-oping switching quasi-periodic Lyapunov function method,mean-square stability criteria are derived in terms of linear matrix inequality,which are applied to the controller design.These stability criteria not only reveal the influence mechanism of the noise intensity,im-pulse frequency and amplitude,and impulse-delay on the stability,but also solve the stability problem of sampled-data control systems.2.The stability problems of switched linear stochastic systems with/without state delays under dwell-time constraints are studied separately.For the non-delay case,a multiple quasi-period discretized Lyapunov function method is proposed to establish uni-fied dwell-time based stability criteria in the mean square and almost sure sense.Based on the obtained stochastic stability criteria,state feedback controllers are designed and the intermittent stabilization problem via stochastic noise is solved accordingly.For the switched delayed stochastic systems with fast-varying delays or slowly varying delays,novel mode-dependent mean square stability criteria irrespective of the sizes of the time delay are established by multiple quasi-periodic discretized Lyapunov function/functional methods.These criteria have the advantages of less conservativeness and high general-ization,and do not impose restrictions on the stability of the subsystems.3.The 2pth moment stability of linear,impulsive,sampled-data,and switched s-tochastic systems is investigated.By the matrix derivative operator and vectorial It?o's formula,a recursive computation algorithm is proposed to derive two extended systems:one is described by SDE and the other by ODE.It is shown that the stochastic system is 2pth-moment exponentially stable if and only if the SDE is mean-square exponentially stable or the ODE is exponentially stable.Subsequently,combining the quasi-periodic homogeneous polynomial Lyapunov function methods with the proposed techniques,a series of nonconservative stability criteria are established for periodic impulsive,periodic sampling,and switched stochastic systems with minimum dwell time.The proposed re-cursive computation technique establishes a deterministic representation method for the high-order moment properties of stochastic systems.4.Event-triggered design,modeling,and stability analysis of linear stochastic sys-tems with discrete-time sampled measurements are studied.Firstly,a discrete-time event-triggering mechanism based on discrete sampled output is designed.Then an impulsive system and a switched time-delay system modeling method are proposed.For the closed-loop system modeled by the impulsive switched system,mean square stability and almost sure stability criteria are established for the noise disturbance and noise stabilization,respectively.For the closed-loop system modeled by switched time-delay system,a de-scriptor system approach and a free-weighting approach are proposed for deriving the sufficient conditions for mean square stability and stability in probability.Finally,the advantages and disadvantages of the two modeling and analysis methods are compared by numerical examples.5.Static and dynamic,periodic and continuous event-triggering schemes are system-atically presented for nonlinear stochastic systems under linear growth conditions.Using the sampling information to estimate the current state and state error,a perturbed sys-tem approach based on the switching modeling strategy is proposed to analyze the mean square stability of the closed-loop system.All the event-triggering mechanisms proposed herein not only have a guaranteed positive minimum inter-event time but also implies that under the same event triggering parameters,the inter-event time generated by the dynamic event-generators is not less than their static counterparts.6.Two novel dynamic discrete-time event-triggered control strategies in both impul-sive and continuous types are designed for the networked stochastic systems with sporadic measurement and communication delay.An impulsive switched system approach and a switched time-delay system approach are developed for modeling and stability analysis for the resulting closed-loop systems with small and large communication delays,respec-tively.Different from the existing methods,the proposed switched time-delay system approach does not need to split the interval of events,thus solving the problem of the well-posedness of stochastic modeling.Moreover,the impulsive switched system approach can capture the stabilizing effect of communication delays.7.A unified framework of recursive impulsive system approach is proposed for mod-eling,stability,and L₂-gain analysis of periodic event-triggered dynamical systems with large delays.By introducing recursive auxiliary variables to identify the actual trans-mitted data at the current instant,the closed-loop system is modeled as an impulsive delay-free system.Necessary and sufficient conditions for the stability of the periodic sampled-data systems with large constant delays are established.Extensions to the ex-ponential stability and L₂-gain properties of periodic event-triggered deterministic and stochastic systems with large time-varying delays are then derived.The proposed recur-sive impulsive system approach not only perfectly solves the problem of large communi-cation delay,but also reveals the mechanism that time delay may stabilize sampled-data systems.