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This article addresses the event-triggered stabilization for continuous-time stochastic systems. Due to stochastic effects, the system state is hard to predict and dominate, and the system behavior would vary with every trial (i.e., sample path) even for the same initial condition. This gives rise to substantial challenges, especially, in determining the execution/sampling times and assessing the closed-loop performance, which urges us to develop powerful and sophisticated tools/methods for the analysis and design of stochastic event-triggered control. In this article, basic theorems, particularly a stochastic convergence theorem, are first proposed for stochastic event-triggered controlled systems. Then, a framework of event-triggered stabilization is established for the stochastic systems without applying the well-known Lyapunov theorems. Specifically, we present conditions under which event-triggered stabilization is feasible for the systems. Accordingly, static and dynamic event-triggering mechanisms are proposed with enforcing a fixed positive lower bound for the interexecution times. While avoiding infinitely fast execution/sampling, both asymptotic stabilization and exponential stabilization are achieved for the systems by the proposed stochastic convergence theorem. The involved analysis is helpful to form a pattern for stochastic event-triggered controlled systems. As the direct application of the established framework, the constructive design of event-triggered controller is realized, respectively, for two representative classes of stochastic systems. [ABSTRACT FROM AUTHOR]

This paper considers the control design with prescribed performance for uncertain nonlinear systems. Different from the existing literature, the systems under investigation possess unknown control directions and nonparametric uncertainties. Even so, the control objective to be achieved is still refined, not only to ensure the basic performance on stabilization, but also to guarantee certain prescribed performance required in real applications. Motivated by the funnel control method, a time-varying stabilizing scheme is developed for the systems, to effectively handle the serious uncertainties and to successfully guarantee the states to converge to zero with a prescribed rate. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis methods/tools to stochastic convergence and stochastic adaptive output-feedback control. As the first contribution, a general stochastic convergence theorem is proposed for stochastic nonlinear systems. The theorem doesn't necessarily involve a positive-definite function of the system states with negative-semidefinite infinitesimal, essentially different from stochastic LaSalle's theorem (see e.g., [1]), and hence can provide more opportunities to achieve stochastic convergence. Moreover, as a direct extension of the convergence theorem, a general version of stochastic Barb ă lat's lemma is obtained, which requires the concerned stochastic process to be almost surely integrable, rather than absolutely integrable in the sense of expectation, unlike in [2]. As the second contribution, supported by the general stochastic convergence theorem, an adaptive output-feedback control strategy is established for the global stabilization of a class of stochastic nonlinear systems with severe parametric uncertainties coupled to unmeasurable states. Its feasibility analysis takes substantial effort, and is largely based on the general stochastic convergence theorem. Particularly, for the resulting closed-loop system, certain stochastic boundedness and integrability are shown by the celebrated nonnegative semimartingale convergence theorem, and furthermore, the desired stochastic convergence is achieved via the general stochastic convergence theorem. [ABSTRACT FROM PUBLISHER]