Abstract
For nonlinear Itô-type stochastic systems, the problem of event-triggered optimal control (ETOC) is studied in this paper, and the adaptive dynamic programming (ADP) approach is explored to implement it. The value function of the Hamilton–Jacobi–Bellman(HJB) equation is approximated by applying critical neural network (CNN). Moreover, a new event-triggering scheme is proposed, which can be used to design ETOC directly via the solution of HJB equation. By utilizing the Lyapunov direct method, it can be proved that the ETOC based on ADP approach can ensure that the CNN weight errors and states of system are semi-globally uniformly ultimately bounded in probability. Furthermore, an upper bound is given on predetermined cost function. Specifically, there has been no published literature on the ETOC for nonlinear Itô-type stochastic systems via the ADP method. This work is the first attempt to fill the gap in this subject. Finally, the effectiveness of the proposed method is illustrated through two numerical examples.
Highlights
The control problem of nonlinear stochastic systems is diffusely considered in different fields, such as biological systems, chemical reaction processes, financial systems [1, 2]
– event-triggered optimal control (ETOC) for nonlinear Ito-type stochastic systems is designed for the first time in this paper by using adaptive dynamic programming (ADP) methods, which can get the numerical solution of Hamilton–Jacobi Bellman (HJB) equation
A new ETOC is presented to ensure the predetermined upper bound of the corresponding performance index for Ito-type stochastic optimal control problem. – For ETOC problems, the main purpose of most works is to achieve the numerical solution of the eventtriggered HJB equation by applying ADP methods [24,25,26,27]
Summary
The control problem of nonlinear stochastic systems is diffusely considered in different fields, such as biological systems, chemical reaction processes, financial systems [1, 2]. According to event-trigger mechanism and ADP approaches, a new optimal control method for unknown nonlinear continuous-time systems was proposed in [22]. – ETOC for nonlinear Ito-type stochastic systems is designed for the first time in this paper by using ADP methods, which can get the numerical solution of HJB equation. It can reduce computational load and savings communication resource. – In the existing researches, there is no literature to study the influence of ETOC on the corresponding performance index of Ito-type stochastic optimal control problem. A new ETOC is presented to ensure the predetermined upper bound of the corresponding performance index for Ito-type stochastic optimal control problem.
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