Event-based optimization approach for solving stochastic decision problems with probabilistic constraint

In many practical control systems or management systems, the manager of systems may allow that the statistic probability of system error or parameter deviation occurs within a certain range. The problem of decision optimization under probabilistic constraint is thus an issue needs to be addressed urgently. In this paper, we consider to develop an event-based approach which can solve the probabilistic constrained decision problems in discrete events dynamic systems. The framework of the event-based optimization is first introduced, and then with the methodology of the performance sensitivity analysis, we present an online event-based policy iteration algorithm based on the derived performance gradient formula. We apply the event-based idea and propose the concept of “risk state”, “risk event” and “risk index” which can be used to better describe the nature of the probabilistic constrained problem. Furthermore, by taking the Lagrangian approach, the constrained decision problem can be solved with two steps. Finally, numerical experiments are designed to verify the efficiency of the proposed method.