Probabilistic DHP Adaptive Critic for Nonlinear Stochastic Control Systems

TL;DR

This paper extends probabilistic control design to nonlinear stochastic discrete-time systems using a dual heuristic programming adaptive critic method, demonstrating promising simulation results.

Contribution

It formulates and solves the fully probabilistic control problem for nonlinear stochastic systems, advancing previous work with a new randomized control algorithm.

Findings

Successful simulation demonstration of the algorithm

Close approximation of the ideal joint probability density function

Encouraging results indicating effectiveness of the method

Abstract

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems [15], [18], this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method [15] and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work [15], [18] by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained.