Neural network based stochastic optimal control for nonlinear Markov jump systems

Abstract

This paper deals with the problem of stochastic optimal control for a class of nonlinear systems subject to Markovian jump parameters. The nonlinearities in the different jump modes are initially parameterized by multilayer neural networks (MNNs), which lead to neural Markovian jump systems. A stochastic neural Lyapunov function (NLF) is used to analyze the stability of the resulting neural control MJSs. Then, based on this stochastic NLF and the neural model, a linear state feedback controller is designed to stabilize the closed-loop nonlinear system and guaranteed an upper bound of the system performance for all admissible approximation errors of the MNNs. The control gains can be derived by solving a set of linear matrix inequalities. Finally, a single link robot arm is demonstrated to show the effectiveness of the proposed design techniques.