Stochastic optimal control of nonlinear jump systems using neural networks

Abstract

For a class of nonlinear stochastic Markovian jump systems, a novel feedback control law design is presented, which includes three steps. Firstly, the multi-layer neural networks are used to approximate the nonlinearities in the different jump modes. Secondly, the overall system is represented by the mode-dependent linear difference inclusion, which is suitable for control synthesis based on Lyapunov stability. Finally, by introducing stochastic quadratic performance cost, the existence of feedback control law is transformed into the solvability of a set of linear matrix inequalities. And the optimal upper bound of stochastic cost can be efficiently searched by means of convex optimization with global convergence assured. © Springer-Verlag Berlin Heidelberg 2006.