Potentials based optimization with embedded Markov chain for stochastic constrained system

Abstract

In this paper, a RBF neural network based on-line optimization algorithm with performance potentials analysis method is presented for a class of stochastic constrained dynamic systems. The control signals of the considered systems are constrained to a range according to a subset of the whole state space. With the conception of an embedded Markov chain, an optimization approach on the basis of potentials is presented for a stochastic constrained system, where the optimization criterion is the long-time average performance. With this approach, the computation burden has been reduced because it only requires one to compute the control strategy on the states concerned, which are a subset of the whole state space. Furthermore, with the characteristic of approximation performance of RBF neural network, the potentials and the transition probability matrix are estimated conveniently by a sample path compared with the statistic approach or the method by solving the Poisson equation. The effectiveness of the optimization approach has been shown by the simulation results, finally.