Optimal control of nonlinear discrete-time stochastic system with model-reality differences

In the presence of random disturbances, control and optimization problems of the nonlinear discrete-time stochastic dynamic systems are more difficult to solve rather than the linear stochastic optimal control problem. This is due to the nonlinear structure of plant and the partially known state information. In this paper, we discuss the approach of model-reality differences to solve the nonlinear discrete-time stochastic optimal control problem. We modify the dynamic integrated system optimization and parameter estimation (DISOPE) algorithm, which developed by Roberts and Becerra, with applying the Kalman filtering for state estimation and choosing the linear quadratic Gaussian as the model-based optimal control problem. The algorithm integrates the problems of system optimization and parameter estimation. The different structures and parameters among the real plant and the model employed are taken into account in the computations. The iterative procedure required for solving the model-based optimal control problem where the value of setpoint are updated. This will gives the optimum of the real plant in spite of model-reality differences when the convergence achieved. For illustration, the solution of a single degree of freedom inverted pendulum with multiplicative white noise is investigated. The computed solution of model used satisfies the necessary optimality conditions. Hence, the efficient of the algorithm is presented.