Numerical Synthesis of Optimal Control for Some Stochastic Systems

Abstract

The problems of synthesis of optimal control in dynamic systems with disturbances of the white-noise Gauss type and with constrained control inputs are discussed. The method of synthesis of optimal systems based on numerical solution of the Bellman equation is described. For the problems with unconstrained phase space an effective technique is suggested for constructing a numerical solution of that equation in constrained region of the phase space. This solution is obtained by solving a first boundary problem with boundary conditions defined by loss function for uncontrollable motion of the system. Application of the proposed synthesis procedure is illustrated by computating the controller for the second order system of optimal damping of random oscillations. For this example the computational difference-scheme for solving synthesis problem is given. Some results of the computational work which was carried out on the computer are cited.