Optimization of Stochastic Dynamic System with Random Coefficients

摘要

The problem of optimization of stochastic dynamic systems with random coefficients is discussed. Systems with both Wiener processes and uncertain random-process disturbances are dealt with, and these include certain bilinear stochastic systems. It is the purpose to study the optimal control and, to some extent, state estimation of such bilinear stochastic systems. By means of the stochastic Bellman equation, the optimal control of stochastic dynamic models with observable and unobservable coefficients is derived. The stochastic-system model considered is the observable system with random coefficients that are a function of the solution of a certain unobservable Markov process with information data. Under the assumptions that the solution of the stochastic differential equation for the dynamic model involved in the problem formulation results in an admissible control and that the measurable information of all random parameters depend on the conditional-mean estimate to the unobservable stochastic process, the optimal control is a linear function of the observable states and a nonlinear function of random parameters.