Optimization of Stochastic Dynamic System with Random Coefficients.

The problem of optimization of stochastic dynamic systems with random coefficients is discussed. Systems with both Weiner processes and uncertain random-process disturbances are dealt with in this dissertation, and these include certain bilinear stochastic systems. It is the purpose of this thesis to study the optimal control and, to some extent, state estimation of such bilinear stochastic systems. By means of 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. The theory is then applied to an optimal-control design of an aircraft landing with a bad weather situation, to the control problem of longitudinal motion of an aircraft in wind gust, and to nonlinear filtering and tracking of the maneuvering target. The flare path compared with the desirable exponential-linear path provides a safe and comfortable landing for the optimal-control policy. Using the decoupled feedback law of longitudinal aircraft motion, it is shown that optimal-control policies for the elevator control angle and the aileron control angle is synthesized with the attack angle, the orientation rate of the aircraft and an unknown random parameter. In the final example, a maneuvering target's state is estimated. Here, a bilinear stochastic model is assumed such that discrete velocity changes are at random times.