On the design of optimal stochastic terminal control systems

The problem of optimizing a class of discrete-time stochastic systems in such a way as to make a prescribed set of terminal conditions "most likely" is treated. The class of systems in question is described by a set of time-varying difference equations which are linear in the state and nonlinear in the control where the performance index is quadratic in the state but not necessarily in the control. Random disturbances are present in both the plant equations and the observation equations. "Hard" constraints on the set of admissible controls are also permitted. The equivalence of this problem to two "standard" deterministic optimization problems is demonstrated.