Deterministic optimal control, given only a partial observation of the initial state

Abstract

The deterministic linear-system, quadratic-cost optimal control problem is considered when the only state information available is a partial linear observation of the initial statex0. Thus, it is only known that the initial condition belongs to a particular linear variety. A control function is found which is optimal, in the sense (roughly) that (i) it can be computed using available information aboutx0 and (ii) no other control function which can be found using that information gives lower cost than it does for every initial condition that could have given rise to the information. The optimal control can be found easily from the conventional Riccati equation of optimal control. Applications are considered in the presence of unknown exponential disturbances and to the case with a sequence of partial state observations.