Partial Observability and Optimal Control†

Abstract

Optimal control theory usually assumes that the state vector components of the controlled object can be measured exactly. However, practical measuring instruments frequently give significant error; also it is often impossible to monitor each component of the state. It is pointed out that in many situations, including adaptive ones, it is still possible to compute an optimal control even with both observational restrictions. Some simple examples are presented to illustrate the methods. These examples lead to a useful extension of the Certainty Equivalence Principle. These methods give an approach to the fundamental problem of partial observability, which is to say what kinds of observational restrictions allow effective controllers to be devised. Some tentative remarks are made about this.