Generalizing the Certainty Equivalence Principle and Separation Theorems Beyond the Usual Heuristics

In the existing literature the certainty equivalence principle is often used as an accepted heuristic. The certainty equivalence principle allows one replace exact knowledge of the state by an estimate while preserving stability and performance. Separation theorems specify when the design of the controller with full state feedback is independent of the design of the state observer. The purpose of this paper is to emphasize that there is no need for the use of heuristics in applying the certainty equivalence principle and the separation principle in many control applications. Instead, this paper suggests using existing theorems that state when the certainty equivalence principle and separation theorems are applicable in the stabilization problem for a given system and outlines an approach for extending and refining these results.