Achieving optimality in adaptive control: the "bet on the best" approach

Over the last two decades, the certainty equivalence principle has been the fundamental paradigm in the design of adaptive control laws. It is well known, however, that for general control criterions the performance achieved through its use is strictly suboptimal. In this paper, we introduce a new general philosophy based on the certainty equivalence idea-so as to ensure optimality in adaptive control problems under general conditions. Rather than focusing on a particular control scheme, we present the method in a general control setting. Specific control algorithms to cope with different situations can be derived from this general method.