On multiple model adaptive controllers and the minimax criterion

An approximate solution to the dual control problem is proposed. The new algorithm is based on a minimax criterion and a loss function which penalizes the difference between the quadratic loss associated with a given controller and that which could be achieved if all unknown parameters were known. The approximate solution, while using Lainiotis´ multiple model adaptive controller (MMAC) avoids most of the difficulty associated with the standard application of MMAC. In particular, it is no longer required (or even desired) that the parametric uncertainty space be finite. Two or three control-MMAC´s perform extremely well in the presence of convex uncertainty spaces. Furthermore, the practical problems uncovered in the F8 DFBW MMAC effort are eliminated because they are automatically handled by the minimax design algorithm. Finally, in contrast with other dual control algorithms, the proposed technique requires only a relatively small amount of real time processing (that required by standard MMAC algorithms).