A suboptimal n-step-ahead cautious controller for adaptive control applications

If there is little a priori knowledge of the plant parameters, the performance of certainty equivalence based adaptive controllers during the transient period, before the parameter estimates have converged, is usually less than adequate. This paper introduces a new suboptimal loss function with an N-step-ahead prediction horizon, similar in principle to standard predictive control loss functions, for adaptive control applications. However, the new loss function is modified so that the resulting control law possesses caution in the sense that the uncertainty in the parameter estimates is taken into account automatically. As such, the cautious controller achieves more robust performance than the corresponding certainty equivalence controller during the transient period when there is large uncertainty in the parameter estimates. The new cautious controller has a closed-form solution that involves only slightly more computational expense than the corresponding certainty equivalence predictive controller.