On the Tuning of Predictive Controllers: The Minimum Back-Off Operating Point Selection Problem

Abstract

In this work we propose a new formulation of the stochastic based minimum back-off operating point selection problem. It is shown that this formulation has a convex/reverse-convex form and is thus readily solved globally via a branch and bound search scheme. The formulation is then extended to the partial state information case as well as the discrete-time framework. The formulation is unique in that the controller feedback gain is not specified a priori but rather is to be determined by the proposed optimization. It is further shown that the obtained feedback gain is such that an LQR inverse optimal feedback is guaranteed to exist within the set of feasible feedback gains. A postprocessing procedure is proposed for the synthesis of such a feedback as well as the corresponding LQR objective function weights. This connection between the economics of operating point selection and the dynamics of predictive controller tuning (i.e., the selection of objective function weighs) is expected to significantly enha...