A new approach to explicit MPC using self-optimizing control

Abstract

Model predictive control (MPC) is a favored method for handling constrained linear control problems. Normally, the MPC optimization problem is solved on-line, but in 'explicit MPC' an explicit piecewise affine feedback law is computed and implemented [1]. This approach is similar to 'self-optimizing control,' where the idea is to find simple pre-computed policies for implementing optimal operation, for example, by keeping selected controlled variable combinations c constant. The 'nullspace' method [2] generates optimal variable combinations, which turn out to be equivalent to the explicit MPC feedback laws, that is, c = u kx, where K is the optimal state feedback matrix in a given region. More importantly, this link gives new insights and also some new results. One is that regions changes may be identified by tracking the variables c for neighboring regions.