Explicit MPC with output feedback using self-optimizing control

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 precomputed feedback law is used for each region of active constraints (Bemporad et al., 2002). In this paper we make a link between this and the ‘self-optimizing control’ idea of finding simple policies for implementing optimal operation. The ‘nullspace’ method (Alstad and Skogestad, 2007) generates optimal variable combinations, c = u − Kx, which for the case with perfect state measurements are equivalent to the explicit MPC feedback laws, where K is the optimal state feedback matrix in a given region. More importantly, this link makes it possible to derive explicit feedback laws for cases with (1) state measurement error included and (2) measurement (rather than state) feedback. We further show how to generate optimal low-order controllers for unconstrained optimal control, also in the presence of noise.