A computationally efficient formulation of simultaneous constrained model predictive control and identification

Model predictive control and identification (MPCI) introduced by Genceli and Nikolaou (1996) is a novel approach to the identification of processes under constrained model predictive control. MPCI relies on an online optimization problem that involves (a) a standard MPC objective; (b) standard MPC constraints; and (c) persistence of excitation (PE) constraints. The resulting optimization problem is computationally demanding. In this work, a frequency domain approach to formulating the PE constraints is taken. This approach relies on the following fact: A signal is persistently exciting of order n, if its two-sided power spectrum is nonzero at no fewer than n points. Therefore, one can parametrize persistently exciting input signals over a finite horizon as a sum of sinusoid terms with nonzero coefficients. Used in the MPCI framework, the last requirement generates a set of completely decoupled reverse-convex constraints. This renders the online optimization problem a nonconvex quadratic programming (QP) problem, that is combinatorially tractable from a computational point of view. The effectiveness of the proposed MPCI method is demonstrated through simulations. For the SISO systems studied, computation of the global optimum could be handled combinatorially in real-time using PC hardware.