Constrained MPCI: A weak persistent excitation approach

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Abstract
Model‐predictive control and identification (MPCI) introduced by Genceli and Nikolaou in 1996 is a novel approach to the identification of processes under constrained model‐predictive control. MPCI solves an on‐line optimization problem that involves (a) a standard MPC objective; (b) standard MPC constraints; and (c) persistent excitation (PE) constraints. The on‐line optimization problem is computationally demanding. To alleviate that problem, we take a frequency‐domain approach to formulating the PE constraints. 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, persistently exciting input signals can be parametrized 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 that are 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.