Learning MPC: System stability and convergent identification under bounded modelling error

The dual-control problem of simultaneously regulating a plant and identifying its dynamics is addressed in a linear model predictive control (MPC) framework. We propose and study an approach where two optimal control problems are solved in series, online: the first is a standard regulating linear quadratic MPC problem, which achieves exponential nominal stability; the second is an ancillary optimization problem that promotes persistency of excitation, in order to facilitate online learning of the system dynamics. Maximization of the minimum eigenvalue of predicted information matrix increments, in a recursive least squares (RLS) scheme, is used. Our main result, achieved by employing inherent robustness from exponentially stabilizing MPC, establishes a bound on the permitted magnitude of excitation applied by the secondary optimization; in terms of the system model error. Satisfaction of this bound guarantees stability of the closed-loop uncertain system, despite the exciting perturbations.