Switching Adaptive Model Predictive Control for Perturbed Linear Time-Varying Systems

In this paper we implement robust switching model predictive control to solve the dual control problem of simultaneous regulation and system identification, for linear time varying systems subject to bounded external disturbances and confined instances of variation. We leverage the piece-wise linear control law resulting from a fictitious switching architecture to generate closed-loop data that ensures strong system identifiability, while guaranteeing stability and constraint satisfaction under unknown—but bounded—disturbances and parameter variation. We pair the switching controller with a standard recursive estimation algorithm with forgetting factor, which yields unbiased estimates with variance associated to the external disturbance, showcasing the success of the switching at producing information in the closed-loop trajectories.