Dual Adaptive MPC for output tracking of linear systems

In this paper, we present a dual adaptive model predictive control scheme for linear systems with single output subject to noise and parametric uncertainty. The proposed MPC approach incentives exploration of the unknown parameters by minimizing the expected output error, and hence results in a closed-loop behaviour as is typical in dual control. Parameters estimation results from a recursive least squares approach combined with a set-membership estimate. We show that the resulting dual adaptive MPC scheme ensures closed-loop practical stability and robust constraint satisfaction for state, input and output, despite parametric uncertainty and bounded output noise. In a numerical example, we show the practicality of the approach during set-point tracking, and we compare it with a certainty equivalence MPC scheme.