Recursive data–driven predictive control with persistence of excitation conditions

In this paper we develop a recursive linear predictive control algorithm with integral action and plug-and-play capabilities. Typically, adaptive model predictive control requires a recursive estimation step for updating the prediction model and then builds prediction matrices on-line. In contrast to this approach, we develop a least-squares algorithm for recursively estimating the prediction matrices directly. We then exploit an analytic relation between standard and integral prediction matrices to recursively estimate the latter. Furthermore, to assess the convergence of the closed-loop estimation, we discuss various methods that generate a persistently exciting input. The efficiency of the recursive integral predictive controller is demonstrated on a motion control application.