Sub-Optimal MPC With Dynamic Constraint Tightening

Abstract

Limited computation resources forces early (sub-optimal) termination of the solvers used for model predictive controllers (MPCs). This can compromise the feasibility and stability guarantees of the initial MPC design. In this letter, we consider a dual gradient descent algorithm for solving linear MPC problems with state and input constraints under a fixed number of optimization iterations. To address feasibility issues caused by sub-optimal solutions, we propose a novel sub-optimal MPC scheme with a dynamic constraint tightening strategy. We characterize the interaction between the sub-optimally controlled system and the constraint tightening update process as two interconnected subsystems. By constructing a positive invariant set for the interconnected system and utilizing the small-gain theorem, we show sufficient conditions on the number of iterations of the optimization algorithm and the initial tightening parameter which guarantee recursive feasibility and asymptotic stability of the closed-loop system.