Stabilizing predictive control with persistence of excitation for constrained linear systems
It addresses the challenge of combining persistent excitation with constraint satisfaction in adaptive MPC for linear systems, offering theoretical guarantees that are incremental over standard MPC.
The paper introduces an adaptive predictive controller for constrained linear systems that splits input into an excitation component for parameter estimation and a regulation component via tube MPC, achieving robust exponential stability and convergent estimates under mild conditions.
A new adaptive predictive controller for constrained linear systems is presented. The main feature of the proposed controller is the partition of the input in two components. The first part is used to persistently excite the system, in order to guarantee accurate and convergent parameter estimates in a deterministic framework. An MPC-inspired receding horizon optimization problem is developed to achieve the required excitation in a manner that is optimal for the plant. The remaining control action is employed by a conventional tube MPC controller to regulate the plant in the presence of parametric uncertainty and the excitation generated for estimation purposes. Constraint satisfaction, robust exponential stability, and convergence of the estimates are guaranteed under design conditions mildly more demanding than that of standard MPC implementations.