Constrained finite-time stabilization by model predictive control: an infinite control horizon framework

Existing results on finite-time model predictive control (MPC) often rely on terminal equality constraint, switching inside one-step region, or terminal cost with short control horizon, leading to limited initial feasibility. This paper proposes an infinite-horizon Model Predictive Control (MPC) framework for the constrained finite-time stabilization of discrete-time systems, overcoming limitations found in existing finite-time MPC results. The proposed framework is built upon a terminal cost strategy, but expands it by replacing the short-horizon terminal cost with the sum of stage costs over an infinite control horizon. This design choice significantly enlarges the initial feasibility region and avoids the need for terminal equality constraints or switching strategies during implementation. It is proved that the proposed finite-time MPC guarantees finite-time stabilization performance once the state trajectory enters the predefined terminal set. The infinite-horizon finite-time MPC is shown to be equivalently implementable as a finite-horizon MPC with a terminal cost, thereby ensuring computational tractability. The proposed finite-time MPC is systematically extended and shown to be applicable to both constrained multi-input linear systems and a class of constrained nonlinear systems that are feedback linearizable.