A Trajectory-based Approach to the Computation of Controlled Invariants with application to MPC
This work addresses the challenge of ensuring recursive feasibility in model predictive control for linear systems, offering a practical computational method that could benefit control engineering applications, though it appears incremental as it builds on existing backward fixed-point algorithms.
The paper tackles the problem of computing controlled invariant sets for linear discrete-time systems by introducing a trajectory-based viewpoint and convex feasible points, enabling the computation of maximal invariant sets and the design of MPC schemes that ensure recursive feasibility without terminal sets, with effectiveness demonstrated through numerical examples.
In this paper, we revisit the computation of controlled invariant sets for linear discrete-time systems through a trajectory-based viewpoint. We begin by introducing the notion of convex feasible points, which provides a new characterization of controlled invariance using finitely long state trajectories. We further show that combining this notion with the classical backward fixed-point algorithm allows us to compute the maximal controlled invariant set. Building on these results, we propose two MPC schemes that guarantee recursive feasibility without relying on precomputed terminal sets. Finally, we formulate the search for convex feasible points as an optimization problem, yielding a practical computational method for constructing controlled invariant sets. The effectiveness of the approach is illustrated through numerical examples.