Two level model predictive control for the maximum control invariant set

This paper presents an extension of the Two-Level Model Predictive Control (MPC) scheme presented in [13]. The procedure in [13] allows for computationally efficient MFC over a subset of the controllable state-space. The first controller level provides a stability guarantee and the second level optimizes performance. This two-level control scheme allows for a transparent tradeoff between the necessary on-line computation power and performance. However, the scheme also suffers from two drawbacks. The two-level controller [13] does not cover all controllable states and in order to guarantee constraint satisfaction in closed-loop, it is necessary to resort to open-loop control for certain initial states. These issues are dealt with in this paper. We will extend the procedure such that the controller covers the infinite time controllable set ∞(χ _I) with closed-loop stability and feasibility guarantee. The set ∞ (χ _I) denotes all states which may be driven to the set χ _I by an admissible control law.