Model Predictive Control, Cost Controllability, and Homogeneity *

Jean-Michel Coron (1) , Lars Grüne (2) , Karl Worthmann (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Mathematisches Institut [Bayreuth]
3 TU - Technische Universität Ilmenau

We are concerned with the design of Model Predictive Control (MPC) schemes such that asymptotic stability of the resulting closed loop is guaranteed even if the linearization at the desired set point fails to be stabilizable. Therefore, we propose to construct the stage cost based on the homogeneous approximation and rigorously show that applying MPC yields an asymp-totically stable closed-loop behavior if the homogeneous approximation is asymptotically null controllable. To this end, we verify cost controllability-a condition relating the current state, the stage cost, and the growth of the value function w.r.t. time-for this class of systems in order to provide stability and performance guarantees for the proposed MPC scheme without stabilizing terminal costs or constraints.

Mots clés: Cost controllability; homogeneity; homogeneous approximation; model predictive control; stability guarantee

Domaines: Optimisation et contrôle [math.OC]

Jean-Michel Coron, Lars Grüne, Karl Worthmann. Model Predictive Control, Cost Controllability, and Homogeneity *. 2019. ⟨hal-02151402v1⟩