Prof. Timm Faulwasser: Necessary and Sufficient Conditions for Stability in Predictive Control?

Full title: Necessary and Sufficient Conditions for Stability in Predictive Control? - The Optimal Control Point of View Abstract: Model Predictive Control (MPC) - or receding horizon optimal control - is a success story of advanced control in terms of industrial impact and continued research interest. Powerful numerical tools, MPC formulations which cover a variety of settings, as well as convergence and stability results evidence the maturity of MPC. Indeed numerous results in the literature state sufficient conditions for convergence and/or stability. Yet, necessary and sufficient conditions are - to the best of the author's knowledge - not known, and, given the variety of choices for MPC design, appear to be challenging. In this talk, we approach the stability problem from the optimal control point of view, i.e. we analyze the closed loop leveraging the continuous-time maximum principle. We introduce the receding-horizon Hamiltonian - i.e., the value of the optimal control Hamiltonian along the sequence of OCPs solved - as a novel tool for closed-loop analysis. We show how this tool allows the statement of necessary and sufficient conditions for asymptotic convergence of the closed loop to the optimal steady state. We discuss the role of suboptimality and dissipativity in our analysis and we comment on possible extensions.