A New Framework for Model Predictive Control Stability Analysis

Model predictive control (MPC) is a well performing control strategy that historically has been applied only to systems with slow dynamics due to the time consuming optimization problem that is solved in every iteration. With increased computational power, also systems with faster dynamics have more recently been controlled by MPC.

To theoretically guarantee stability, the problem must typically be solved to optimality, while numerical evidence suggests that only a few iterations of the optimization algorithm can be enough.

To push the applicability of MPC with maintained stability guarantees to systems with even faster dynamics, theoretical stability tools must be able to analyze MPC systems with a finite number of algorithm iterations.

The main objective and foundation of this work is to develop a novel computer-aided automated Lyapunov analysis framework to analyze stability of MPC schemes given an iteration constraint on the optimization algorithm. The framework will build upon the performance estimation (PEP) and the integral quadratic constraint (IQC) frameworks.

These are very powerful tools, but has never been used for this purpose.

Besides applying these tools to MPC, we will provide insights on their connection, advance their understanding, and extend their applicability. The project will have one PhD student (80%) with the research proposer as supervisor and contributor (30%).