Input-Output Stability of Barrier-Based Model Predictive Control
For control engineers, this work provides a theoretical framework to certify stability of barrier-based MPC, but it is incremental as it extends existing IQC methods to a specific control formulation.
This paper establishes conditions for input-output stability of barrier-based model predictive control for linear systems with constraints, using integral quadratic constraints (IQCs) to derive sufficient conditions for global closed-loop stability and robust stability under model uncertainty. The approach is demonstrated with a numerical example.
Conditions for input-output stability of barrier-based model predictive control of linear systems with linear and convex nonlinear (hard or soft) constraints are established through the construction of integral quadratic constraints (IQCs). The IQCs can be used to establish sufficient conditions for global closed-loop stability. In particular conditions for robust stability can be obtained in the presence of unstructured model uncertainty. IQCs with both static and dynamic multipliers are developed and appropriate convex searches for the multipliers are presented. The effectiveness of the robust stability analysis is demonstrated with an illustrative numerical example.