LMI-based Data-Driven Robust Model Predictive Control
This work addresses robust control for systems with uncertain models, but it appears incremental as it builds on existing data-driven and LMI-based methods.
The authors tackled the problem of robust model predictive control when system models are uncertain or unavailable by proposing a data-driven approach using linear matrix inequalities, which stabilizes the closed-loop system and ensures constraint satisfaction.
Predictive control, which is based on a model of the system to compute the applied input optimizing the future system behavior, is by now widely used. If the nominal models are not given or are very uncertain, data-driven model predictive control approaches can be employed, where the system model or input is directly obtained from past measured trajectories. Using a data informativity framework and Finsler's lemma, we propose a data-driven robust linear matrix inequality-based model predictive control scheme that considers input and state constraints. Using these data, we formulate the problem as a semi-definite optimization problem, whose solution provides the matrix gain for the linear feedback, while the decisive variables are independent of the length of the measurement data. The designed controller stabilizes the closed-loop system asymptotically and guarantees constraint satisfaction. Numerical examples are conducted to illustrate the method.