Robust Data-Driven Predictive Control using Reachability Analysis
This work addresses safety-critical control applications by providing a robust, model-free alternative to traditional predictive control, though it is incremental as it builds on existing reachability methods.
The paper tackles the problem of controlling unknown linear systems with bounded noise by proposing a data-driven predictive control scheme using reachability analysis, which guarantees robust constraint satisfaction and matches model-based performance in noise-free cases.
We present a robust data-driven control scheme for an unknown linear system model with bounded process and measurement noise. Instead of depending on a system model in traditional predictive control, a controller utilizing data-driven reachable regions is proposed. The data-driven reachable regions are based on a matrix zonotope recursion and are computed based on only noisy input-output data of a trajectory of the system. We assume that measurement and process noise are contained in bounded sets. While we assume knowledge of these bounds, no knowledge about the statistical properties of the noise is assumed. In the noise-free case, we prove that the presented purely data-driven control scheme results in an equivalent closed-loop behavior to a nominal model predictive control scheme. In the case of measurement and process noise, our proposed scheme guarantees robust constraint satisfaction, which is essential in safety-critical applications. Numerical experiments show the effectiveness of the proposed data-driven controller in comparison to model-based control schemes.