Robust Model Predictive Control with Polytopic Model Uncertainty through System Level Synthesis

21 Mar 2022  ·  Shaoru Chen, Victor M. Preciado, Manfred Morari, Nikolai Matni ·

We propose a novel method for robust model predictive control (MPC) of uncertain systems subject to both polytopic model uncertainty and additive disturbances. In our method, we over-approximate the actual uncertainty by a surrogate additive disturbance which simplifies constraint tightening of the robust optimal control problem. Using System Level Synthesis, we can optimize over a robust linear state feedback control policy and the uncertainty over-approximation parameters jointly and in a convex manner. The proposed method is demonstrated to achieve feasible domains close to the maximal robust control invariant set for a wide range of uncertainty parameters and significant improvement in conservatism compared with tube-based MPC through numerical examples.

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