Robust MPC for Large-scale Linear Systems
Georg Schildbach
TL;DR
This work targets robust control for large-scale linear systems where traditional Robust MPC relies on precomputing intractable robust positively invariant (RPI) sets. It introduces Deadbeat Robust MPC (DRMPC), which uses a deadbeat disturbance-feedback prestabilization with offline gains to circumvent RPI computation while preserving recursive feasibility and ISS guarantees. The online DRMPC problem retains identical structure and computational complexity to Nominal MPC, while tightening constraints to account for disturbances; the offline design avoids the curse of dimensionality associated with RPI sets. A numerical study on randomly generated large-scale systems demonstrates DRMPC’s scalability and practicality, pushing robust MPC applicability to hundreds of states with similar online effort as nominal control.
Abstract
State-of-the-art approaches of Robust Model Predictive Control (MPC) are restricted to linear systems of relatively small scale, i.e., with no more than about 5 states. The main reason is the computational burden of determining a robust positively invariant (RPI) set, whose complexity suffers from the curse of dimensionality. The recently proposed approach of Deadbeat Robust Model Predictive Control (DRMPC) is the first that does not rely on an RPI set. Yet it comes with the full set of essential system theoretic guarantees. DRMPC is hence a viable option, in particular, for large-scale systems. This paper introduces a detailed design procedure for DRMPC. It is shown that the optimal control problem generated for DRMPC has exactly the same computational complexity as Nominal MPC. A numerical study validates its applicability to randomly generated large-scale linear systems of various dimensions.