Deadbeat Robust Model Predictive Control for Linear Parameter‐Varying Systems

The concept of Deadbeat Robust Model Predictive Control (DRMPC) has recently been established for linear systems, providing full system theoretic guarantees, while reducing the computational and conceptual complexity. This article extends DRMPC to systems with multiplicative uncertainty (“robust linear”) and systems that depend on a (slowly) varying parametric uncertainty (“linear parameter‐varying”), for which the uncertainty can be converted to a bounded additive disturbance to a nominal linear system. Besides avoiding the reliance on a Robust Positive Invariant (RPI) set, LPV‐DRMPC allows to shift a significant portion of the computations offline. Rigorous proofs of recursive feasibility and robust exponential stability can be established, as shown in the article. The performance of LPV‐DRMPC is evaluated in a simulation study, based on a commonly used benchmark example. The study demonstrates that the proposed LPV‐DRMPC, using the origin as the terminal set and a slightly increased prediction horizon, is almost comparable to other, state‐of‐the‐art LPV‐MPC schemes, while offering a much simpler setup and a lower computational complexity.