Robust MPC design for multi-model infinite-dimensional distributed parameter systems

Abstract

Infinite-dimensional systems are essential for describing complex phenomena that exhibit continuous spatial and temporal variations. This article introduces a robust model predictive control (RMPC) design to regulate constrained multi-model infinite-dimensional systems governed by a class of hyperbolic/parabolic partial differential equations (PDEs). Model uncertainty stems from system parameters that are imprecisely determined, but can be quantitatively characterized within a certain range. The RMPC algorithm is designed in a discrete-time infinite-dimensional setting, achieved through the structure-preserving Cayley–Tustin transformation without model reduction nor spatial approximation. Robustness of the controller is ensured via constraining the future cost for each model dynamics accounting for uncertainty description. Properties of the closed-loop system are discussed, including feasibility, convergence, and asymptotic stability. The proposed controller is implemented by considering three typical infinite-dimensional distributed parameter process models, with simulation demonstrating the effectiveness and enhanced performance of the RMPC over the nominal model predictive controller.