Design of low-dimensional controllers for high-dimensional systems

This article presents proposals for the design of reduced-order controllers for high-dimensional dynamical systems. The objective is to develop efficient control strategies that ensure stability and robustness with reduced computational complexity. By leveraging the concept of partial pole placement, which involves placing a subset of the closed-loop system’s poles, this study aims to strike a balance between reduced-order modeling and control effectiveness. The proposed approach addresses the challenges posed by high-dimensional systems and provides a systematic framework for controller design. When an infinite-dimensional operator is Riesz spectral, our theoretical analysis highlights the potential of partial pole placement in advancing control design. Model uncertainties, introduced by an error in the spectral decomposition, can also be allowed. This is particularly illustrated in the case of systems modeled by coupled ordinary-partial differential equations (ODE-PDE).