Distributed control of spatially invariant systems

TLDR

Distributed parameter systems with spatially invariant dynamics arise in applications such as vehicular platoons, flow control, MEMS, smart structures, and PDEs with constant coefficients. For fully actuated distributed control problems with quadratic criteria (LQR, H₂, H∞), optimal controllers are obtained by solving a parameterized family of standard finite‑dimensional problems. Optimal controllers exhibit inherent decentralization, inherit the plant’s spatial invariance, and thus enable practical distributed architectures while extending to partially distributed control and various performance criteria.

Abstract

We consider distributed parameter systems where the underlying dynamics are spatially invariant, and where the controls and measurements are spatially distributed. These systems arise in many applications such as the control of vehicular platoons, flow control, microelectromechanical systems (MEMS), smart structures, and systems described by partial differential equations with constant coefficients and distributed controls and measurements. For fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator (LQR), H/sub 2/ and H/sub /spl infin//, optimal controllers can be obtained by solving a parameterized family of standard finite-dimensional problems. We show that optimal controllers have an inherent degree of decentralization, and this provides a practical distributed controller architecture. We also prove a general result that applies to partially distributed control and a variety of performance criteria, stating that optimal controllers inherit the spatial invariance structure of the plant. Connections of this work to that on systems over rings, and systems with dynamical symmetries are discussed.