Distributed control of spatially invariant systems

• Published in: IEEE transactions on automatic control Vol. 47; no. 7; pp. 1091 - 1107
• Main Authors: Bamieh, B., Paganini, F., Dahleh, M.A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2002; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Computer science; control theory; systems; Control equipment; Control system synthesis; Control systems; Control theory. Systems; Controllers; Criteria; Distributed control; Distributed parameter systems; Dynamical systems; Dynamics; Exact sciences and technology; Fluid flow measurement; Intelligent structures; Invariants; Microelectromechanical systems; Micromechanical devices; Optimal control; Optimization; Partial differential equations; Vehicle dynamics; System structure; Invariant; Electromechanical device; Differential equation; Precision engineering; H; Distributed system; Micromachine; Linear control; Partial differential equation; LQ control; optimization; Flow control; Decentralization; Miniaturization; Invarying system; Distributed parameter system; Intelligent system; Electromechanical system
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2002.800646

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.