Title: Convexity of optimal control over networks with delays and arbitrary topology

Authors: Michael Rotkowitz, Randy Cogill, Sanjay Lall

Addresses: Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville VIC 3010, Australia. ' Department of Systems and Information Engineering, The University of Virginia, Charlottesville, VA 22904, USA. ' Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305-4035, USA

Abstract: We consider the design of optimal controllers for a networked system (or a spatio-temporal system), where the dynamics of each subsystem may affect those of other subsystems with some propagation delays, and the controllers may communicate with each other with some transmission delays. We show that if a simple condition holds, then the optimal control problem may be recast as a convex optimisation problem. This is shown to unify and broadly generalise the class of such systems amenable to convex synthesis. When we consider the special case of spatially invariant systems, this again broadly generalises the known class of tractable problems.

Keywords: decentralised control; distributed control; networked control; convex optimisation; quadratic invariance; propagation delays; transmission delays; optimal control.

DOI: 10.1504/IJSCC.2010.031157

International Journal of Systems, Control and Communications, 2010 Vol.2 No.1/2/3, pp.30 - 54

Published online: 23 Jan 2010 *

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