Convexity of optimal control over networks with delays and arbitrary topology
Michael Rotkowitz, Randy Cogill, Sanjay Lall · International Journal of Systems Control and Communications · 2010
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.