Accelerated iterative distributed controller synthesis with a Barzilai-Borwein step size

Distributed control of large-scale dynamical systems poses a new challenge to the field of control driven by the technological advances of modern communication networks. A particular challenge is the distributed design of such control systems. Here, a distributed iterative controller synthesis method for continuous time linear systems using a gradient descent method is presented. One of the main contributions is the determination of the step size according to a distributed Barzilai-Borwein (BB) method. As the control objective, we treat the finite horizon linear quadratic cost functional. The gradient approach uses communication only with direct neighbors and is based on the forward simulation of the system states and the backwards simulation of adjoint states. The effectiveness of the approach is shown by means of numerical simulations.