Distributed control design with local model information and guaranteed stability

Abstract

Most results on distributed control design of large-scale interconnected systems assume a central designer with global model knowledge. The wish for privacy of subsystem model data raises the desire to find control design methods to determine an optimal control law without centralized model knowledge, i.e. in a distributed fashion. In this paper we present a distributed control design method with guaranteed stability to minimize an infinite horizon LQ cost functional. The introduction of adjoint states allows to iteratively optimize the feedback matrix using a gradient descent method in a distributed way, based on a finite horizon formulation. Inspired by ideas on stabilizing model predictive control, a terminal cost term is used, which gives a bound on the infinite horizon cost functional and ensures stability. A method is presented to determine that term in a distributed fashion. The results are validated using numerical experiments.

Event-based data scheduling for a class of interconnected networked control systems

“…pair (A, B) is stabilizable, an emulative control law, e.g. [3], ensures the gain L consisting of blocks L i on the diagonal and L ij on the off-diagonal is stabilizing, i.e. the closed-loop matrix (A−BL) is Hurwitz.…”

“…Recently, many results have treated distributed control of interconnected systems, see e.g. [2], [3] among many others.…”