Distributed infinite‐horizon optimal control of continuous‐time linear systems over network

Abstract

This article deals with the distributed infinite‐horizon linear‐quadratic‐Gaussian optimal control problem for continuous‐time systems over networks. In particular, the feedback controller is composed of local control stations, which receive some measurement data from the plant process and regulates a portion of the input signal. We provide a solution when the nodes have information on the structural data of the whole network but takes local actions, and also when only local information on the network are available to the nodes. The proposed solution is arbitrarily close to the optimal centralized one (in terms of cost index) when a design parameter is set sufficiently large. Numerical simulation validate the theoretical results.

Distributed Infinite-Horizon Optimal Control of Discrete-Time Linear Systems over Networks

“…We consider the academic, but challenging, example of [2] in which the network topology is characterized in Figure 2, the system matrices are given by…”

“…G n w L P g T v g h 3 w 9 f / 0 K D X 5 j x h K x a K v 1 l Z 1 Z A = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " A Y P tr(X (2) ) tr(X (3) ) tr(X (4) ) tr(X (5) )…”

“…In these applications, the ability of a network system to fuse information, compute common estimates of unknown quantities, and agree on a common view of the environment in a decentralized/distributed fashion is critical. In particular, sensor networks and multi-agent systems, composed by a set of homogeneous or heterogeneous systems that communicate over a network, represented by a graph, have attracted much attention in recent years due to their potential application in many scenarios, for instance monitoring through wireless sensor networks [39], [22], formation control of mobile vehicles [26], [3], distributed optimization [19], cooperative control [2], [25], power networks [14], and also to systems with time-delay [23], [24], among many others.…”

“…Finally, for the continuous-time analog we refer to [7] for the optimal filtering problem and to [2], [15] for the optimal control problem.…”