Motee, Nader (Univ. of Pennsylvania), Jadbabaie, Ali (Univ. of Pennsylvania)

Stability Analysis of Distributed Receding Horizon Control of Spatially Invariant Systems

Scheduled for presentation during the Mini-Symposium "Cooperative Control" (FrA08), Friday, July 28, 2006, 10:50−11:15, Room I

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 11, 2025

Abstract

In this paper, we present a framework for stability analysis of a receding horizon controller for a particular class of networked systems which possess spatial symmetry, known as spatial invariance. A typical example of such systems is a collection of identical dynamical systems connected as an infinite 1-d or 2-d lattice or in a loop.

Recently, we proved that for such systems, the optimal receding horizon controllers (which can be characterized as a convolution sum plus an offset) are inherently decentralized, and the coupling in the explicit formulation of the optimal controllers decays exponentially in spatial domain resulting in a distributed structure. Based on these results, we will present a method for decomposing the centralized receding horizon control problem into a collection of more tractable, local subproblems. We derive a set of LMI conditions for the stability of the closed loop system when the proposed distributed receding horizon control is used. The key property of the LMI conditions is that they only depend on "local" information.