Duality and network theory in passivity-based cooperative control

• Published in: Automatica (Oxford) Vol. 50; no. 8; pp. 2051 - 2061
• Main Authors: Bürger, Mathias, Zelazo, Daniel, Allgöwer, Frank
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.08.2014; Elsevier
• Subjects: Adaptative systems; Applied sciences; Computer science; control theory; systems; Control system synthesis; Control theory. Systems; Convex optimization; Cooperative control; Exact sciences and technology; Networks; Networks; Convex optimization; Cooperative control; Interconnected power system; Control synthesis; Dynamical system; Passive system; Adaptive control; Passivity; Convex programming; Optimization; Potential flow; Multiagent system; Network analysis; Cooperation; Non linear model; Classification; Distributed control; Asymptotic approximation; Dynamic model; Optimal flow
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2014.06.002

This paper presents a class of passivity-based cooperative control problems that have an explicit connection to convex network optimization problems. The new notion of maximal equilibrium independent passivity is introduced and it is shown that networks of systems possessing this property asymptotically approach the solutions of a dual pair of network optimization problems, namely an optimal potential and an optimal flow problem. This connection leads to an interpretation of the dynamic variables, such as system inputs and outputs, to variables in a network optimization framework, such as divergences and potentials, and reveals that several duality relations known in convex network optimization theory translate directly to passivity-based cooperative control problems. The presented results establish a strong and explicit connection between passivity-based cooperative control theory on the one side and network optimization theory on the other, and they provide a unifying framework for network analysis and optimal design. The results are illustrated on a nonlinear traffic dynamics model that is shown to be asymptotically clustering.