Analysis and Synthesis of MIMO Multi-Agent Systems Using Network Optimization

TL;DR

This paper explores the analysis and synthesis of MIMO multi-agent systems with diffusively coupled nonlinear dynamics, establishing a connection to network optimization problems to facilitate controller design for desired steady-states.

Contribution

It introduces the MEICMP property for nonlinear systems and links network steady-states to optimization problem solutions, enabling systematic controller synthesis.

Findings

Networks of MEICMP systems relate to dual optimization problems.

Steady-state behaviors correspond to optimization problem minimizers.

Demonstrated synthesis method on a network of damped oscillators.

Abstract

This work studies analysis and synthesis problems for diffusively coupled multi-agent systems. We focus on networks comprised of multi-input multi-output nonlinear systems that posses a property we term maximal equilibrium-independent cyclically monotonone passivity (MEICMP), which is an extension of recent passivity results. We demonstrate that networks comprised of MEICMP systems are related to a pair of dual network optimization problems. In particular, we show that the steady-state behavior of the multi-agent system correspond to the minimizers of appropriately defined network optimization problems. Exploiting this connection between the dynamic networked system and static optimization problems, we propose a synthesis procedure for designing the coupling controllers in the network to achieve a desired output state for the network. We provide detailed examples of dynamical networked systems satisfying these properties and demonstrate the results for a network of damped planar oscillators.