Robust Performance Analysis of Cooperative Control Dynamics via Integral Quadratic Constraints

TL;DR

This paper introduces a novel framework using integral quadratic constraints to analyze the convergence and stability of cooperative control systems with uncertain interactions, applicable to formation control and flocking dynamics.

Contribution

It develops an $ ext{α}$-IQC-based approach for stability analysis of cooperative control with uncertain, time-invariant communication graphs, including new derivations of Zames-Falb IQCs in the time domain.

Findings

Convergence rate estimates are obtained for stable systems.

Linear matrix inequalities are used for stability conditions, independent of network size.

Numerical examples demonstrate the effectiveness of the theoretical framework.

Abstract

We study cooperative control dynamics with gradient based forcing terms. As a specific example, we focus on source-seeking dynamics with vehicles embedded in an unknown scalar field with a subset of agents having gradient information. As interaction mechanisms, formation control dynamics and flocking dynamics are considered. We leverage the framework of $\alpha$-integral quadratic constraints to obtain convergence rate estimates whenever exponential stability can be achieved. The communication graph and the interaction potential are assumed to be time-invariant and uncertain. Sufficient conditions take the form of linear matrix inequalities independent of the size of network. A derivation (purely in time-domain) of the so-called \textit{hard} Zames-Falb $\alpha$-IQCs involving general non-causal higher order multipliers is given along with a suitably adapted parameterization of the multipliers to the $\alpha$-IQC setting. The time-domain arguments facilitate a straightforward extension to linear parameter varying systems. Numerical examples illustrate the application of the theoretical results.