Robust Performance Analysis of Cooperative Control Dynamics via Integral Quadratic Constraints

In this article, 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. We consider time-invariant and uncertain interaction potentials common in formation control and flocking. We leverage the framework of $\alpha$-integral quadratic constraints (IQCs) to obtain convergence rate estimates whenever exponential stability can be achieved. 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 hard Zames–Falb $\alpha$-IQCs involving general noncausal higher order multipliers is given along with a suitably adapted parameterization of the multipliers to the $\alpha$-IQC setting. Numerical examples illustrate the application of theoretical results.