Robust Performance Analysis of Cooperative Control Dynamics via Integral Quadratic Constraints

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, strongly convex scalar field with a subset of agents having gradient based forcing terms and consider formation control dynamics (with convex interactions) and flocking dynamics (with non-convex interactions) as possible interaction mechanisms. 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 flocking interaction potential is assumed time-invariant and uncertain. Sufficient conditions take the form of linear matrix inequalities independent of the size of the 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. Numerous examples illustrate the application of theoretical results.Comment: arXiv admin note: substantial text overlap with arXiv:2110.06369 author's note: added a main contributions list, minor changes to title, abstract, introduction, added a better example in Fig. 8, all other results unchange

Electrokinetic Lattice Boltzmann solver coupled to Molecular Dynamics: application to polymer translocation

We develop a theoretical and computational approach to deal with systems that involve a disparate range of spatio-temporal scales, such as those comprised of colloidal particles or polymers moving in a fluidic molecular environment. Our approach is based on a multiscale modeling that combines the slow dynamics of the large particles with the fast dynamics of the solvent into a unique framework. The former is numerically solved via Molecular Dynamics and the latter via a multi-component Lattice Boltzmann. The two techniques are coupled together to allow for a seamless exchange of information between the descriptions. Being based on a kinetic multi-component description of the fluid species, the scheme is flexible in modeling charge flow within complex geometries and ranging from large to vanishing salt concentration. The details of the scheme are presented and the method is applied to the problem of translocation of a charged polymer through a nanopores. In the end, we discuss the advantages and complexities of the approach

A Decomposition Approach to Multi-Agent Systems with Bernoulli Packet Loss

In this paper, we extend the decomposable systems framework to multi-agent systems with Bernoulli distributed packet loss with uniform probability. The proposed sufficient analysis conditions for mean-square stability and $H_2$-performance - which are expressed in the form of linear matrix inequalities - scale linearly with increased network size and thus allow to analyse even very large-scale multi-agent systems. A numerical example demonstrates the potential of the approach by application to a first-order consensus problem.Comment: 11 pages, 4 figure