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Coordination of groups of mobile autonomous agents using nearest neighbor rules
A theoretical explanation for the observed behavior of the Vicsek model, which proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
On the stability of the Kuramoto model of coupled nonlinear oscillators
We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to
Flocking in Fixed and Switching Networks
This note analyzes the stability properties of a group of mobile agents that align their velocity vectors, and stabilize their inter-agent distances, using decentralized, nearest-neighbor interaction
Safety Verification of Hybrid Systems Using Barrier Certificates
This paper presents a novel methodology for safety verification of hybrid systems by proving that all trajectories of a hybrid system do not enter an unsafe region using a function of state termed a barrier certificate.
Online optimization in dynamic environments: Improved regret rates for strongly convex problems
A regret bound is derived that captures the path-length of the time-varying parameter, defined in terms of the distance between its consecutive values, which represents the natural connection of tracking quality to the rate of change of the parameter.
A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates
This paper presents a methodology for safety verification of continuous and hybrid systems in the worst-case and stochastic settings, and computes an upper bound on the probability that a trajectory of the system reaches the unsafe set, a bound whose validity is proven by the existence of a barrier certificate.
Online Optimization : Competing with Dynamic Comparators
A fully adaptive method is presented that competes with dynamic benchmarks in which regret guarantee scales with regularity of the sequence of cost functions and comparators, and adapts to the smaller complexity measure in the problem environment.
Stable flocking of mobile agents, part I: fixed topology
This first part generates stable flocking motion for the group using a coordination control scheme which gives rise to smooth control laws for the agents, ensuring collision avoidance and cohesion of the group and an aggregate motion along a common heading direction.
Distributed Online Optimization in Dynamic Environments Using Mirror Descent
A decentralized variation of the celebrated mirror descent algorithm is proposed, according to which agents perform a consensus step to follow the global function and take into account the dynamics of the global minimizer, to address decentralized online optimization in nonstationary environments.