Velocity-Free Distributed Optimization Algorithms for Second-Order Multi-Agent Systems

This paper concerns the distributed optimization problem of dynamical systems using partial state information. Such a problem is motivated by the fact that optimization missions are often subject to dynamical constraints and sensor malfunction. To cooperatively deal with the optimization problem for second-order multi-agent systems in the absence of velocity information, we design two velocity-free distributed optimization algorithms over different communication topologies. First, for the case of the continuous communication, a fully velocity-free distributed optimization algorithm is designed by leveraging a novel auxiliary dynamics, and each local cost function is just required to be convex. It is shown that all the agents are capable of achieving rendezvous on one of the optimal solutions of interest despite the absence of velocity information. Next, to relieve the communication burden, a modified velocity-free distributed optimization algorithm is designed by introducing an event-based communication mechanism, where all the local cost functions are required to be strongly convex. Particularly, a communication trigger condition is built such that the undesirable Zeno phenomenon is circumvented. Also, an adaptive gain is introduced to make the modified optimization algorithm fully distributed. Simulations are finally given to verify the optimization performance.