Cooperative Optimization with Nonconvex Input Constraints and Dynamically Changing Graphs

Abstract

This paper addresses a cooperative optimization problem of first-order discrete-time multiagent systems with nonconvex control input constraints and dynamically changing graphs. We introduce a cooperative optimization algorithm with a switching mechanism to ensure all agents reach a consensus point, while their control inputs are constrained in a nonconvex region. The mechanism is performed to tackle the coexistence of the nonconvex constraint operator and the optimization gradient term. Based on the dynamic transformation technique, the primitive nonlinear dynamic system was transformed into an equivalent system with error term. By utilizing the nonnegative matrix theory, it's clear that the proposed optimization problem could be addressed when the union of dynamically changing graphs is jointly connected.