Distributed Fixed-Time Optimization for Second-Order Nonlinear Multiagent Systems: State and Output Feedback Designs

This paper addresses the problem of distributed fixed-time optimization for heterogeneous second-order nonlinear multiagent systems with local time-varying cost functions. The objective is to cooperatively minimize a convex global time-varying cost function formed by a sum of local time-varying cost functions in a fixed time, where each local cost function is not necessarily required to be convex. A state feedback distributed fixed-time optimization controller with an estimator-based distributed optimization term is first presented. In order to overcome the lack of the absolute velocity measurements, a distributed fixed-time observer is designed to estimate the absolute velocity information of each agent. Based on the designed observer, a novel output feedback distributed fixed-time optimization controller using only local output measurements is further presented. Both of the presented state and output feedback distributed fixed-time optimization controllers ensure that all agents reach a consensus while minimizing the global cost function within a fixed time. The restrictive bound of the fixed time is estimated explicitly, which is irrelevant to any initial conditions. Finally, a numerical simulation is provided to validate the results.