Distributed finite-time optimization algorithms of higher-order multiagent systems with uncertain nonlinearities

There are few distributed finite-time optimization results of nonlinear multiagent systems in the published literatures, especially in the case that system nonlinearities are unknown. In this paper, distributed finite-time optimization problem is investigated for higher-order multiagent systems with uncertain nonlinearities. The agent dynamics are permitted to be heterogeneous with different nonlinearities and different orders. This problem is solved by embedded control approach-based distributed finite-time optimization algorithms, which consist of two parts. In the first part, a first-order finite-time optimal signal generator is designed, of which outputs reach the minimizer of the global cost function in finite time. In the second part, embedding the generator into the feedback loop and taking the outputs of the generator as the reference outputs of the agents, and combining finite-time control and feedback domination technique together, tracking controllers are designed for the higher-order nonlinear multiagent systems to track their local optimal reference outputs in finite time. It is rigorously proven that under the proposed distributed optimization algorithms, all the agent outputs reach a bounded neighbor region of the global minimizer in finite time. The effectiveness of the proposed control algorithms is illustrated by simulations.