Convergence analysis of distributed optimization for multi-agent systems with nonlinear intertwining uncertainties

The paper investigates the distributed optimization for continuous-time multi-agent systems in the presence of nonlinear intertwining uncertainties. The agents only communicate with their neighbors and are expected to reach the optimal point such that the global cost function comprising a sum of local cost functions is minimized. The uncertainties are dependent on the states of all agents and have nonlinear growth rate. To handle the nonlinear intertwining uncertainties, a new distributed optimization algorithm is proposed, which consists of four parts: the estimation of uncertainties by reduced order extended state observer, uncertainty compensation, distributed coordination strategy, and local gradient descent. Then the bound of optimal error is provided as a function with respect to the tunable parameters in the developed method. Moreover, by analyzing the coupling dynamics of agents and estimating errors, the convergence of the proposed method is proved under a mild condition for nonlinear uncertainties.