Predefined-time distributed constrained multi-conflicting objective optimization with nonlinear uncertainty over directed graph

This paper addresses the constrained multi-conflicting objective optimization (MCOO) problem for multi-agent systems under strong nonlinear uncertainty over directed graph. Each agent is subject to multiple conflicting local objectives. To enable agents to autonomously seek the Pareto optimality of the MCOO problem, three distributed algorithms are developed. First, by utilizing the online updating weighted $L_p$ preference index, the MCOO problem is reformulated into a single-objective optimization problem, and two essential parameters are determined by solving auxiliary optimization subproblems. Next, to actively eliminate and compensate for the impact of strong nonlinear uncertainty in three optimization problems, three reduced-order extended vector observers are utilized. By the three proposed algorithms employing time-based generator, state feedback, and disturbance compensation, all agents converge to an arbitrarily small neighborhood of the Pareto optimality within predefined time, although strong nonlinear uncertainty exists and the predefined time can be set arbitrarily. Furthermore, simulation example verifies the effectiveness of the proposed algorithms.