Distributed Practical Fixed-Time Resource Allocation Algorithm for Disturbed Multiagent Systems: An Integrated Framework
针对受扰多智能体系统，提出一种融合固定时间控制与梯度一致性的集成框架，通过输出反馈反步设计实现全局等式与局部不等式约束下的资源分配，确保系统在固定时间内稳定且输出接近最优解。
The practical fixed-time resource allocation problem is investigated for multi-input-multi-output nonlinear uncertain multiagent systems with disturbed dynamics, subject to global equality and local inequality constraints. Due to the coexistence of distributed high-order dynamics system within agents and decision-making constraints, decision variables in resource allocation optimization problems cannot be directly obtained from the system. Existing strategies are insufficient to solve such complex fixed-time optimization control problems with coupled decision-making constraints. To address these challenges, a novel integrated framework is proposed, fusing symbolic-function-based fixed-time control theory with gradient consistency. The proposed algorithm is implemented through an output-feedback backstepping design process, which involves two stages. First, in the output-feedback design stage, a fixed-time high-order extended state observer estimates the uncertain dynamics and disturbances. Second, in the backstepping design stage, a time-switching controller is developed. This controller's virtual control law has two components: the first employs the proportional-integral control method to satisfy the equality constraints, while the second uses gradient information from the $\epsilon $ -exact penalty function to address the inequality constraints. Using the Lyapunov stability criterion, the proposed algorithm can ensure that all signals remain practical fixed-time stable, and that the error between the outputs of all agents and the optimal solution is maintained within a neighborhood of the origin. Finally, simulations are presented to demonstrate the effectiveness of the approach.