Distributed Practical Fixed-Time Resource Allocation Algorithm for Disturbed Multiagent Systems: An Integrated Framework

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.