Prescribed‐Time Distributed Optimization With Set Constraints Based on Time‐Domain Transformation

ABSTRACT This paper delves into the prescribed‐time distributed optimization problem for multi‐agent systems (MASs), considering set constraints. First, we transform the challenging optimization problem from the prescribed‐time ‐domain into the asymptotic time ‐domain through a time‐domain transformation (TDT) technique. This strategic shift substantially mitigates the analytical complexities inherent in the original formulation. Second, we develop a novel class of TDT‐based optimization algorithms, utilizing gradient projection and Lagrange multipliers. This algorithm is tailored to efficiently tackle the distributed optimization problem while adhering to the set constraints. To further alleviate the computational and communication overheads, we introduce a corresponding TDT‐based event‐triggered optimization algorithm. Moreover, a rigorous analysis of both the optimal solution to the optimization problem and the system's stability is given by using optimization theory and Lyapunov stability theory. This comprehensive analysis provides valuable insights into the behavior and performance of our proposed approach. Finally, two numerical simulation results are presented to demonstrate the feasibility as well as effectiveness of the offered distributed control arrangement.