Predefined‐Time Distributed Time‐Varying Optimization of Multi‐Agent Systems in Directed Graphs

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ABSTRACT This paper proposes novel distributed optimization algorithms, which exhibit predefined‐time convergence for two classes of distributed time‐varying optimization problems—consensus optimization and resource allocation—over the directed communication network. First, based on the time‐varying scaling function mechanism, a distributed average estimator is ingeniously designed to estimate the global states of the optimized multi‐agent systems (MASs). Utilizing the estimator's outputs, a predefined‐time convergence algorithm is constructed, which makes the decision variable of the MASs converge to the optimal solution of the consensus optimization problem after . Then, for the quadratic objective functions, a distributed optimization algorithm based on Lagrangian multipliers is developed to solve the time‐varying resource allocation problem within the predefined time . Finally, two simulation cases verify the effectiveness of the proposed algorithms.

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