Abstract
This brief is concerned with a distributed optimization problem over an undirected multi-agent network, where each agent is assigned a private cost function which is strongly convex with a Lipschitz gradient. First, an event-triggered communication strategy is adopted to reduce network communication, and an event-based auxiliary system is constructed to estimate the optimal solution. The estimation is used to generate a reference signal and its high-order derivatives, which is an approximation of the optimal solution. Then, a backstepping control algorithm is developed to drive all agents’ output to the reference signal. In terms with the Lyapunov stability theory and the algebraic graph theory, it can be proved that the distributed optimization problem is solved by the developed control algorithm. Different from the existing algorithms, eigenvalues of the Laplacian matrix are not used in our proposed control design. Finally, a simulation example is presented to validate the theoretical result.
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