Distributed extremum-seeking based resource allocation algorithm with input dead-zone

This paper studies distributed resource allocation problem for agents with input dead-zone, which is not considered in the existing work. At first, the primal problem is transformed to an auxiliary problem by using the exact penalty method to deal with local inequality constraints. It is assumed that the explicit expressions of cost functions and local inequality constraints are unknown to agents but the values of the cost and constraint functions can be obtained. Under such a setup, the extremum seeking control is used to estimate the gradient information. Thus, to obtain the optimal allocation, a novel distributed algorithm is designed by the virtue of the extremum seeking control and a dynamic compensating mechanism which is used to handle the effects of the input dead-zone. Due to a two time-scale structure of the designed distributed algorithm, the semi-globally practically asymptotical convergence of all agents' decisions to the optimal allocation is obtained by the singular perturbation technique. Finally, numerical examples of economic dispatch in smart grids are given to verify the effectiveness of our proposed method.