Initialization-Free Distributed Fixed-Time Convergent Algorithms for Optimal Resource Allocation

Abstract

This article considers the distributed fixed-time resource allocation problem subject to global equality and local inequality constraints. In the case that the optimal solutions are strictly feasible, a projection-gradient-based continuous-time algorithm is first proposed to minimize a team of cost functions in the fixed time. As some optimal solutions locate on the boundary of local constraints, we further provide an alternative suboptimal solution based on the <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>-exact penalty function method. Different from the existing distributed optimal allocation results, the (sub)optimal solutions can be obtained in the fixed time and the optimization protocols can be implemented in an initialization-free manner. Thus, the convergence time can be offline preassigned and the initial states can be chosen arbitrarily such that a better robust performance is achieved for the new algorithms. Case studies of the widely discussed economic dispatch problems are performed to validate the effectiveness of the obtained results.