Cooperative fixed-time/finite-time distributed robust optimization of multi-agent systems

Abstract

A new robust continuous-time optimization algorithm for distributed problems is presented which guarantees fixed-time convergence. The algorithm is based on a Lyapunov function technique and applied to a class of problems with coupled local cost functions. The algorithm applies a methodology with no expansion of the local variables. This reduces the computation complexities of the solution and improves scalability. Using an integral sliding mode strategy we incorporate effective disturbances rejection on the decision variables as experienced in a wide range of industrial applications. It is shown that the algorithm can easily be modified to a finite-time solution when evaluations of the optimization variables are required to be bounded. Two illustrative examples with different simulation scenarios are considered to study the effectiveness of the results.