Prescribed-Time Optimization for Multiagent System With Inconsistent Constraint Sets

In this article, the prescribed-time optimization problem is considered for multiagent systems (MASs) with inconsistent constraint sets. First, the constrained optimization problem is transformed into an unconstrained one using the sliding mode control approach, in which the sliding surface is constructed based on the projection errors. Subsequently, three distinct prescribed-time optimization control protocols are developed by utilizing the sliding mode variables and optimization algorithms. In particular, compared with the existing works in which the gain of each controller approaches infinity at the prescribed instant, this article effectively mitigates singularity by integrating fixed-time theory with the time-domain transformation method. Furthermore, it can be verified that all agents achieve optimization consensus under the three different algorithms by the Lyapunov stability theory and convex optimization analysis. Finally, we provide an application example to verify the validity of theoretical results.