Prescribed-time distributed optimization for multi-agent system subject to inequality constraints

This paper investigates the prescribed-time distributed optimization control problem of multi-agent system subject to inequality constraints over directed networks. The log-barrier penalty function method is utilized to cope with the effects of inequality constraints. First, the relationship between the original problem and the processed unconstrained optimization problem is presented. By means of the zero-gradient-sum method and the integral sliding mode technique, the controller is designed such that the state of each agent converges to a vicinity of the optimal solution in a specified time. The interior point theorem ensures that the inequality constraints always hold. Numerical example is provided to verify the effectiveness of the theoretical analysis.