Achieving violation-free distributed optimization under coupling constraints

TL;DR

This paper develops distributed optimization algorithms that guarantee constraint satisfaction at all times in systems with coupling constraints, ensuring safety and reliability in multi-agent control and power systems.

Contribution

It introduces a novel reformulation with auxiliary variables and linear mappings, enabling violation-free distributed optimization with provable convergence.

Findings

Algorithms achieve violation-free constraint satisfaction.

Reformulation preserves original feasible set properties.

Effective in distributed control applications.

Abstract

Constraint satisfaction is a critical component in a wide range of engineering applications, including but not limited to safe multi-agent control and economic dispatch in power systems. This study explores violation-free distributed optimization techniques for problems characterized by separable objective functions and coupling constraints. First, we incorporate auxiliary decision variables together with a network-dependent linear mapping to each coupling constraint. For the reformulated problem, we show that the projection of its feasible set onto the space of primal variables is identical to that of the original problem, which is the key to achieving all-time constraint satisfaction. Upon treating the reformulated problem as a min-min optimization problem with respect to auxiliary and primal variables, we demonstrate that the gradients in the outer minimization problem have a locally computable closed-form. Then, two violation-free distributed optimization algorithms are developed and their convergence under reasonable assumptions is analyzed. Finally, the proposed algorithm is applied to implement a control barrier function based controller in a distributed manner, and the results verify its effectiveness.