Singularity-Free Prescribed-Time Distributed Optimization for Nonlinear Multi-Agent Systems with Time-Varying Cost Functions

This paper proposes a singularity-free prescribed-time distributed optimization algorithm for nonlinear multi-agent systems with time-varying cost functions and dynamic communication topologies. The proposed algorithm avoids singularity, and it does not require the local cost functions to have identical Hessian matrices. First, a novel time-varying scaling function based on time-space deformation theory is designed to address the singularity issue in the proposed distributed optimization algorithm. Second, a distributed prescribed-time optimization estimator by introducing an intermediate driving variable to counteract the inconsistency disturbances is designed to track the average of the global gradients, global Hessian matrices, and the global partial derivatives of gradients, respectively. Furthermore, under this estimator, all local cost functions need not have identical Hessians. Third, refined theoretical analysis demonstrates that our algorithm converges to the globally optimal trajectory. Meanwhile it is also shown to avoid the singularity problem and achieve prescribed-time estimation. Finally, a UAV formation experiment verifies the effectiveness of our proposed algorithm, including its singularity-free property, prescribed-time convergence, and optimality.