Robust Neural Dynamics for Distributed Time-Varying Optimization With Application to Multi-Robot Systems

Abstract

This paper develops a robust neural dynamics method for the distributed time-varying optimization problem with time-varying constraints. First, instead of assuming the objective functions and constraints to be static like a majority of the existing research, we consider distributed optimization from a time-varying perspective. Second, by employing the Lagrangian framework, we transform constraints and the concerned objective function that takes the summation of all local functions into a dynamic error function. Third, the robust neural dynamics method is capable of utilizing the time-varying information while solving constrained distributed optimization problems, and meanwhile handling disturbances purely based on its structure, thus lightening the communication and privacy burden. We provide proof of the convergence of the proposed method with activation functions under different disturbances. The comparative results on both illustrative examples and applications validate the efficiency. Note to Practitioners—The highlight of this paper lies in the co-design of time-varying computation and noise-tolerant ability for the proposed distributed optimization method, which could be beneficial to real-world scenarios. Different from existing methods focusing on static objective functions and constraints, we investigate how to find the trajectory formed by the time-varying optimal solutions even with the perturbation of noises. Besides, saturated or even nonconvex activation functions mimicking the synapses of the brain are incorporated into the proposed optimization methods to help accelerate the convergence and counteract the instability induced by noises, without heavily adding to the system’s burden. We also provide theoretical proof to not only guarantee its capability but also guide how to set the involved parameters. This paper proposes a noise-tolerant method for accurately solving distributed time-varying optimization problems and validates its performance on a multi-robot system, which could be suitable for plenty of real-world distributed optimization problems.