Neural dynamics solver for time-dependent infinity-norm optimization based on ACP framework with robot application

Abstract

In general, infinity-norm optimization (INO) is commonly deemed as a subset of nonlinear optimization. In the last decade, there have been relatively few reports on solving INO problems, specifically from the time-dependent aspect originating from the real-time motion planning of robots. Therefore, to compensate for the vacancy, this paper proposes a class of neural dynamics (ND) solvers utilizing an ACP framework that combines artificial systems (A), computational experiments (C), and parallel execution (P), respectively. Specifically, two improved ND solvers are constructed by exploiting simplified sign-bi-power and saturation activation functions for solving time-dependent INO (TDINO) problems subject to equality and inequality constraints. Moreover, the corresponding theoretical analysis and proof are conducted, which ensures that residual errors of the proposed improved ND solvers based on the ACP framework converge in a short time. Compared with a SOTA (state-of-the-art) zeroing neural network model presented recently, the average error of the proposed ones is reduced by 52%, the speed of error convergence is increased by 152%, and the transient state is extended by 4% on average. Finally, simulation results of an illustrative example and an application in the robot are provided, which illustrates the effectiveness, superiority, and feasibility of the proposed ND solvers.