Abstract:

Aiming at the problems that traditional iterative algorithm is easy to generate large drifting error and prediction correction algorithm has poor convergence performance in the process of solving time-varying optimization problem， a fixed-time time-varying optimization algorithm based on neurodynamic approach was proposed. Firstly， the time-varying optimization problem with time-varying objective function and time-varying constraint function was transformed into an unconstrained optimization problem by the logarithmic barrier penalty function method. Then， by introducing the concept of fixed-time stability， an algorithm was designed to track the optimal solution of the time-varying optimization problem. At the same time， the convergence and fixed-time stability of the proposed algorithm were proved by Lyapunov theory. Compared with the limited-time convergence algorithm， the proposed algorithm was able to converge to the optimal solution of the time-varying problem in fixed time， and the convergence time was independent of the initial value of the system. Numerical simulation results show that the proposed algorithm can track down the optimal solution of the time-varying optimization problembefore about 0.5 s and keep the convergence accuracy below 10^-5. Compared with the prediction correction algorithm， the proposed algorithm maintains a better convergence accuracy and has the convergence time shortened by about 0.3 s at the same time. The proposed algorithm was applied to two groups of robot navigation experiments， and the experimental results show that the proposed algorithm can realize the real-time obstacle avoidance and navigation of mobile robots under different initial conditions.

Key words: time-varying optimization, neurodynamic approach, fixed-time stability, Lyapunov theory, robot navigation

摘要：

针对在求解时变优化问题的过程中传统的迭代算法容易产生较大的漂移误差，以及预测矫正算法收敛性能不佳等问题，提出一种基于神经动力学方法的固定时间时变算法。首先，通过对数障碍罚函数法将具有时变目标函数和时变约束函数的时变优化问题转化为无约束优化问题；其次，引入固定时间稳定性的概念设计算法，用于跟踪时变优化问题的最优解；同时，通过李雅普诺夫理论证明了所提算法的收敛性和固定时间稳定性。与有限时间收敛算法相比，所提算法能在固定时间内收敛到时变问题的最优解，且收敛时间与系统的初始值无关。数值仿真实验结果表明：所提算法能在约0.5 s之前追踪到时变优化问题的最优解且收敛精度保持在10^-5以下。与预测矫正算法相比，所提算法在保持良好的收敛精度的同时，收敛时间缩短了约0.3 s。将所提算法应用到2组机器人导航实验中，实验结果表明：所提算法能在不同初始条件下实现移动机器人的实时避障和导航。

关键词: 时变优化, 神经动力学方法, 固定时间稳定性, 李雅普诺夫理论, 机器人导航