A Robust Fixed-Time Piecewise Dynamic Network for Convex Programming

To solve optimization problems in real-time and robustly, we propose a piecewise dynamic network for solving convex programming constrained by inequalities and linear equalities. The network is proposed based on the penalty method and includes two stages. The network in the first stage is a zeroing dynamic network to solve an equation. It makes sure that for any initial point, the state of the network enters the linear equality constraint set within a fixed time. The optimal solution to this convex programming is obtained by the network in the second stage which is a gradient-type dynamic network. A lower bound of the penalty parameter is given to ensure the validity of the network, which makes up for the deficiency of the existing works. A suitable activation function is introduced to promote fixed-time convergence of the network and to improve its anti-interference capability. As a result, the proposed piecewise dynamic network is robust against additional interferences. Some tests are presented to show the effectiveness of our network.