Sliding-mode-based robust predefined-time optimization for single-integrator systems - Chen, Siyu; Jiang, Haijun; Yu, Zhiyong; Zhao, Fengyang (Nonlinear dynamics, 2024)
In this article, a novel class of fully distributed practical predefined-time algorithms (FDPPTAs) is developed for three types of convex optimization problems of single-integrator systems with bounded disturbances. The task of this work is to reach an optimal state that minimizes the global cost function expressed by the sum of all convex local cost functions. Firstly, a two-stage robust FDPPTA, combined with two time-varying functions, zero-gradient-sum and integral sliding mode control, is constructed to solve the unconstrained optimization problem. Secondly, a two-stage robust FDPPTA is applied to the case with linear equality constraint by introducing auxiliary variables. On this basis, the exact penalty function is further introduced to deal with the difficulties caused by linear inequality constraint. Unlike the existing optimization algorithms, the developed FDPPTA, which does not rely on any global information, shows excellent performance from the three aspects of robustness, initialization-free and predefined-time. Finally, four cases are given to verify the effectiveness and superiority of proposed algorithms.