A New Approach to Designated-Time Stabilizing Strategy of Stochastic Nonlinear Systems and its Application to Mass-Spring Mechanical System
针对传统指定时间镇定中控制幅值无限大、状态响应不可控的问题，提出一种混合镇定控制器，保证系统在指定时间几乎必然唯一解，并实现概率收敛与快速有限时间收敛，通过质量-弹簧系统仿真验证有效性。
This article explores a new strategy for designated time stabilization of stochastic time-varying nonlinear systems. Conventional prescribed-time stabilization has limitations in practical engineering due to singularities induced by infinite control amplitude and a lack of manipulation of the state response after a prescribed time. To address these challenges, we build a hybrid stabilization controller using state-scale techniques and a finite-time stabilization process that is bounded in probability over the full range, guaranteeing that the closed-loop system has a solution that is almost surely unique at a designated time. Compared to the current prescribed stabilization results, the proposed strategy not only ensures that the state of the system converges in probability to a compact set at a designated time and belongs to the set after which it eventually enjoys fast finite-time convergence. Finally, the effectiveness of the strategy is verified by simulating a real mass-spring mechanical system.