Singularity-Free Finite-Time Tracking Control of Stochastic Nonlinear Systems With Unknown Measurement Sensitivity
针对一类具有未知测量灵敏度和全状态跟踪误差约束的随机非线性系统，提出了一种无奇点的有限时间跟踪控制算法，通过改进误差变换和滤波器避免奇点与复杂度爆炸问题，并利用对称障碍李雅普诺夫函数处理约束，仿真验证了有效性。
The finite-time tracking control issue is researched for a class of stochastic nonlinear systems with unknown measurement sensitivity and full-state tracking error constraints. Primarily, an improved error transformation technique based on the prescribed performance function (PPF) is introduced to avoid the “singularity” issue in the backstepping design process. Subsequently, the “explosion of complexity” matter is circumvented dexterously by the improved first-order filter. Then, a novel feedback control algorithm is developed to deal with the unknown measurement sensitivity. Furthermore, the symmetric barrier Lyapunov function (BLF) is employed to cope with the requirement of full-state tracking error performance constraints. Moreover, the finite-time stability theorem proves that the developed control project guarantees the boundedness of all system variables, and the tracking errors within the predesigned range in the finite time. Definitively, the validity of the designed scheme is demonstrated by simulations.