Ni Junkang, Liu Chongxin, Liu Hang
State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
PLoS One. 2017 Apr 13;12(4):e0175645. doi: 10.1371/journal.pone.0175645. eCollection 2017.
This paper presents a continuous composite control scheme to achieve fixed-time stabilization for nonlinear systems with mismatched disturbances. The composite controller is constructed in two steps: First, uniformly finite time exact disturbance observers are proposed to estimate and compensate the disturbances. Then, based on adding a power integrator technique and fixed-time stability theory, continuous fixed-time stable state feedback controller and Lyapunov functions are constructed to achieve global fixed-time system stabilization. The proposed control method extends the existing fixed-time stable control results to high order nonlinear systems with mismatched disturbances and achieves global fixed-time system stabilization. Besides, the proposed control scheme improves the disturbance rejection performance and achieves performance recovery of nominal system. Simulation results are provided to show the effectiveness, the superiority and the applicability of the proposed control scheme.
本文提出了一种连续复合控制方案，以实现具有不匹配干扰的非线性系统的固定时间镇定。复合控制器分两步构建：首先，提出均匀有限时间精确干扰观测器来估计和补偿干扰。然后，基于增加幂积分器技术和固定时间稳定性理论，构建连续固定时间稳定状态反馈控制器和李雅普诺夫函数，以实现系统的全局固定时间镇定。所提出的控制方法将现有的固定时间稳定控制结果扩展到具有不匹配干扰的高阶非线性系统，并实现了系统的全局固定时间镇定。此外，所提出的控制方案提高了干扰抑制性能，并实现了标称系统的性能恢复。提供了仿真结果以表明所提出控制方案的有效性、优越性和适用性。
