具有输出/全状态约束的固定时间滑模控制

Fixed-time sliding mode control with output/full-state constraints

中文关键词  二阶系统  输出约束  全状态约束  固定时间收敛  滑模控制

英文关键词  second-order system  output constraint  full-state constraint  fixed time control  sliding mode control

中文摘要

      本文主要解决具有约束的二阶系统的固定时间跟踪控制问题, 分别讨论了具有输出约束与具有全状态约 束的控制算法设计. 首先, 为解决输出约束下的固定时间控制问题, 本文构建了具有输出约束的新型终端滑模变量, 并设计了具有扰动抑制能力的固定时间滑模控制律, 保证系统输出始终满足约束条件, 同时跟踪误差在固定时间内 收敛到原点的充分小的邻域内. 进一步, 为了处理具有全状态约束的控制问题, 本文构建了具有全状态约束的终端 滑模变量并设计了相应的固定时间滑模控制律. 鉴于系统控制律的不连续性, 文章采用非光滑分析及Lyapunov稳定 性理论证明了闭环控制系统的稳定性. 最后, 在数值仿真中, 将本文提出的方法与传统固定时间滑模方法进行对比, 验证了所建立算法的有效性.

英文摘要

      This paper focuses on the fixed-time control problems for the second-order system subject to output/ full-state constraints. First, to address the fixed-time control problem with output constraint, a novel terminal sliding mode variable with output constraint is designed. Based on the proposed sliding mode variable, a fixed-time sliding mode control law is constructed considering external disturbances. By the proposed approach, the output of the controlled system will always meet the constraint and the tracking error converges to a sufficiently small neighborhood of the origin within fixed time. Further, to deal with the control problem with full-state constraint, a terminal sliding mode variable with full-state constraint is designed and the corresponding fixed-time sliding mode control law is derived. Since the designed control law is discontinuous, a non-smooth analysis is performed to prove the stability of the controlled system. Finally, the performance of the proposed approach is compared with that of the traditional fixed-time sliding mode approach in numerical simulations, which reflects the effectiveness of the established control algorithm.