严格反馈系统约束迭代学习控制

针对一类含有状态约束和任意初态的严格反馈非线性系统,本文提出了基于二次分式型障碍李雅普诺夫函数的误差跟踪学习控制算法.二次分式型障碍李雅普诺夫函数保证了系统跟踪误差在迭代过程中限制于预设的界内,进而保持状态在约束区间内.引入一级数收敛序列用于处理扰动对系统跟踪性能的影响.构造期望误差轨迹解决了系统的初值问题.经迭代学习后,所设计的学习控制器能够实现系统输出在预指定作业区间上精确跟踪参考信号.最后的仿真结果验证了所提控制算法的有效性.

Constrained iterative learning control of a class of strict-feedback systems

For a class of strict-feedback nonlinear systems in the presence of state constraints and arbitrary initial state, an error-tracking iterative learning control strategy based on quadratic-fraction barrier Lyapunov function is proposed. The system tracking error is enforced to stay in the pre-specified range based on the quadratic-fraction barrier Lyapunov function to realize the state constraint in the iterative process. A kind of expected error trajectory is constructed to solve the initial condition problem. A series convergence sequence is introduced to deal with the influence of disturbance term. After iterative learning, the system output can accurately track the reference signal on the specified interval. Finally, numerical results demonstrate the effectiveness of the learning control schemes.