含有未知控制方向的非线性时滞系统学习控制
Learning control for nonlinear systems with unknown control direction and unknown time-varying delay

本文对于一类含有未知控制方向及时滞的非线性参数化系统, 设计了自适应迭代学习控制算法. 在设计控 制算法过程中采用了参数分离技术和信号置换思想来处理系统中出现的时滞项, Nussbaum增益技术解决未知控制 方向等问题. 为了对系统中出现的未知时变参数和时不变参数进行估计, 分别设计了差分及微分参数学习律. 然后 通过构造的Lyapunov-Krasovskii复合能量函数给出了系统跟踪误差渐近收敛及闭环系统中所有信号有界的条件. 最后通过一个仿真例子说明了控制器设计的有效性.
In this work, we propose an adaptive iterative learning control algorithm for a class of nonlinearly parameterized systems with unknown control direction and unknown time-varying delay. The existing unknown time-varying delay is well resolved by using parameter separation method and signal replacement mechanism in the process of the design, and the lack of a priori knowledge of the control direction is also dealt with by the Nussbaum-gain technique incorporated into the control design. Moreover, both difference and differential updating laws are configured for the estimates of the unknown time-varying parameter and the constant parameter. Then based on a constructed Lyapunov-Krasovskii composite energy function, a sufficient condition of the convergence of the system error asymptotically along the iteration axis and the boundedness of all signals in the closed-loop system is given. A simulation example is presented to validate the effectiveness of the proposed control method.