非线性时滞系统的未知方向自适应学习控制

Unknown Direction Adaptive Learning Control for Nonlinear Time-delay Systems

针对一类控制方向未知的非参数化不确定非线性时滞系统的控制问题,设计了一种鲁棒自适应学习控制算法。在控制器设计中引入Nussbaum增益函数,避免对系统控制方向未知问题的讨论,进而利用双曲正切函数的有界性,为参数估计值设定估计界,采用线性参数化的Fourier级数展开对周期期望输入函数进行估计,保证学习算法的鲁棒性。理论分析表明,所提自适应学习控制律能够保证系统闭环信号的有界性,且系统误差能够渐近地收敛于零。最后通过数值仿真进一步验证了所提控制算法的有效性。

A robust adaptive learning control algorithm is proposed for a class of uncertain nonlinear time-delay systems with unknown control direction. Nussbaum gain function is introduced in controller design, so as to avoid the discussion of unknown control direction, then by using of the boundness of hyperbolic tangent function and setting the boundaries of the estimated value, the linear parametric Fourier series are used to estimate the period expected input function and ensure the robustness of the learning algorithm. Theoretical analysis shows the proposed adaptive learning control law can ensure the boundness of the closed-loop system signal, and the error of the system can also converge to zero asymptotically. Finally, numerical simulation results further prove the effectiveness of the algorithm.