一类复杂非线性系统的迭代学习控制算法

Iterative Learning Control Algorithm for a Class of Complicated Nonlinear Systems

针对一类可重复运行的复杂非线性系统,考虑系统中未知变量的变化模式为时域-迭代域变化并满足高阶内模规律,设计一种复杂非线性系统迭代学习控制算法。当系统中还存在非严格重复规律未知的初态定位和跟踪参考轨迹时,充分利用实际系统中未知变量的已知边界条件和高阶内模规律,将最小二乘法与已知边界条件结合,解决系统中的多种非严格重复问题。研究结果表明,在系统同时具有未知控制增益和扰动的情况下,所设计的控制律能保证跟踪误差的渐近收敛,以及控制输入、状态变量和参数估计矩阵的有界性。多个仿真实例进一步验证了所设计算法的有效性。

Considering time-iteration-varying uncertainties satisfied high-order internal model(HOIM),a complex nonlinear iterative learning control(ILC)algorithm is investigated for a class of complicated nonlinear systems in iterative operation process.By virtue of boundary conditions and HOIM in the real systems,multiple non-repetitive problems are solved by combining least-square method with boundary conditions when non-repetitive problems with unknown varying law are also existed in initial state and reference trajectory.Multiple non-repetitive problems are solved by combining least-square method with boundary conditions.The results show that,with the proposed ILC method,tracking error converges to zero asymptotically and control inputs,state variable and estimation matrix for unknowns are bounded in the presence of unknown control gain and disturbances.Multiple simulation examples verify the effectiveness of the method.