指数变增益迭代学习控制最优增益研究

On Optimal Gain of Exponential Variable GainIterative Learning Control

针对指数变增益迭代学习控制(ILC)算法难以进一步改进且缺乏优化理论等问题,提出一种指数变增益迭代学习控制(ILC)算法在线性时不变(LTI)系统中的控制增益优化方法。首先,由托普利茨矩阵特性和矩阵迭代理论得到单输入单输出(SISO)离散LTI系统中的收敛充要条件,并证明算法的收敛性;其次,由最优化理论得到算法单调收敛条件,最终得到最优控制增益的精确解,并得出指数增益与最优控制增益之间的关系。该方法根据系统状态方程得到最优控制策略,可计算得到精确最优控制值,进一步提高系统收敛速度。仿真结果表明,该方法能有效提高算法学习速度,具有良好的控制性能。

Aiming at the problems that the exponentially variable gain Iterative Learning Control(ILC)algorithm is difficult to be further improved and lacks optimization theory,a control gain optimization method of exponentially variable gain Iterative Learning Control(ILC)algorithm in Linear Time-Invariant(LTI)systems is proposed.Firstly,the necessary and sufficient conditions for convergence in Single-Input Single-Output(SISO)discrete LTI systems are obtained from the Toeplitz matrix properties and matrix iteration theory,and the convergence of the algorithm is proved.Secondly,the monotonic convergence condition of the algorithm is obtained from the optimization theory.Finally,the exact solution of the optimal control gain is obtained,and the relationship between the exponential gain and the optimal control gain is obtained.The method obtains the optimal control strategy according to the state equation of the system,and can calculate the precise optimal control value,which further improves the system convergence speed.The simulation results show that the method can effectively improve the learning speed of the algorithm and has good control performance.