On Iterative Learning Control-a Tikhonov Approach

In recent years, data-driven control theory and method have been deeply studied anddeveloped, and are widely applied to the practical problems. Compared with other datadriven control methods, the iterative learning control(ILC) method is the most abundantand systemic for the way of using data. Ill-posedness is the essential difficulty when wesolute the inverse problem, which is mainly the instability of approximate solution, i.e. thesolution of the equation (if it exists) does not depend continuously on the right end of thedata. General method for solving ill-posed problems is the regularly method.The iterative learning control method can be used to study a class of measuringoutput problems of the single input single output system with noise. Since the output ofthe system relating to the actual problems is unknown, which is often accompanied bynoise, the traditional iterative learning process may be ill-posed. The algorithm used hereis based on Tikhonov regularization theory, therefore the algorithm can solve the ill-posedproblem in the process of learning.This paper firstly introduces the related knowledge of iterative learning controltheory, regularization theory and Bayes theory. Then it explains the reason of ill-posedproblems in solving the impulse response. Afterwards, this paper presents a method tosolve the ill-posed problem by introducing a regularization theory. In the process ofsolving the regularization parameter, combining with the theory of Bayes, the hyperparameters are used to indicate the regularization parameter, so we obtain theregularization parameter by solving these two hyper parameters.Finally, through the simulation experiments, we take the same initial state and makethree curves as the desired trajectories respectively. The simulate results confirm ouralgorithm greatly.