Journal of Intelligent and Robotic Systems 36: 223–234, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands. 223 A Learning Control for a Class of Linear Time Varying Systems Using Double Differential of Error M. ARIF, T. ISHIHARA and H. INOOKA GSIS Tohuku University, Prof. Inooka’s Laboratory, Graduate School of Information Sciences, Aramaki-aza 01, Aoba-ku, 980-8579 Sendai, Japan; e-mail: arif@control.is.tohoku.ac.jp (Received: 5 June 2001; in final form: 7 May 2002) Abstract. In this paper, a new iterative learning control based on the double differential of the error is proposed for the linear time varying system having relative degree greater than one. The convergence criterion of the proposed method is proved. Furthermore, it is shown by simulations that convergence of error can be increased considerably by using our proposed controller as compared to the iterative learning controller using error or single differential of the error for the modification of the control input without increasing the learning gain. Key words: linear time varying system, learning control, convergence. 1. Introduction In the control theory, especially for the applications related to robots, tracking of a desired trajectory with high precision is one of the main research issues. In many industrial applications, a desired trajectory has to be tracked repeatedly. For such cases, iterative learning controller is an strong candidate especially when the exact model of the system is unknown. The beauty of the iterative learning control lies in its structural simplicity and it does not require the identification of the system. It needs some information in terms of norms or bounds of the system to check its convergence property. An iterative learning controller modifies the control input using the experience of the previous iterations in a way that the control input converges to the desired control input. Iterative learning control method is first proposed by Uchiyama [11] and later elaborated as a formal theory by Arimoto et al. [2] in 1984. Since then, there has been great deal of efforts by the researchers to synthesize a better iterative learning control scheme [3, 5, 7, 8]. Lot of work has been published on the application of iterative learning control in the area of robotics [1, 6, 10]. Some applications of iterative learning control in process control has also been explored by some researchers [4]. Although sufficient conditions are derived for the convergence of the learning process, the convergence rate is often slow in most of the proposed control laws. For iterative learning control of continuous time systems, design of iterative learning control can be categorized into D-type iterative learning control