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Adaptive ILC for a class of discrete-time systems with iteration-varying trajectory and random initial condition. (English) Zbl 1283.93329

Summary: In this work we present a discrete-time adaptive iterative learning control (AILC) scheme to deal with systems with time-varying parametric uncertainties. Using the analogy between the discrete-time axis and the iterative learning axis, the new adaptive ILC can incorporate a Recursive Least Squares (RLS) algorithm, hence the learning gain can be tuned iteratively along the learning axis and pointwisely along the time axis. When the initial states are random and the reference trajectory is iteration-varying, the new AILC can achieve the pointwise convergence over a finite time interval asymptotically along the iterative learning axis.

MSC:

93E35 Stochastic learning and adaptive control
68T05 Learning and adaptive systems in artificial intelligence
93C40 Adaptive control/observation systems
93E24 Least squares and related methods for stochastic control systems
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[1] Chen, F.C.; Kalil, H.K., Adaptive control of nonlinear systems using neural networks, International journal of control, 55, 1299-1317, (1992) · Zbl 0759.93046
[2] Chen, Y.Q.; Wen, C.Y., ()
[3] Chien, C.J.; Liu, J.S., A P-type iterative learning controller for robust output tracking of nonlinear time-varying systems, International journal of control, 64, 2, 319-334, (1996) · Zbl 0863.93040
[4] Chien, C.J.; Yao, C.Y., Iterative learning of model reference adaptive controller for uncertain nonlinear systems with only output measurement, Automatica, 40, 855-864, (2004) · Zbl 1050.93046
[5] Chin, I.; Qin, S.J.; Lee, K.S.; Cho, M., A two-stage iterative learning control technique combined with real-time feedback for independent disturbance rejection, Automatica, 40, 1913-1922, (2004) · Zbl 1060.93510
[6] Choi, J.Y.; Lee, J.S., Adaptive iterative learning control of uncertain robotic systems, IEE Proceedings D, control theory application, 147, 2, 217-223, (2000)
[7] Fang, Y.; Chow, T.W.S., 2-D analysis for iterative learning controller for discrete-time systems with variable initial conditions, IEEE transactions on circuits and systems-I: fundamental theory and applications, 50, 5, 722-727, (2003)
[8] French, M.; Rogers, E., Nonlinear iterative learning control by an adaptive Lyapunov technique, International journal of control, 73, 10, 840-850, (2000) · Zbl 1006.93596
[9] Goodwin, G.C.; Sin, K.S., Adaptive filtering prediction and control, (1984), Prentice-Hall, Inc. Englewood Cliffs, NJ, 07632 · Zbl 0653.93001
[10] Ham, C.; Qu, Z.; Johnson, R., A nonlinear iterative learning control for robot manipulators in the presence of actuator dynamics, International journal of robotics and automation, 15, 3, 119-130, (2000)
[11] Heinzinger, G.; Fenwick, D.; Paden, B.; Miyazaki, F., Stability of learning control with disturbances and uncertain initial conditions, IEEE transactions on automatic control, 37, 110-114, (1992)
[12] Hwang, D.H.; Bien, Z.; Oh, S.R., Iterative learning control method for discrete-time dynamic systems, IEE Proceedings part-D, 138, 2, 139-144, (1991) · Zbl 0738.93019
[13] Kanellakopoulos, I., A discrete-time adaptive nonlinear system, IEEE transactions on automatic control, 39, 11, 2362-2365, (1994) · Zbl 0825.93422
[14] Kuc, T.Y.; Nam, K.; Lee, J.S., An iterative learning control of robot manipulators, IEEE transactions on robotics and automation, 7, 6, 825-841, (1991)
[15] Lee, K.S.; Lee, J.H.; Kim, W.C., Model-based iterative learning control with a quadratic criterion for time-varying linear systems, Automatica, 36, 5, 641-657, (2000) · Zbl 0959.93019
[16] Norrlöf, M., An adaptive iterative learning control algorithm with experiments on an industrial robot, IEEE transactions on robotics and automation, 18, 2, 245-251, (2002)
[17] Norrlöf, M.; Gunnarsson, S., A note on causal and CITE iterative learning control algorithms, Automatica, 41, 345-350, (2005) · Zbl 1067.93030
[18] Saab, S.S., A discrete-time learning control algorithm for a class of linear time-invariant systems, IEEE transactions on automatic control, 40, 6, 1138-1141, (1995) · Zbl 0831.93032
[19] Saridis, G.; Wang, F.Y., Suboptimal control of nonlinear stochastic systems, Control theory and advanced technology, 10, 4, 847-871, (1994)
[20] Sun, M.; Wang, D., Initial shift issues on discrete-time iteratiave learning control with system relative degree, IEEE transactions on automatic control, 48, 1, 144-148, (2003) · Zbl 1364.93890
[21] Tso, S.K.; Ma, Y.X., Discrete learning control for robots: strategy, convergence and robustness, International journal of control, 57, 2, 273-291, (1993) · Zbl 0777.93068
[22] Verhaegen, M.; Yu, X., A class of subspace model identification algorithms to identify periodically and arbitrarily time-varying systems, Automatica, 31, 2, 201-206, (1995) · Zbl 0821.93031
[23] Xu, J.X., Analysis of iterative learning control for a class of nonlinear discrete-time systems, Automatica, 33, 10, 1905-190799, (1997)
[24] Xu, J.X.; Viswanathan, B., Adaptive robust iterative learning control with dead zone scheme, Automatica, 36, 91-99, (2000) · Zbl 0939.93018
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