在多變數系統中，一個線性二次最佳化學習控制的方法在本論文被提出以達到在有限時間內最佳化控制的目的。即使並沒有詳細的系統資訊且此系統會被不明但重覆的干擾所影響，此學習效果依然會達到最佳化。最佳解將由每一次新增的基底函數所合成，且會使輸出結果在有限次的學習下達到最佳化。這系統的相依基底函數有下列兩樣特性：首先，每一次新增的基底函數將不會改變之前已最佳化的基底函數；第二，每一組基底函數是利用之前學習試驗的資訊所選出的。此外，一些對於所提方法在不同系統矩陣及輸出的觀察也被提出。因此，在此論文中一個有關於預先設計的控制將在學習過程之前被指出。而此預先設計的控制將會顯著地改善學習過程的效用。數值性的例題被用來說明所提的方法。

A linear quadratic optimal learning control solution to the problem of finding a finite-time optimal control history for multivariable systems is proposed in this thesis. Even though there is no detailed information of the system that is influenced by unknown but repetitive disturbances, it yields the learning achieve optimization. The newly added basis functions synthesize the optimal solution at a time, and it makes the outcome reaches optimality in a finite number of trials. These system-dependent basis functions have two characteristics: first, each newly added basis function will not alter the previously optimized ones; second, each basis function is selected by using the data from previous learning trials. Furthermore, some remarkable observations on the proposed approach for various system matrices and outputs are also presented. As a result, a desired connection with a pre-design feedback control before the learning process for the proposed learning control is newly pointed out in this thesis, which will significantly improve the effectiveness of the learning process. Numerical examples are used to illustrate the proposed methodology.

ARIMOTO, S., KAWAMURA, S., and MIYAZAKI, F., 1984, Bettering operation of robots by learning. Journal of Robotic Systems, 1, pp. 123-140.

BIEN, Z., and XU, J.-X. (Eds), 1998, Recent Advances in Iterative Learning Control (Boston, Massachusetts, USA: Kluwer Academic Publishers).

CASALINO, G., and BARTOLINI, B., 1984, A learning procedure for the control of movements of robotic manipulators. IASTED Symposium on Robotics and Automation, pp. 108-111.

CRAIG, J. J., 1984, Adaptive control of manipulators through repeated trials. Proceedings of the American Control Conference, pp. 1566-1573.

FRUEH, J. A., and PHAN, M. Q., 1997, System identification and inverse control using input-output data from repetitive trials. Proceedings of the 2nd Asian Control Conference, 2. ASCC, Seoul, South Korea, pp. 251-254.

FRUEH, J. A., and PHAN, M. Q., 2000, Linear quadratic optimal learning control (LQL). International Journal of Control , 73(10), pp. 832-839.

HARA, S., and YAMAMOTO, Y., 1985, Synthesis of repetitive control systems and its applications. Proceedings of the 24th IEEE Conference on Decision and Control, pp. 326-327.

HOROWITZ, R., 1993, Learning control of robot manipulators. ASME Journal of Dynamic Systems, Measurement, and Control, 115, pp. 402-411.

INOUE, T., NAKANO, M., and IWAI, S., 1981, High accuracy control of a proton synchrotron magnet power supply. Proceedings of the 8th World Congress of IFAC, pp. 216-221.

LONGMAN, R. W., 1991, Supplementary material: tutorial on learning control. IEEE Conferences on Intelligent Control, Arlington, VA.

LONGMAN, R. W., and CHANG, C.-K., 1990, Learning control for minimizing a quadratic cost during repetitions of a task. AIAA/AAS Astrodynamics Conference: A Collection of Technical, Papers, 2, pp. 530-536.

MIDDLETON, R. H., GOODWIN, G. C., and LONGMAN, R. W., 1989, A method for improving dynamic accuracy of a robot performing a repetitive task. International Journal of Robotics Research, 8, pp. 67-74.

MOORE, K. L., 1993, Iterative Learning Control for Deterministic Systems (London, UK: Springer-Verlag).

PHAN, M. Q., and FRUEH, J. A., 1996, Learning control for trajectory tracking using basis functions. Proceedings of the IEEE Conference on Decision and Control, Kobe, Japan, pp. 2490-2492.

PHAN, M. Q., and FRUEH, J. A., 1998, System Identification and Learning Control (Boston, Massachusetts, USA: Kluwer Academic Publishers), chapter 15.

PHAN, M. Q., and JUANG, J.-N., 1996, Design of learning controllers based on anauto-regressive representation of a linear system. Journal of Guidance, Control, and Dynamics, 19, pp. 355-362.

PHAN, M. Q., and LONGMAN, R. W., 1988, A mathematical theory of learning control for linear discrete multivariable systems. Proceedings of the AIAA/AAS Astrodynamics Specialist Conference, Minneapolis, Minnesota, pp. 740-746.

PHAN, M. Q., and RABITZ, H., 1997, Learning control of quantum-mechanical systems by identification of effective input-output maps. Chemical Physics, 217, pp. 389-400.

TOMIZUKA, M., TSAO, T. C., and CHEW, K. K., 1989, Discrete-time-domain analysis and synthesis of repetitive controllers. ASME Journal of Dynamics, Measurements, and Control, 3, pp. 353-358.

TSAY, Y. T., and SHIEH, L. S., 1981, State-space approach for self-tuning feedback control with pole assignment. IEE Proc., 128(3), pp. 93-101

UCHIYAMA, M., 1978, Formulation of high-speed motion pattern of a mechanical arm by trial. Transactions of the Society for Instrumentation and Control Engineers, 14, pp. 706-712.