Abstract
This paper concerns with Direct Gradient Descent Control (DGDC) of nonlinear systems. DGDC manipulates control inputs directly so as to decrease a performance function like the squared error, based on the gradient of the performance function and the steepest descent method. The convergence speed or the asymptotical stability of DGDC is improved by considering the time derivative of the performance function. Namely, in order to improve the convergence, we modify the DGDC by decreasing both the performance function and its time derivative. The proposed method can be implemented in a very simple and practical manner. Our simulation results with the modified DGDC showed remarkably good performance for various plants.
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References
Fradkov, A. L. (1996), Swing control of nonlinear oscillations, Int. J. Contr., Vol. 64, pp. 1189–1202.
Freeman, R. A. and Kokotović, P. V. (1996), Robust Nonlinear Control Design: State-Space and Lyapunov Techniques, Birkhäuser, Boston.
Isidori, A. (1995), Nonlinear Control Systems, 3rd ed., Springer-Verlag, London.
Kristic, M., Kanellakopoulos, I. and Kokotović, P. (1995), Nonlinear and Adaptive Control Design, Wiley, New York.
Mayne, D. Q. and Michalska, H. (1990), Receding horizon control of nonlinear systems, IEEE Trans. Automat Contr., Vol. 35, pp. 814–824.
Moylan, P. J. and Anderson, B. D. O. (1973), Nonlinear regulator theory and an inverse optimal control problem, IEEE Trans. Automat. Contr., Vol. 18, pp. 460–465.
Saerens, M., Renders, J. M. and Bersini, N. (1996), Neuro control based on the backpropagation algorithm, in Intelligent Control Systems (Gupta, M. M. and Sinha, N. K., eds.), IEEE Press, New York.
Shimizu, K., Nukumi, H. and Ito, S. (1996), Direct steepest descent control of nonlinear dynamical systems, in Nonlinear Control Systems Design1995 (Krener, A. J. and Mayne, D. Q., eds.), Pergamon, Oxford, pp. 801–806.
Shimizu, K., Ito, S. and Suzuki, S. (1998), Tracking control of general nonlinear system by direct gradient descent method, in Proceedings of the IFAC Nonlinear Control Systems Design Symposium, Vol. 1, pp. 185–190.
Shimizu, K., Otsuka, K. and Naiborhu, J. (1999), Improved direct gradient descent control of general nonlinear systems, in Proceedings of the 1999 European Control Conference (CD-ROM), No. F676.
Sontag, E. D. (1990), Mathematical Control Theory: Deterministic Finite Dimensional Systems, Springer-Verlag, New York.
van der Schaft, A. (1996), L 2 -Gain and Passivity Techniques in Nonlinear Control, Springer-Verlag, London.
Vincent, T. L. and Grantham, W. J. (1997), Nonlinear and Optimal Control Systems, Wiley, New York.
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Shimizu, K., Ito, S., Otsuka, K. (2001). Modified Direct Gradient Descent Control of Nonlinear Systems. In: Yang, X., Teo, K.L., Caccetta, L. (eds) Optimization Methods and Applications. Applied Optimization, vol 52. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3333-4_8
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DOI: https://doi.org/10.1007/978-1-4757-3333-4_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4850-2
Online ISBN: 978-1-4757-3333-4
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