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Direct Gradient Descent Control and Sontag's Formula on Asymptotic Stability of General Nonlinear Control System

Naiborhu J.    (Department of Mathematics, Faculty of Mathematics and Natural Science, Bandung Institute of Technology   ); Nababan S. M.    (Department of Mathematics, Faculty of Mathematics and Natural Science, Bandung Institute of Technology   ); Saragih R.    (Department of Mathematics, Faculty of Mathematics and Natural Science, Bandung Institute of Technology   ); Pranoto I.    (Department of Mathematics, Faculty of Mathematics and Natural Science, Bandung Institute of Technology  );
  • 초록

    In this paper, we study the problem of stabilizing a general nonlinear control system by means of gradient descent control method which is a dynamic feedback control law. In this method, the general nonlinear control system can be considered as an affine nonlinear control systems. Then by using Sontag's formula we investigate the stability (asymptotic) of the general nonlinear control system.


  • 주제어

    Direct gradient descent control .   Sontag's formula .   asymptotic stability.  

  • 참고문헌 (9)

    1. J. Tsinias, 'Stabilization of affine in control nonlinear systems,' Nonlinear Analysis, vol. 12, no. 11, pp. 1283-1296, 1988 
    2. J. Naiborhu and K. Shimizu, 'Direct gradient descent control for global stabilization of general nonlinear control systems,' IEICE Trans. on Fundamental, vol. E83-A, no. 3, pp. 516-523, March 2000 
    3. M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design, John Wiley & Sons, Inc., 1995 
    4. L. Praly, B.d'Andrea-Novel, and J. M. Coron, 'Lyapunov design of stabilizing controllers,' Proc. of the 28th Conf. on Decision and Control, Tampa, Florida, pp.1047-1052, December 1989 
    5. K. Shimizu, H. Nukumi, and S. Ito, 'Direct steepest descent control of nonlinear dynamical systems,' in A. J Krener and D. Q. Mayne (eds.), Nonlinear Control System Design, pp. 801-806, Pergamon, 1996 
    6. A. M. Bloch, Nonholonomic Mechanics and Control, Springer-Verlag, Inc., New York, 2003 
    7. E. D. Sontag, 'Feedback stabilization of nonlinear systems,' in M. A. Kaashoek, J. H. van Schuppen and A. C. M. Ran (eds.), Robust Control of Linear Systems and Nonlinear Control, Birkhauser, Cambridge, MA, pp.61-81, 1990 
    8. J. Naiborhu and K. Shimizu, 'Stabilization of single input nonlinear control systems by gradient descent control algorithm,' in Theory and Practice of Control and Systems, eds. A. Tornambe, G. Conte and A. M. Peron, Proc. of 6th IEEE Mediterranean Conf. on Control and Systems, pp. 544-549, Word Scientific, 1998 
    9. W. Lin, 'Feedback stabilization of general Nonlinear Control Systems,' in A. J. Krener and D. Q. Mayne (eds.), Nonlinear Control System Design, pp. 403-408, Pergamon, 1996 

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