Stabilization of nonlinear systems: Radial optimal control approach

• Autorzy: Sangelaji Z. , Banks S.P.
• Języki publikacji: EN

Abstrakty

EN

This paper represents the optimal control of nonlinear systems based upon the associated angular approach. In the latter a general class of nonlinear systems is converted to two associated systems: a nonlinear equation on a sphere (spherical), and a radial differential system. By decoupling the two subsystems and considering only the radial system, a finite-horizon radial optimal control is designed which minimizes the radial cost function. Successive approximation technique is then introduced in which the equations are replaced by a sequence of linear, time-varying approximations. The resulting optimal control is then applied to the original angular system. This control forces the original angular system to the origin.

Słowa kluczowe

EN

optimal control systems; angle measurement; nonlinear equations; differential equations; spheres; linearization; time varying system; set theory; computer simulation

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Systems Science
• Rocznik: 2003
• Tom: Vol. 29, nr 4
• Strony: 29--41
• Opis fizyczny: Bibliogr. 15 poz.,

Twórcy

autor

Sangelaji Z.

• Department of Automatic Control, University of Sheffield, Sheffield S1 3JD, United Kingdom

autor

Banks S.P.

• Department of Automatic Control, University of Sheffield, Sheffield S1 3JD, United Kingdom

Bibliografia

• [1] Banks S. P., Mathematical theories of nonlinear systems, Prentice-Hall, London 1988.
• [2] Utkin V. L, Sliding modes in control and optimisation, Springer-Verlag, Berlin 1992,
• [3] Lukyanov A. G., Utkin V. I., Method of reducing equations for dynamic systems to a regular form, Automation and Remote Control, 42,1981, 413-420.
• [4] Knobloch H. W., Isidori A., Flokerzi D., Topics in control theory, DMV seminar band 22, Birkhouser, Berlin 1993.
• [5] Banks S. P., Stabilization of nonlinear systems using the associated angular system, Proc. the 14th World IFAC Congress, Beijing 1999.
• [6] Sangelaji Z., Stabilization of Nonlinear System Via the Associated Angular System, MEng. Dissertation, The University of Sheffield, 1999.
• [7] Colonius F., Кliemann W., The Lyapunov spectrum of families of time-varying matrices, Trans. Amer. Math. Soc., 348, No. 11, 1996,4389-4407.
• [8] Sangelaji Z., Banks S. P., Control design of nonlinear systems using the associated angular, Proceeding of the 10th IEEE Mediterranean conference on control and automation, Portugal 2002.
• [9] Banks S. P., Sangelaji Z., Stabilizability of nonlinear systems using the associated angular system, Proceedings of the IASTED International Conference on Control and Applications, 27-29, Banff, Alberta 2001.
• [10] Sangelaji Z., An approximation method for control design using nonlinear angular system, Proceeding of UKACC Conference, Sheffield 2002.
• [11] Sangelaji Z., Banks S. P., Stabilization of inverted pendulum by the associated angular method, Proc. 1EE Control Conf., Cambridge 2000.
• [12] Banks S. P., McCaffrey D., Lie algebras, structure of nonlinear systems and chaotic motion, Int. J. Bifurcation & Chaos, 8, 1437-1462.
• [13] Banks S. P., Nonlinear delay systems, Lie algebras and Lyapunov transformations, IMA J. Math. Cont. Inf., 19, 59-72.
• [14] Banks S. P., Dinesh K., Approximate optimal control and stability of nonlinear finite- and infinite- dimensional systems, Annal of Operations Research, 98, 2000, 19-44.
• [15] Sangelaji Z., Banks S. P., Stabilization of nonlinear systems: Associated angular approach, Proc. IEE Control Conf., Cambridge 2000.