Regular Papers

International Journal of Control, Automation and Systems 2008; 6(3): 364-377

© The International Journal of Control, Automation, and Systems

Locally Optimal and Robust Backstepping Design for Systems in Strict Feedback Form with C1 Vector Fields

Juhoon Back, Sejin Kang, Hyungbo Shim*, and Jin Heon Seo

Seoul National University, Korea

Abstract

Due to the difficulty in solving the Hamilton-Jacobi-Isaacs equation, the nonlinear optimal control approach is not very practical in general. To overcome this problem, Ezal et al. (2000) first solved a linear optimal control problem for the linearized model of a nonlinear system given in the strict-feedback form. Then, using the backstepping procedure, a nonlinear feedback controller was designed where the linear part is same as the linear feedback obtained from the linear optimal control design. However, their construction is based on the cancellation of the high order nonlinearity, which limits the application to the smooth (C∞) vector fields. In this paper, we develop an alternative method for backstepping procedure, so that the vector field can be just C1, which allows this approach to be applicable to much larger class of nonlinear systems.

Keywords Disturbance attenuation, inverse optimality, optimal control, robust control.

Article

Regular Papers

International Journal of Control, Automation and Systems 2008; 6(3): 364-377

Published online June 1, 2008

Copyright © The International Journal of Control, Automation, and Systems.

Locally Optimal and Robust Backstepping Design for Systems in Strict Feedback Form with C1 Vector Fields

Juhoon Back, Sejin Kang, Hyungbo Shim*, and Jin Heon Seo

Seoul National University, Korea

Abstract

Due to the difficulty in solving the Hamilton-Jacobi-Isaacs equation, the nonlinear optimal control approach is not very practical in general. To overcome this problem, Ezal et al. (2000) first solved a linear optimal control problem for the linearized model of a nonlinear system given in the strict-feedback form. Then, using the backstepping procedure, a nonlinear feedback controller was designed where the linear part is same as the linear feedback obtained from the linear optimal control design. However, their construction is based on the cancellation of the high order nonlinearity, which limits the application to the smooth (C∞) vector fields. In this paper, we develop an alternative method for backstepping procedure, so that the vector field can be just C1, which allows this approach to be applicable to much larger class of nonlinear systems.

Keywords: Disturbance attenuation, inverse optimality, optimal control, robust control.

IJCAS
May 2024

Vol. 22, No. 5, pp. 1461~1759

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