Output Regulation of Perturbed Nonlinear Systems by Nested Sliding Mode Control

In this paper, we consider nested sliding mode control of SISO nonlinear systems, perturbed by bounded matched and unmatched uncertainties. The systems are assumed to be in strict-feedback form. A step wise procedure is introduced to obtain the controller. In each step, a continuous sliding mode controller is designed as virtual control law. Then the next step sliding surface is defined by using this virtual controller. These sliding surfaces are selected as nonlinear static functions of the system states. Finally in the last step, smooth static state feedback control law is determined such that the output reaches the desired set-point while the system is forced arbitrary close to the intersection of sliding surfaces and the states remain bounded.

• Aras Adhami Mirhoseini
• Mohammad J. Yazdanpanah

• Sliding mode control
• Strict-feedback form
• Unmatched uncertainty
• output regulation.

[1] V. I. Utkin, Sliding modes in control and optimization, Springer-Verlag, Berlin, 1992. [2] V. I. Utkin, Sliding mode control in electromechanical systems, Taylor and Francis, 1999. [3] C. Edwards and S. K. Spurgeon, Sliding mode control: Theory and application, Taylor and Francis, 1998. [4] J. J. Slotine and W. Li, Applied Nonlinear Control, Englewood Cliffs, NJ, Prentice-Hall. 1991. [5] H. K. Khalil, Nonlinear Systems, Upper Saddle River, NJ, Prentice-Hall. 1996. [6] M. J. Yazdanpanah, and A. Ghafari, "A Systematic Approach for Computing Nonlinear Sliding Surfaces," submitted to 16th IFAC world congress, 2005. [7] Y. A. Jiang, T. Hesketh, and D. J. Clements, "High Order Sliding Mode Control of Uncertain Linear Systems", in Proc. 14th IFAC world congress, vol. G, pp. 437-442, Beijing, 1999. [8] R. Eaton, T. Hesketh, and D. J. Clements, "Dynamical Sliding Mode Control of Perturbed Nonlinear System in Strict Feedback Form", inProc. 38th Conference on Decision & Control, pp. 5146-5151, Dec. 1999.