Chapter 1 - An introduction to backstepping control

Abstract

In the last few decades, several control techniques are deployed for the stabilization, regulation, and control of linear and nonlinear dynamical systems. For linear autonomous systems, it is easy to find a control Lyapunov function for stability and optimization problems. However, finding a suitable control Lyapunov function is a challenging problem for nonlinear control systems. The backstepping control method is a recursive design procedure that links the choice of a control Lyapunov function with the design of a feedback controller and guarantees global asymptotic stability of strict feedback systems. The active backstepping control method is a practical tool to overcome the limitations of the feedback linearization approach in the control literature. The block backstepping control method is a general backstepping control method with more applicability in the control literature. The adaptive backstepping control method is a modified form of backstepping control method that uses estimates for unknown parameters in the systems. The robust backstepping control method is an effective backstepping technique for control systems with uncertainties. In this chapter, we describe an introduction to backstepping control with some basic examples and simulations. We also state some basic results for active backstepping control method.