ABSTRACT
This chapter reviews basic backstepping tools for state feedback control. Backstepping is a recursive Lyapunov-based scheme for the class of “strict-feedback” systems. The idea of backstepping is to design a controller recursively by considering some of the state variables as “virtual controls” and designing for them intermediate control laws. Backstepping achieves the goals of stabilization and tracking. The recursive backstepping design step back toward the control input starting with a scalar equation and involves the systematic construction of feedback control laws and Lyapunov functions. The chapter considers unknown parameters which appear linearly in system equations. It shows that a new backstepping design is presented to avoid such a case from happening, which employs the minimal number of parameter estimates. The chapter illustrates the potential of backstepping control applied for stabilization of unstable flow in oil wells. The proposed backstepping controller is shown in simulations to perform better than proportional-integral and proportional-derivative controllers for low pressure set points.
