Tutorial on nonlinear backstepping: Applications to ship control

Abstract

The theoretical foundation of nonlinear backstepping designs is presented in a tutorial setting. This includes a brief review of integral backstepping, extensions to SISO and MIMO systems in strict feedback form and physical motivated case studies. Parallels and differences to feedback linearization where it is shown how so-called "good nonlinearities" can be exploited in the design are also made. Nonlinear, optimal and robust backstepping are discussed in a separate section where parallels to linear quadratic optimal control and H∞-control are drawn. In addition, inverse optimality is discussed as a nonlinear design tool. Physics is put into control by using mechanical systems like mass-damper-springs and ship models in the case studies. Lyapunov theory is used to prove convergence and stability for all control laws where energy dissipation is obtained by exploiting physical model properties.