Single-Input Systems with Full Relative Degree

Abstract

This chapter analyzes single-input systems with full relative degree. The primary approach is based on the adaptive backstepping control with Kreisselmeier-filters. In output-feedback adaptive problems, the relative degree plays a major role in determining the difficulty of a problem. The chapter focuses on a special class of LTI systems with its relative degree being equal to its system dimension. Moreover, in this chapter the actuator state is assumed to be measured. The chapter also presents a combination of prediction-based boundary control with adaptive backstepping to address unknown parameters and time delay. It then develops two Lyapunov-based identifiers to estimate unknown plant parameters and actuator time delay.