Continuous-time Orthonormal Basis Functions

Abstract

This chapter introduces orthonormal basis functions and their applications in dynamic system modelling. The chapter begins with an introduction to the basic concepts in approximating an arbitrary function with a set of orthonormal basis functions. Laguerre functions not only satisfy these properties, but also possess simple Laplace transforms. The chapter discusses how Laguerre functions are used in modelling the impulse response of a stable system with convergence. A more general class of orthonormal basis functions, called Kautz functions, are introduced towards the end of this chapter. Kautz functions allow complex poles to be used in their structures, however, they require more effort in computing the realization. The modelling idea using a set of orthonormal basis functions forms a fundamental principle of the model predictive control design methods presented in this book. It is helpful if we understand these basic ideas.