Discrete function approximation: numerical tools for nonlinear control

We describe a method for discrete representation of continuous functions and show how this may be used for typical computations in nonlinear control design. The method involves representing functions by their values and finitely many derivatives at discrete set of points on the domain. We propose a grid structure based on a hierarchy of rectangular boxes that provides flexibility in placing grid points densely in some regions and sparsely in the other. The grids possess enough structure to facilitate easy interpolation schemes based on piecewise polynomials. We illustrate the method using a simple example where we compute the feedback linearizing output of a system.