Towards a multiresolution approach to linear control

We develop a multiresolution approximation framework for linear control. We construct a multiresolution analysis of the set of input functions of a linear system. The approximation of an input u at a scale j is defined as the input u
_j
of minimal energy such that the trajectories of the system associated with u and u
_j
coincide on a grid of step length 2
^-j
. We propose a set of wavelet functions which generate this multiresolution analysis. These functions, called control theoretic wavelets, satisfy useful properties for the representation of control inputs of a linear system. As an example of application of our multiresolution approximation framework, we propose a method for efficient encoding of control inputs with regard to several criteria