Multiresolutional controller design: sensitivity minimization

The capability of having equivalent representations of a signal at various levels of resolution is the crux of multiresolution theory. This paper extends the concept of multiresolution to a control system. In a multiresolutional control system, both the plant and the controller have multiresolutional representations. A multiresolutional controller can be utilized at multiple resolutions or at only one resolution. This paper takes a first step towards achieving a multiresolutional control system. The work presented herein demonstrates the modelling of a plant using several orthonormal wavelet packet bases and also presents a general theorem for designing a multiresolutional controller which minimizes the sensitivity function for a SISO system.