Control of Switched Networks via Quantum Methods

We illustrate a technique for specifying piecewise constant controls for classes of switched electrical networks, typically used in converting power in a dc-dc converter. This procedure makes use of decompositions of SU(2) to obtain controls that are piecewise constant and can be constrained to be bang-bang with values 0 or 1. Complete results are presented for a third order network first. An example, which shows that the basic strategy is viable for fourth order circuits, is also given. The former evolves on SO(3), while the latter evolves on SO(4). Since the former group is intimately related to SU(2) while the latter is related to SU(2)xSU(2), the methodology of this paper uses factorizations of SU(2). The systems in this paper are single input systems with drift. In this paper, no approximations or other artifices are used to remove the drift. Instead, the drift is important in the determination of the controls. Periodicity arguments are rarely used.