Kinematic Reducibility of Multiple Model Systems

This paper considers the relationship between second order multiple model systems and first order multiple model systems. Such a relationship is important to, among other things, studying path planning for mechanical control systems. This is largely due to the fact that the computational complexity of a path planning problem rapidly increases with the dimension of the state space, implying that being able to reduce a path planning problem from TQ to Q can be helpful. Not surprisingly, the necessary and sufficient condition for such a reduction is that each model constituting a multiple model control system be reducible. We present an extensive example in order to illustrate how these results can provide insight into the control of some specific physical systems.