Mathematical strategies common to mechanics and control

This paper deals with strategies common to mechanics and control. Design methods, well known from simple mechanical control systems, are extended to the broader class of affine input systems. Since here exterior differential systems are used for the description of control systems, methods of exterior calculus, like the derived flag, can be applied to the problems of accessibility, observability, and exact linearization. The H∞-design of nonlinear control can be considered as an application of the theory of differential games. By refining this design for Hamiltonian control systems we present an exact solution of the Hamilton-Jacobi-Isaacs- equation for a special problem of optimal damping. On the basis of an infinite dimensional Hamiltonian system, in this case a beam with piezoelectric layers, the applicability of the presented methods, as well as the realizability of the feedback law. is shown.