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Mathematical strategies common to mechanics and control. (English) Zbl 1080.93500

Summary: 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 \(H_\infty\)-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.

MSC:

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93B36 \(H^\infty\)-control
70Q05 Control of mechanical systems
74M05 Control, switches and devices (“smart materials”) in solid mechanics
93C20 Control/observation systems governed by partial differential equations
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