Duality System in Applied Mechanics and Optimal Control

Abstract

Under the computer impact, optimal control theory is proposed based on the state space model, which should at least trace back to the Hamilton canonical equation system. On the other hand, introducing the state space approach, the dual equations derived in structural mechanics have the same form as those in optimal control theory, and then the analogy between structural mechanics and optimal control is established. Both the LQ control and the Kalman-Bucy filter correspond to structural static, and both the H-infinity control and H-infinity\textbackslash{} filter critical (optimal) parameters correspond to Euler critical load factor in structural stability, i.e. the extended Rayleigh quotient. Further, the parameter identification of plant matrix corresponds to inverse problem in structural analysis, and also the large scale de-centralized control corresponds to sub-structural combination and its H-infinity critical parameter can be solved by the modal synthesis method in structural vibrations. All these relationships of analogy theory and the respective precise integration method are described in this paper, perspectively.