Duality System in Applied Mechanics and Optimal Control

A unified approach is proposed for applied mechanics and optimal control theory. The Hamilton system methodology in analytical mechanics is used for eigenvalue problems, vibration theory, gyroscopic systems, structural mechanics, wave-guide, LQ control, Kalman filter, robust control etc. All aspects are described in the same unified methodology. Numerical methods for all these problems are provided and given in meta-language, which can be implemented easily on the computer. Precise integration methods both for initial value problems and for two-point boundary value problems are proposed, which result in the numerical solutions of computer precision. Key Features of the text include: Unified approach based on Hamilton duality system theory and symplectic mathematics; Gyroscopic system vibration, eigenvalue problems; Canonical transformation applied to non-linear systems; Pseudo-excitation method for structural random vibrations; Precise integration of two-point boundary value problems; Wave propagation along wave-guides, scattering; Precise solution of Riccati differential equations; Kalman filtering; HINFINITY theory of control and filter.