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Duality System in Applied Mechanics and Optimal Control
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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.§
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