New approach to nonlinear control theory by Hamiltonian mechanics

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In this research we proposed a new approximate solution method to the Hamilton-Jacobi equation, which is one of the most important equations in nonlinear control theory such as optimal control and H-infinity control. We also developed computation programs and applied them to numerous problems. They include numerical problems, aircraft attitude control and control of a magnetic levitation system with experiments. Our results solve the longstanding problem for over 40 years that has been a bottle neck in control theory. The proposed method is suitable for computer implementation and the experimental verification of controllers by the Hamilton-Jacobi equation is, to the best of our knowledge, one of very few important achievements in this field. The concrete problems from engineering are the following. Optimal stabilization problem of an aircraft at high angle-of-attack, magnetic levitation system, systems with input saturation, and systems with input rate saturation related to Pilot-Induced-Oscillation suppression. The proposed algorithm is implemented in computer program in a numerically way and this approach has advantages in application in that non-analytic nonlinearities, such as saturations, can be handled.