In this paper, structural control algorithms for the hybrid systems, that are combinations of passive and active control devices such as active base isolation, with nonlinear hysteresis are studied. First, by solving the equation directly, that is derived by the necessity condition for optimization, the meanings of the Ricatti matrix are considered from the standpoint of vibration theory, and the relationship between the global optimization and the local optimization such as the instantaneous optimal control algorithms is clarified. Next, a control method, that selects the global and the local optimization by judging vibration conditions by using hysteretic and velocity components, is presented.
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