Swing up control question about circular rail double Inverted pendulum is studied. To known swing up time, divide them into time intervals. Make controlled quantity in each time interval as design variables and end-points related with controlled quantities as objective function. Limit condition of controlled quantities is formed into objective function. And a optimization question about determining controlled quantity is established. Control law of circular rail double Inverted pendulum is computed and simulated. Validity and feasibility are showed. The foundation is proposed for the control of non-linear system.
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