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Under-actuated system refers to a kind of nonlinear system in which the number of independent control variables of the system is less than the number of its degrees of system freedom. Compared with the full-actuated mechanical system, the under-actuated system reduces the number of independent control variables, reduces the weight and the design cost of the system, saves the energy and enhances the flexibility of the system. At the same time, due to the simple structure of the system, it is convenient to construct and analyze the mechanical experiments. In this book, the double-pendulum tower crane is taken as the research object, and a variety of stability control strategies are proposed for this kind of under-actuated system.