Abstract
The problem of stabilizing an inverted pendulum on a cart while enabling manual control of the cart velocity is treated. Introduction of an input saturation nonlinearity makes the problem challenging in the sense that the system may be driven to a state where recovery is not possible. A controller based on the controllability set of the inverted pendulum, which ensures stability and tracking of constant reference velocities for the cart is developed. The controller also offers a tradeoff between performance and robustness.
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