This paper considers a stabilizing hybrid scheme to control a class of underactuated mechanical systems. The hybrid controller consists of a collection of state feedback controllers plus a discrete-event supervisor. When the continuous-state hits a switching boundary, a new controller is applied to the plant. Lyapunov theory is used to determine the switching boundaries and to guarantee the stability of the closed-loop hybrid system. This approach is applied to the well-known swing up and balancing control problem of the inverted pendulum.

A disturbance control scheme for the concentration control of differential recycle reactors is developed which is based on the learning feedforward control strategy. Steady-state decoupling eliminates interactions between the closed loops of this non-linear, multivariable control system, thereby significantly improving the response to disturbances. Since the process model is iteratively updated, the control strategy can be regarded as a model identification adaptive control. Simulation experiments show the performance of the overall control concept.

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