A model is developed of a non-circular wheel rolling on a road and colliding with a short wall. It is modeled as a hybrid dynamical system with a combination of continuous- and discrete-time dynamics. Input-output feedback linearization is used to design a controller to stabilize the wheel via the application of torque such that the wheel is balanced on the wall. A proof of asymptotic stability is provided for the feedback linearized control. To compute an optimal control signal, the problem is discretized into a finite-dimensional constrained optimization problem and solved with a numerical solver. An elliptical wheel is presented as an example and comparisons between various implementations are provided.