Asymptotically Stabilizing Potential Control for the Eye Movement Dynamics

In this paper, we analyze the problem of stabilizing a rotating eye movement control system satisfying the Listing’s constraint. The control system is described using a suitably defined Lagrangian and written in the corresponding Hamiltonian form. We introduce a damping control and show that this choice of control asymptotically stabilizes the equilibrium point of the dynamics, while driving the state to a point of minimum total energy. The equilibrium point can be placed by appropriately locating the minimum of a potential function. The damping controller has been shown to be optimal with respect to a suitable cost function. We choose alternate forms of this cost function, by adding a term proportional to the potential energy, and synthesize stabilizing control, using numerical solution to the the well known Hamilton Jacobi Bellman equation. Using Chebyshev collocation method, the newly synthesized controller is compared with the damping control.