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Optimal Control Theory of Normal and Pathological Slow Eye Movements

Journal Name:

  • Journal of Control Engineering and Technology

Publication Year:

  • 2013

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Abstract (Original Language): 
Biological eye movements serve vision by controlling the orientation of the retinas. They are under adaptive control implying a control objective, which we frame as minimising a “visual Lagrangian” that does not depend on motor control. Using optimal control theory, we show that the global optimum can be reached if the motor plant is linear and the zero is cancelled (singular control). It appears that the zero needs to be cancelled before the full Lagrangian can be optimised, implying the need for sequential adaptive controllers. We apply this theory to infantile nystagmus syndrome to argue that oscillatory eye movements are optimal, but the waveform depends on whether or not the zero is cancelled. We also show that the role of saccades is crucial in determining the boundary conditions and hence the local optima (fields of extremals). The local optima could be reached but saccades need to change eye velocity as well as eye position. We conclude that optimal control theory can be applied usefully to understanding adaptive biological processes without the need for detailed knowledge of the adaptive control circuits.
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