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. 2010 Jul 15;6(7):e1000857. doi: 10.1371/journal.pcbi.1000857

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Nagengast et al.

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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A risk-neutral optimal control model [4], [17] attempts to minimize the mean of the cost function. As a result, its policy (that is the motor command applied for a given state of the world) is independent of the noise variance N. In contrast, a risk-sensitive optimal control model [22], [34] minimizes a weighted combination of the mean and variance of the cost. Additional variance is an added cost for a risk-averse controller (), whereas it makes a movement strategy more desirable for a risk-seeking controller (). As a consequence, the policy of the controller changes with the noise level N depending on its risk-attitude . A.–C. Changes in motor command with the state of the ball (its positional deviation from the center) for a low noise level (green) and for a high noise level (red) for the risk-neutral (A), risk-averse (B) and risk-seeking (C) controllers. The slope of the lines is equivalent to the control gain of the controller. D.–F. Contribution of control cost to total cost (control cost+error cost) for the risk-neutral (D), risk-averse (E) and risk-seeking (F) controllers.

Inline graphic — A risk-neutral optimal control model [4], [17] attempts to minimize the mean of the cost function. As a result, its policy (that is the motor command applied for a given state of the world) is independent of the noise variance N. In contrast, a risk-sensitive optimal control model [22], [34] minimizes a weighted combination of the mean and variance of the cost. Additional variance is an added cost for a risk-averse controller (), whereas it makes a movement strategy more desirable for a risk-seeking controller (). As a consequence, the policy of the controller changes with the noise level N depending on its risk-attitude . A.–C. Changes in motor command with the state of the ball (its positional deviation from the center) for a low noise level (green) and for a high noise level (red) for the risk-neutral (A), risk-averse (B) and risk-seeking (C) controllers. The slope of the lines is equivalent to the control gain of the controller. D.–F. Contribution of control cost to total cost (control cost+error cost) for the risk-neutral (D), risk-averse (E) and risk-seeking (F) controllers.