Fractional Order Crowd Dynamics by Kecai Cao YangQuan Chen

Author:Kecai Cao, YangQuan Chen
Language: eng
Format: epub
Publisher: Walter de Gruyter
Published: 2018-06-15T00:00:00+00:00

From the above discussions, we know that there are some v minimizing the following expression:

and ṽ = −v maximizes the following:

As seen from (4.24), á¹½ as a function of p should satisfy

Thus the derivative of H (p) can be obtained using the chain rule as follows:

and the following velocity for each pedestrian to move in the next step is derived:

(2) Stochastic case

When the pedestrian’s movement evolves according to the controlled stochastic differential equation shown in (4.4), the behavior of the pedestrians can now be evaluated by the following stochastic cost function:

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