Determination of flight route using optimal control theory

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A method for optimal route planning is presented with the assumption that the overall defended area is known in terms of threat potential function. This approach employes tangent plane to reduce the dimension of the state space for optimal programming problems with a state equality constraint. One-dimensional search algorithm is used to select the optimal route among the extermal fields which are obtained by integrating three differential equations from the initial values. In addition to being useful for the route planning through threat potential area, the trajectory planning will be suitable for general two-dimensional searching problems.