Aircraft movement in a vertical plane with state constraints

The problem under consideration is trajectory planning of an aircraft in a vertical plane with variable state constraints. The time of maneuver is considered to be known. The main problem is to find the permissible trajectory which meets given requirements. The most developed methods for solving similar problems do not allow us to take into account the restrictions on the system condition. The approach applied in this work allows us to automatically take into account the current restrictions during the required trajectory construction, not using any iterative methods. Building a program trajectory is carried out in a certain class of functions. The paper proposes an optimization approach to choosing the trajectory. The program control implementing this trajectory is based on the concept of inverse dynamic problems. It enables us to synthesize a proper program control, to build the control stabilizing program trajectories and to choose numerical optimization of the trajectory by a definite criterion. We describe a nonlinear mathematical model of the plane movement as a material point in the trajectory reference frame. We illustrate the findings of the research with examples and show the results of numerical modeling.

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