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Differential equations play a prominent role in aerospace engineering by modeling aerospace structures, describing important phenomena, and simulating mathematical behavior of aerospace dynamical systems. Presently, aerospace systems have become more complex, space vehicle missions require more hours of simulation time to complete a maneuver, and high-performance missiles require more logical decisions in there phases of flight. Because of these conditions, a computationally efficient algorithm for solving these differential equations is highly demanded to significantly reduce the computing time. This paper presents an efficient method for solving the differential equations by using variational iteration method, which can be implemented into software package to dramatically reduce the computing time for simulating the aerospace systems thereby significantly improving computer's performance in real-time design and simulation of aircrafts, spacecrafts, and other aerospace vehicles.

The autonomous collision avoidance problem for multi-trailer vehicle maneuvering is investigated in this paper. Different from conventional vehicle systems that contain one single moving part or multi-parts that can be considered as one rigid body, the interconnection between the tractor and each trailer, and interactions between trailers in the multi-trailer system introduce a high dimensional and highly complex dynamic system for the controller design. The external disturbance and parametric uncertainties further increase the difficulty in system identification and state space formulation. To implement a real time control system for various scenarios where the locations and states of the obstacles are not known beforehand, a supervisory algorithm is designed to convert the control problem to a discrete event system. The model predictive control (MPC) using limited lookahead policy is employed in the proposed algorithm.