Adaptive Radau pseudo-spectral optimization for descending trajectory of a hypersonic cruise vehicle
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ORIGINAL PAPER
Adaptive Radau pseudo-spectral optimization for descending trajectory of a hypersonic cruise vehicle Xinle Feng1 · Yali Lv1 · Yang Gao1 · Yuankai Li1 Received: 27 April 2020 / Revised: 21 August 2020 / Accepted: 9 October 2020 / Published online: 2 November 2020 © Shanghai Jiao Tong University 2020
Abstract During descending flight of a hypersonic cruise vehicle (HCV), the flight environment is complicated due to the drastically changed atmosphere. It is necessary for the flight trajectory to perform accurate and fast optimization. To solve the nonlinear optimization problem, in this paper, a global adaptive Radau pseudo-spectral method, which is introduced with an hp adaptive strategy (p method to increase the number of points in time interval and h method to refine the interval) is presented. The maximum range and the shortest engagement time are considered, respectively, as performance index to optimize controlling of the attack angle. Using Lagrange interpolation polynomial approximation, the optimal control problem is transformed into a problem of nonlinear programming and solved by a sequence quadratic programming algorithm. Simulation results have shown that the presented method has high computational efficiency and desirable accuracy, with the flying constraints satisfied. It is an effective trajectory optimization method for HCVs. Keywords Adaptive Radau pseudo-spectral method · Optimal control · Nonlinear programming · Aerodynamic data fitting · Trajectory optimization
1 Introduction Hypersonic cruise vehicle (HCV) is powered by supercombustion ram engine and can perform hypersonic cruise flight. The HCVs are equipped on a variety of launch platforms such as land based, sea based or air based, which can damage and attack high-value time-sensitive targets on land, sea and air with hypersonic speed and are used as main weapon equipment in the hypersonic vehicles. The descending flight trajectory of HCVs is a complicated process with large maneuvers, wide field, nonlinear constraints and strong uncertainties. It is necessary for such a descending trajectory to establish an effective, accurate and fast optimization method [1]. The trajectory optimization problem involves two aspects: numerical method and numerical optimization method. To solve the problem, optimal control is converted into parameter optimization using a numerical method, and then the
B 1
Yuankai Li [email protected] Province Key Laboratory of Aircraft Swarm Intelligent Sensing and Cooperative Control, University of Electronic Science and Technology of China, Chengdu 611731, China
parameter optimization is realized by applying a numerical optimization method. Numerical methods are generally divided into direct methods (DM) and indirect methods (IM) according to whether to directly optimize the performance index. The IM does not directly optimize the performance indicator function, and the DM directly optimizes the performance indicator function. With the improvement of computer performance, the current numerical method
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