A novel mesh discretization strategy for numerical solution of optimal control problems in aerospace engineering |
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| Institution: | 1. Hubei Key Laboratory for High-efficiency Utilization of Solar Energy and Operation Control of Energy Storage System, Hubei University of Technology, Wuhan 430068 Hubei, China;2. State Key Laboratory of Industrial Control Technology, College of Control Science & Engineering, Zhejiang University, Hangzhou 310027, China;3. Xi''an Modern Control Technology Research Institute, Xi''an, Shanxi 710065, China;4. The First Research Institute of China Aerospace Science and Technology Corporation, Beijing 100076, China;1. Department of Civil Engineering, Birjand University of Technology, P.O. Box 97175-569, Birjand, Iran;2. Department of Electrical Engineering, Technical and Vocational University (TVU), Tehran, Iran;3. Independent researchers, Birjand, Iran;1. School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074, China;2. Artificial Intelligence School, Wuchang University of Technology, Wuhan 430223, China;1. Faculty of Electrical Engineering, Shahrood University of Technology, Shahrood 36199-95161, Iran;2. Department of Applied Science, School of Computing, Engineering and Built Environment, Glasgow Caledonian University, Glasgow G4 0BA, UK;3. Electrical and Computer Engineering Department, University of Louisiana at Lafayette, P.O. Box 43890, Lafayette, LA 70504, USA |
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| Abstract: | An effective approach is proposed for optimal control problems in aerospace engineering. First, several interval lengths are treated as optimization variables directly to localize the switching points accurately. Second, the variable intervals are usually refined into more subintervals homogeneously to obtain the trajectories with high accuracy. To reduce the number of optimization variables and improve the efficiency, the control and the state vectors are parameterized using different meshes in this paper such that the control can be approximated asynchronously by fewer parameters where the trajectories change slowly. Then, the variables are departed as independent variables and dependent variables, the gradient formulae, based on the partial derivatives of dependent parameters with respect to independent parameters, are computed to solve nonlinear programming problems. Finally, the proposed approach is applied to the classic moon lander and hang glider problems. For the moon lander problem, the proposed approach is compared with CVP, Fast-CVP and GPM methods, respectively. For the hang glider problem, the proposed approach is compared with trapezoidal discretization and stopping criteria methods, respectively. The numerical results validate the effectiveness of the proposed approach. |
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