求解含复杂约束非线性最优控制问题的改进Gauss伪谱法

孙勇; 张卯瑞; 梁晓玲

doi:10.3724/SP.J.1004.2013.00672

求解含复杂约束非线性最优控制问题的改进Gauss伪谱法

doi: 10.3724/SP.J.1004.2013.00672

1.
哈尔滨工业大学控制理论与制导技术研究中心哈尔滨 150001;
2.
南京电子技术研究所南京 210039

详细信息

通讯作者:
孙勇

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出版历程
- 收稿日期: 2012-05-15
- 修回日期: 2012-08-31
- 刊出日期: 2013-05-20

Improved Gauss Pseudospectral Method for Solving Nonlinear Optimal Control Problem with Complex Constraints

1.
Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001;
2.
Nanjing Research Institute of Electronics Technology, Nanjing 210039

摘要

摘要: 针对含有复杂约束条件的非线性最优控制问题,提出了一种改进的Gauss伪谱法 (Improved Gauss pseudospectral method, IGPM). 这类问题难以得到解析解,特别是有些问题不存在解析的模型, 一些参数只能通过查表得到,使得传统方法难以求解. 在传统的Gauss伪谱法的基础上,将非线性的终端状态积分约束等价地转化为线性形式,提出了IGPM, 通过协态映射定理可以计算出协态变量,检验最优性,使得IGPM具有间接法一样的精度. 并且给出了初始时刻协态变量和端点时刻控制变量的计算方法. 为了提高解的精度,基于IGPM提出了迭代算法, 最后将该算法应用于求解高超声速飞行器上升段轨迹优化问题,结果表明最优轨迹基本满足路径约束条件和最优性条件.
- 非线性最优控制 /
- 改进的Gauss伪谱法 /
- 协态映射 /
- 路径约束
Abstract: An improved Gauss pseudospectral method (IGPM) is proposed to solve the nonlinear optimal control problem with complex constraints, which is difficult to get the analytical solution. Traditional methods can hardly solve these problems by getting some parameter values from the look-up table. Based on the traditional Gauss pseudospectral method, the IGPM is put forward by transforming the nonlinear final state integral constraints into linear type. The costate obtained by the costate mapping theorem is used to check the optimality, which makes the IGPM have the same accuracy with the indirect method. Besides, the computation methods of the initial costate and the boundaries controls are proposed. In order to increase the accuracy, an iterative algorithm is given based on the IGPM. Finally, the ascent trajectory optimization problem of the hypersonic vehicle is solved by the proposed algorithm. The results show that the optimal trajectory almost satisfies the path constraints and the optimality.
- Nonlinear optimal control /
- improved Gauss pseudospectral method (IGPM) /
- costate mapping /
- path constraints

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参考文献(1)

[1]

Betts J T. Survey of numerical methods for trajectory optimization. Journal of Guidance, Control, and Dynamics, 1998, 21(2): 193-207[2] Wei Q L, Zhang H G, Liu D R, Zhao Y. An optimal control scheme for a class of discrete-time nonlinear systems with time delays using adaptive dynamic programming. Acta Automatica Sinica, 2010, 36(1): 121-129[3] Kong S L, Zhang Z S. Optimal control of stochastic system with Markovian jumping and multiplicative noises. Acta Automatica Sinica, 2012, 38(7): 1113-1118[4] Li Jia-Feng, Zhou Hao, Chen Wan-Chun. Indirect method for the hypersonic vehicle maximum-glide problem. Flight Dynamics, 2009, 27(3): 41-44, 49 (李佳峰, 周浩, 陈万春. 高超声速飞行器滑行段最优弹道的间接算法. 飞行力学, 2009, 27(3): 41-44, 49)[5] Li Hui-Feng, Li Zhao-Ying. Indirect method of optimal ascent guidance for hypersonic vehicle. Journal of Astronautics, 2011, 32(2): 297-302 (李惠峰, 李昭莹. 高超声速飞行器上升段最优制导间接法研究. 宇航学报, 2011, 32(2): 297-302)[6] Hager W W. Runge-Kutta methods in optimal control and the transformed adjoint system. Numerische Mathematik, 2000, 87(2): 247-282[7] Conway B A, Larson K M. Collocation versus differential inclusion in direct optimization. Journal of Guidance, Control and Dynamics, 2000, 21(5): 780-785[8] Elnagar G, Kazemi M A, Razzaghi M. The pseudospectral Legendre method for discretizing optimal control problems. IEEE Transactions on Automatic Control, 1995, 40(10): 1793-1796[9] Peng Hai-Jun, Gao Qiang, Wu Zhi-Gang, Zhong Wan-Xie. A mixed variable variational method for optimal control problems with applications in aerospace control. Acta Automatica Sinica, 2011, 37(10): 1248-1255 (彭海军, 高强, 吴志刚, 钟万勰. 求解最优控制问题的混合变量变分方法及其航天控制应用. 自动化学报, 2011, 37(10): 1248-1255)[10] Fahroo F, Ross I M. Costate estimation by a Legendre pseudospectral method. Journal of Guidance, Control, and Dynamics, 2001, 24(2): 270-277[11] Benson D A, Huntington G T, Thorvaldsen T P, Rao A V. Direct trajectory optimization and costate estimation via an orthogonal collocation method. Journal of Guidance, Control, and Dynamics, 2006, 29(6): 1435-1440[12] Huntington G T, Rao A V. Optimal reconfiguration of spacecraft formations using the gauss pseudospectral method. Journal of Guidance, Control, and Dynamics, 2008, 31(3): 689-698[13] Sun Y, Zhang M R. Optimal reentry range trajectory of hypersonic vehicle by Gauss pseudospectral method. In: Proceedings of the 2nd International Conference on Intelligent Control and Information. Harbin, China: IEEE, 2011. 545-549[14] Sun Y, Zhang M R, Li H. New costate estimation of Gauss pseudospectral method for nonlinear optimal control problem. In: Proceedings of the 2011 International Workshop on Engineering Application Research. Hangzhou, China: IEIT, 2011. 31-36[15] Kameswaran S, Biegler L T. Convergence rates for direct transcription of optimal control problems using collocation at radau points. Computational Optimization and Applications, 2008, 41(1): 81-126[16] Garg D, Hager W W, Rao A V. Pseudospectral methods for solving infinite-horizon optimal control problems. Automatica, 2011, 47(4): 829-837[17] Lu P, Sun H S, Tsai B. Closed-loop endoatmospheric ascent guidance. Journal of Guidance, Control, and Dynamics, 2003, 26(2): 283-294[18] Lu P, Pan B F. Highly constrained optimal launch ascent guidance. Journal of Guidance, Control, and Dynamics, 2010, 33(2): 404-414

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