基于PSO和RBF网络的模糊末制导律研究
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摘要
导弹导引系统实质上是一个同时具有非线性、时变性和模型不确定性的复杂系统。近年来,随着被拦截目标速度和机动性能力的增强,导弹导引系统的制导任务变得越来越复杂。传统的末制导律已不能满足日趋严格的拦截要求,尤其是目标大机动规避。基于最新控制理论的新型导引律成为各国精确制导技术的研究热点。其中基于模糊逻辑的导引律研究越来越多,逐渐成为热点。
本文首先分析了导弹运动数学模型,建立了导引律仿真系统,对传统导引律进行了介绍,并从理论上对盲区所引起的脱靶量进行分析。考虑到粒子群算法(particle swarm optimization, PSO)原理简单,易于实现工程优化,研究了粒子群算法的基本原理以用来优化后来所设计的导引律,提出了一种基于线性递减惯性权重和交叉策略的改进算法。仿真结果表明,该改进算法不仅操作简单,而且有效。
其次,针对模糊导引律中存在的参数优化问题,提出了两种基于粒子群算法优化的模糊导引律,依据导引性能指标对模糊导引律的参数进行优化。一种是基于粒子群优化的模糊导引律,用粒子群算法同时优化模糊控制器中的比例因子、量化因子和模糊规则库的权重;另一种是基于RBF(radial ba-sis function,RBF)神经网络推理的RBF模糊神经网络导引律,并用粒子群算法优化导引律参数。仿真结果表明,粒子群算法可以简化模糊设计过程中的参数优化等问题,优化后的模糊导引律在制导精度等各方面都有显著提高。
最后,针对自适应模糊导引律参数设计的困难,设计了两种基于RBF神经网络的自适应模糊导引律。一种是基于RBF网络整定的自适应模糊导引律,通过对RBF神经网络两个自调整因子增量式公式的推导,得到了RBF网络整定的自调整因子递推公式。另一种导引律是基于RBF网络辨识的自适应模糊导引律,即用RBF网络去辨识这两个自调整因子。仿真结果对比表明,这两种导引律拦截精度更高,拦截时间更短,并且对拦截机动目标有很强的自适应性,是一种具有实用价值的高精度末制导律。
Missile guidance system actually is the complexity system with non-linear, time-varying and model uncertainty. In recent years, with various aircraft to en-hance the speed and maneuverability, the task of the missile guidance system has become increasingly complicated. Traditional homing guidance law has been un-able to meet the increasingly stringent requirements to intercept, especially for coping with intercepting high maneuvering targets. New guidance law based on latest control theory has become a hot spot in precision guidance technology. Re-searches on fuzzy guidance law have been more and more and gradually become hot spots.
Firstly, this paper analyzes the mathematical models of missile movement, and establishes simulation system of guidance law. Then the traditional homing guidance law is introduced, as well as the theoretical analysis of the miss dis-tance caused by the blind spots. Taking into account the simplicity of principle and easiness to implement projects optimization of particle swarm optimization (PSO), we study the basic principle of PSO so that it is used to optimize the de-sign of the guidance law later, and an improved algorithm with linear decrease inertia weight and crossover strategy is presented. The simulation results show that the improved algorithm is not only simple, but also effective.
Secondly, to parameters’optimization problems existing in fuzzy guidance law design, two fuzzy guidance laws based on PSO are presented, according to the guidance performance indicator. One is the fuzzy guidance law based on PSO, using PSO to optimize the fuzzy controller at the same time the proportion of factors, quantitative factors and weights of fuzzy rules; the other is fuzzy RBF neural networks guidance based on RBF reasoning with PSO optimization. The simulation results show that PSO can simplify the design process of fuzzy para-meter optimization problems, and the optimal fuzzy guidance laws have been en-hanced in precision-guided and other aspects.
Finally, to the difficulty of the design parameters in adaptive fuzzy guidance law, two adaptive fuzzy guidance laws based on RBF are designed. One is adap-tive fuzzy guidance law based on parameters set by RBF neural networks, through the RBF neural networks since the two incremental adjustment factors derived formula, the two adjustment factors’recurrence formula are obtained set by RBF; the other was adaptive fuzzy guidance law based on parameters identifi-cation by RBF neural networks, that is to say, RBF network is used to identify these two self-adjustment factors. Comparisons of simulation results show that these two guidance laws are of higher accuracy, shorter time-to-go and better per-formance indicators, and of a highly adaptive and two kinds precision guidance law with practical value.
本文首先分析了导弹运动数学模型,建立了导引律仿真系统,对传统导引律进行了介绍,并从理论上对盲区所引起的脱靶量进行分析。考虑到粒子群算法(particle swarm optimization, PSO)原理简单,易于实现工程优化,研究了粒子群算法的基本原理以用来优化后来所设计的导引律,提出了一种基于线性递减惯性权重和交叉策略的改进算法。仿真结果表明,该改进算法不仅操作简单,而且有效。
其次,针对模糊导引律中存在的参数优化问题,提出了两种基于粒子群算法优化的模糊导引律,依据导引性能指标对模糊导引律的参数进行优化。一种是基于粒子群优化的模糊导引律,用粒子群算法同时优化模糊控制器中的比例因子、量化因子和模糊规则库的权重;另一种是基于RBF(radial ba-sis function,RBF)神经网络推理的RBF模糊神经网络导引律,并用粒子群算法优化导引律参数。仿真结果表明,粒子群算法可以简化模糊设计过程中的参数优化等问题,优化后的模糊导引律在制导精度等各方面都有显著提高。
最后,针对自适应模糊导引律参数设计的困难,设计了两种基于RBF神经网络的自适应模糊导引律。一种是基于RBF网络整定的自适应模糊导引律,通过对RBF神经网络两个自调整因子增量式公式的推导,得到了RBF网络整定的自调整因子递推公式。另一种导引律是基于RBF网络辨识的自适应模糊导引律,即用RBF网络去辨识这两个自调整因子。仿真结果对比表明,这两种导引律拦截精度更高,拦截时间更短,并且对拦截机动目标有很强的自适应性,是一种具有实用价值的高精度末制导律。
Missile guidance system actually is the complexity system with non-linear, time-varying and model uncertainty. In recent years, with various aircraft to en-hance the speed and maneuverability, the task of the missile guidance system has become increasingly complicated. Traditional homing guidance law has been un-able to meet the increasingly stringent requirements to intercept, especially for coping with intercepting high maneuvering targets. New guidance law based on latest control theory has become a hot spot in precision guidance technology. Re-searches on fuzzy guidance law have been more and more and gradually become hot spots.
Firstly, this paper analyzes the mathematical models of missile movement, and establishes simulation system of guidance law. Then the traditional homing guidance law is introduced, as well as the theoretical analysis of the miss dis-tance caused by the blind spots. Taking into account the simplicity of principle and easiness to implement projects optimization of particle swarm optimization (PSO), we study the basic principle of PSO so that it is used to optimize the de-sign of the guidance law later, and an improved algorithm with linear decrease inertia weight and crossover strategy is presented. The simulation results show that the improved algorithm is not only simple, but also effective.
Secondly, to parameters’optimization problems existing in fuzzy guidance law design, two fuzzy guidance laws based on PSO are presented, according to the guidance performance indicator. One is the fuzzy guidance law based on PSO, using PSO to optimize the fuzzy controller at the same time the proportion of factors, quantitative factors and weights of fuzzy rules; the other is fuzzy RBF neural networks guidance based on RBF reasoning with PSO optimization. The simulation results show that PSO can simplify the design process of fuzzy para-meter optimization problems, and the optimal fuzzy guidance laws have been en-hanced in precision-guided and other aspects.
Finally, to the difficulty of the design parameters in adaptive fuzzy guidance law, two adaptive fuzzy guidance laws based on RBF are designed. One is adap-tive fuzzy guidance law based on parameters set by RBF neural networks, through the RBF neural networks since the two incremental adjustment factors derived formula, the two adjustment factors’recurrence formula are obtained set by RBF; the other was adaptive fuzzy guidance law based on parameters identifi-cation by RBF neural networks, that is to say, RBF network is used to identify these two self-adjustment factors. Comparisons of simulation results show that these two guidance laws are of higher accuracy, shorter time-to-go and better per-formance indicators, and of a highly adaptive and two kinds precision guidance law with practical value.
引文
1杨树谦.精确制导技术发展现状与展望.航天控制,2004,22(4):17～20
2杨树谦.国外精确制导技术发展述评.飞航导弹, 2001, (6):66～69
3孟秀云.导弹制导与控制系统原理.北京:北京理工大学出版社,2003:4-20
4方群,陈武群,袁建平.一种抗干扰修正比例导引律的研究[J].宇航学报,2000, 21(3):76～81
5贝茨.攻击机动目标的最优制导规律.宇航出版社, 1989: 76～80
6 M Guelman. A qualitative study of proportional navigation [J]. IEEE Trans. Aer-ospace and Electronic Systems. 1971, 7(4):637～643
7 SN Ghawghawe, D Ghose.Pure proportional navigation against time-varying target manoeuvres[J].IEEE Transactions on Aerospace and Electronic Sys-tems,1996,32(4):1336～1346
8 PR Mahapatra, US Shukla. Accurate solution of proportional navigation for ma-neuvering targets [J].IEEE Transitions on Aerospace and Electronic Systems, 1989, 25(1):81～89
9 IJ Ha, JS Hur, MS Ko, TL Song. Performance analysis of PNG laws for random-ly maneuvering targets [J]. IEEE Transitions on Aerospace and Electronic Sys-tems, 1990, 26(5):713～720
10 P Zarchana. Ballistic missile defense guidance and control issues [J]. Science and Global Security, 1998, 8:99～124
11李忠应.空空导弹全向攻击最优制导规律研究[J].北京航空靛天大学学报,1990, 16(10):110～116
12胡建和,李忠应.地-空导弹自适应最优制导律初探[J].北京航空航天大学学报,1991,17(3):101～116
13 GM Anderson, VS Sament. Differential game guidance laws for intercept mis-siles [A]. Proc. of AIAA Guidance and Control Conference[C], New Mexico, 1991:77～83
14 Y Oshman, DR Rad. Differential-game-based guidance law using target orienta-tion observations [J]. IEEE transactions on aerospace and electronic systems, 2006, 42(1): 316-326
15 SD Brierley, R Longchamp. Application of sliding mode control to air-air inter-ception problem [J]. IEEE Transactions on Aerospace and Electronic Systems, 1990, 26 (2): 306～325
16 Zhou Di, Mu Chundi, et al. Study of optimal sliding-mode guidance law. Chi-nese Journal of Aeronautics, 1999, 12(4):236～241
17 V Rajasekhar, AG Sreenatha. Fuzzy logic implementation of proportional na-vigation guidance [J]. Acta Astronautica, 2000, 46(1): 17～24
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21 PA Creaser, BA Stacey ,BA White. Evolutionary generation of fuzzy guidance laws. UKACC international Conference on Control, 1998:883～888
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25 RG Cottrell, TL Vincent, SH Sadati. Minimizing interceptor size using neural networks for terminal guidance law synthesis [J]. J. of Guidance, Control, and Dynamics, 1996, 19(3): 557～562
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27 Chih-Min Lin. Missile guidance law design using adaptive cerebellar model arti-culation controller [J]. IEEE Trans. On Neural Networks, 2005, 16(5): 636～644
28 FL Lewis, A Yesildirek, K Liu. Multilayer neural-net robust controller withguaranteed tracking performance [J]. IEEE Trans. On Neural Networks, 1996, 7(3): 388～399
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30周荻.寻的导弹新型导引规律[M].北京:国防工业出版社,2002:2～10
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36 CW Reynolds. Flocks, herds and schools: a distributed behavioral model. Com-puter Graphics, 1987, 21(4): 25～34
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2杨树谦.国外精确制导技术发展述评.飞航导弹, 2001, (6):66～69
3孟秀云.导弹制导与控制系统原理.北京:北京理工大学出版社,2003:4-20
4方群,陈武群,袁建平.一种抗干扰修正比例导引律的研究[J].宇航学报,2000, 21(3):76～81
5贝茨.攻击机动目标的最优制导规律.宇航出版社, 1989: 76～80
6 M Guelman. A qualitative study of proportional navigation [J]. IEEE Trans. Aer-ospace and Electronic Systems. 1971, 7(4):637～643
7 SN Ghawghawe, D Ghose.Pure proportional navigation against time-varying target manoeuvres[J].IEEE Transactions on Aerospace and Electronic Sys-tems,1996,32(4):1336～1346
8 PR Mahapatra, US Shukla. Accurate solution of proportional navigation for ma-neuvering targets [J].IEEE Transitions on Aerospace and Electronic Systems, 1989, 25(1):81～89
9 IJ Ha, JS Hur, MS Ko, TL Song. Performance analysis of PNG laws for random-ly maneuvering targets [J]. IEEE Transitions on Aerospace and Electronic Sys-tems, 1990, 26(5):713～720
10 P Zarchana. Ballistic missile defense guidance and control issues [J]. Science and Global Security, 1998, 8:99～124
11李忠应.空空导弹全向攻击最优制导规律研究[J].北京航空靛天大学学报,1990, 16(10):110～116
12胡建和,李忠应.地-空导弹自适应最优制导律初探[J].北京航空航天大学学报,1991,17(3):101～116
13 GM Anderson, VS Sament. Differential game guidance laws for intercept mis-siles [A]. Proc. of AIAA Guidance and Control Conference[C], New Mexico, 1991:77～83
14 Y Oshman, DR Rad. Differential-game-based guidance law using target orienta-tion observations [J]. IEEE transactions on aerospace and electronic systems, 2006, 42(1): 316-326
15 SD Brierley, R Longchamp. Application of sliding mode control to air-air inter-ception problem [J]. IEEE Transactions on Aerospace and Electronic Systems, 1990, 26 (2): 306～325
16 Zhou Di, Mu Chundi, et al. Study of optimal sliding-mode guidance law. Chi-nese Journal of Aeronautics, 1999, 12(4):236～241
17 V Rajasekhar, AG Sreenatha. Fuzzy logic implementation of proportional na-vigation guidance [J]. Acta Astronautica, 2000, 46(1): 17～24
18 Chun-Liang Lin, Hao-Zhen Hung, et al. Development of an integrated fuzzy-logic-based missile guidance law against high speed target [J]. IEEE Trans. on Fuzzy Systems, 2004, 12(2): 157～169
19 Chin-Min Lin, Yung-Yue Chen. Design of fuzzy logic guidance law against hight-speed target. J. of Guidance, Control and Dynamics, 2000, 23(1):17～25
20 Chin-Min Lin, Yi-Jen Mon. Fuzzy-logic-based guidance law design for missile systems [A]. Proceedings of the 1999 IEEE International Conference on Control Applications[C], Kohala Coast-Island of Hawaii, Hawaii, USA, 1999: 22～27
21 PA Creaser, BA Stacey ,BA White. Evolutionary generation of fuzzy guidance laws. UKACC international Conference on Control, 1998:883～888
22刘永善,刘藻珍,李兰忖.攻击机动目标的被动寻的模糊变结构制导律研究[J].系统工程与电子技术, 2007, 29(2): 254～258
23罗德林,沈春林,吴文海,李玉峰.基于遗传算法的飞行器追踪拦截模糊导引律优化设计[J].吉林大学学报(工学版), 2005, 35(7):415～419
24 A Das, R Mukhopadhyay, A Para. Sliding mode congtroller along with feedback linearization for a nonlinear missile model [C]. Systems and Control in Aero-space and ISSCAA 2006, 1st International Symposium on Astronautics, 2006: 952～956
25 RG Cottrell, TL Vincent, SH Sadati. Minimizing interceptor size using neural networks for terminal guidance law synthesis [J]. J. of Guidance, Control, and Dynamics, 1996, 19(3): 557～562
26 ZJ Geng, CL MaCullouth. Missile control using fuzzy cerebella model arithmetic computer neural networks [J]. J. of Guidance, Control and Dynamic, 1997, 20 (3): 557～565
27 Chih-Min Lin. Missile guidance law design using adaptive cerebellar model arti-culation controller [J]. IEEE Trans. On Neural Networks, 2005, 16(5): 636～644
28 FL Lewis, A Yesildirek, K Liu. Multilayer neural-net robust controller withguaranteed tracking performance [J]. IEEE Trans. On Neural Networks, 1996, 7(3): 388～399
29 FP Adler. Missile guidance by three-dimensional proportional navigation [J]. Journal of Applied Physics, 1956, 27 (5):402～424
30周荻.寻的导弹新型导引规律[M].北京:国防工业出版社,2002:2～10
31钱杏芳,林瑞雄,赵亚南.导弹飞行力学[M].北京:北京理工大学出版社,2006:90～113
32刘兴堂.导弹制导控制系统分析、设计与仿真[M].哈尔滨:哈尔滨工业大学,2006:69～75
33刘兴堂.精确制导、控制与仿真技术[M].北京:国防工业出版社, 2006:153～160
34 GM Dimirovski, SM Deskovski, ZM Gacovski. Classical and fuzzy-systems guidance laws in homing missiles systems [J]. IEEE Aerospace Conference Pro-ceedings, 2004:3032～3049
35李君龙,陈杰,胡恒章.目标机动时的一种三维非线性制导律.宇航学报,1998,19(2):37～42
36 CW Reynolds. Flocks, herds and schools: a distributed behavioral model. Com-puter Graphics, 1987, 21(4): 25～34
37 J Kennedy, RC Eberhart. Particle swarm optimization [J]. Proc IEEE Int’1. Conf. on Neural Networks, Piscataway, NJ: IEEE Service Center, 1995:1942～1948
38 F. van den Bergh, AP Engelbrecht. A study of particle swarm optimization par-ticle trajectories [J]. Information Sciences, 2006, 176: 937～971
39 Y Shi, RC Eberhart. Empirical study of particle swarm optimization [J]. In Pro-ceedings of the 1999 Congress on Evolutionary Computation, Piscataway, NJ: IEEE Service Centerm, 1999:1945～1950
40 Y Shi, RCEberhart. Parameter selection in particle swarm optimization [A]. Proc of the 7th Annual Conference on Evolutionary Programming[C], Washington DC, 1998:591～600
41 Y Shi, RC Eberhart. A modified particle swarm optimizer[R].IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, 1998
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