受控拉格朗日函数方法综述

吴凡; 耿志勇

doi:10.3724/SP.J.1004.2012.00145

受控拉格朗日函数方法综述

doi: 10.3724/SP.J.1004.2012.00145

吴凡^,,
耿志勇

1.
北京大学湍流与复杂系统国家重点实验室北京 100871

详细信息

通讯作者:
吴凡, 北京大学力学与空天技术系博士. 主要研究方向为力学系统的非线性控制. E-mail: wufan@pku.edu.cn

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出版历程
- 收稿日期: 2011-05-16
- 修回日期: 2011-10-24
- 刊出日期: 2012-02-20

A Survey for Controlled Lagrangian Method

WU Fan^,,
GENG Zhi-Yong

1.
State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871

摘要

摘要: 受控拉格朗日函数(Controlled Lagrangians, CL)方法是一种以能量观点设计简单力学系统镇定控制律的方法. 自1997年正式提出以来, CL法在理论及应用上都得到了发展. 理论上包括研究CL法的可行性,针对特定类系统简化CL法设计, 利用CL法解决镇定之外的控制问题. 应用上主要是将CL法用于多种实际力学系统, 尤其是欠驱动力学系统的控制. 本综述将介绍CL法的主要思想与理论; 回顾各控制研究团队所作理论与应用推广; 讨论关于CL法一些尚存的问题以及未来研究方向.
- 简单力学系统 /
- 能量整形 /
- 匹配 /
- 非线性镇定
Abstract: The method of controlled Lagrangian (CL) has been developed to stabilize simple mechanical systems based on energy shaping. Since the introduction of this controller design methodology in 1997, many theoretical developments and practical applications have been reported in the literature. The theoretical developments include a series of criteria for its applicability, special shortcuts that are useful when dealing with particular classes of systems, and the incorporation of additional features to handle control scenarios other than just stabilization. On the application side, the method has been applied to a wide variety of practical mechanical control systems, especially under actuated systems. The purpose of this survey is to review the fundamental idea and theory of this controller design methodology, research developments achieved by different research groups, as well as to discuss the current open problems and future research directions.
- Simple mechanical systems /
- energy shaping /
- matching /
- nonlinear stabilization

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参考文献(1)

[1]

Takegaki M, Arimoto S. A new feedback method for dynamic control of manipulators. Journal of Dynamic Systems, Measurement, and Control, 1981, 103(2): 119-125[2] Schaft V D A J. Stabilization of Hamiltonian systems. Nonlinear Analysis, Theory, Methods and Applications, 1986, 10(10): 1021-1035[3] Bloch A M, Leonard N E, Marsden J E. Stabilization of mechanical systems using controlled Lagrangians. In: Proceedings of the 36th IEEE Conference on Decision and Control. San Diego, USA: IEEE, 1997. 2356-2361[4] Bloch A M, Leonard N E, Marsden J E. Controlled Lagrangians and the stabilization of mechanical systems I: the first matching theorem. IEEE Transactions on Automatic Control, 2000, 45(12): 2253-2269[5] Lewis A D. Notes on energy shaping. In: Proceedings of the 43rd IEEE Conference on Decision and Control. Nassau, Bahamas: IEEE, 2004. 4818-4823[6] Lewis A D. Potential energy shaping after kinetic energy shaping. In: Proceedings of the 45th IEEE Conference on Decision and Control. San Diego, USA: IEEE, 2006. 3339-3344[7] Gharesifard B, Lewis A D, Mansouri A R. A geometric framework for stabilization by energy shaping: sufficient conditions for existence of solutions. Communications in Information and Systems, 2008, 8(4): 353-398[8] Reddy C K. Practical Challenges in the Method of Controlled Lagrangians [Ph.D. dissertation], Virginia Polytechnic Institute and State University, USA, 2005[9] Long D, Zenkov D V. Relaxed matching for stabilization of relative equilibria of mechanical systems. In: Proceedings of the 46th IEEE Conference on Decision and Control. New Orleans, USA: IEEE, 2007. 6238-6243[10] Zenkov D V, Bloch A M, Marsden J E. Controlled Lagrangian methods and tracking of accelerated motions. In: Proceedings of the 42nd IEEE Conference on Decision and Control. Maui, USA: IEEE, 2003. 533-538[11] Nair S N, Leonard N E. Stable synchronization of mechanical system networks. SIAM Journal on Control and Optimization, 2008, 47(2): 661-683[12] Nair S N, Leonard N E. Stable synchronization of rigid body networks. Networks and Heterogeneous Media, 2007, 2(4): 595-624[13] Machleidt K, Kroneis J, Liu S. Stabilization of the Furuta pendulum using a nonlinear control law based on the method of controlled Lagrangians. In: Proceedings of the IEEE International Symposium on Industrial Electronics. Vigo, Spain: IEEE, 2007. 2129-2134[14] Freidovich L, Shiriaev A, Gordillo F, Gomez-Estern F, Aracil J. Partial-energy-shaping control for orbital stabilization of high-frequency oscillations of the Furuta pendulum. IEEE Transactions on Control Systems Technology, 2009, 17(4): 853-858[15] Zenkov D V, Bloch A M, Marsden J E. Flat nonholonomic matching. In: Proceedings of the American Control Conference. Anchorage, USA: IEEE, 2002. 2812-2817[16] Li Mao-Qing. Stabilization controller design of Pendubot based on controlled Lagrangians. Control and Decision, 2010, 25(5): 663-668(李茂青. 基于受控拉格朗日函数的Pendubot镇定控制器设计. 控制与决策, 2010, 25(5): 663-668)[17] Li Mao-Qing. Control design for planar vertical takeoff-and-landing aircraft based on controlled Lagrangians. Control Theory and Applications, 2010, 27(6): 688-694(李茂青. 基于受控拉格朗日函数的垂直起降飞机控制器设计. 控制理论与应用, 2010, 27(6): 688-694)[18] Reddy C K, Woolsey C A. Energy shaping for vehicles with point mass actuators. In: Proceedings of the American Control Conference. Minneapolis, USA: IEEE, 2006. 4291-4296[19] Bullo F, Lewis A D. Geometric Control of Mechanical Systems: Modeling, Analysis, and Design for Simple Mechanical Control Systems. New York: Springer, 2005[20] Marsden J E. Lectures on Mechanics. New York: Cambridge University Press, 1992[21] Khalil H K. Nonlinear Systems (Third Edition). New Jersey: Prentice Hall, 2002[22] Woolsey C A. Energy Shaping and Dissipation: Underwater Vehicle Stabilization Using Internal Rotors [Ph.D. dissertation], Princeton University, USA, 2001[23] Bloch A M, Chang D E, Leonard N E, Marsden J E. Controlled Lagrangians and the stabilization of mechanical systems II: potential shaping. IEEE Transactions on Automatic Control, 2001, 46(10): 1556-1571[24] Wu F, Geng Z Y. Energy shaping for coordinating internally actuated vehicles. Theoretical and Applied Mechanics Letters, 2011, 1(2): 023002.1-023002.5[25] Wu F, Geng Z Y. Stabilization of coordinated motion for underwater vehicles. Acta Mechanica Sinica, 2011, 27(3): 438-444[26] Auckly D, Kapitanski L. On the λ -equations for matching control laws. SIAM Journal on Control and Optimization, 2002, 41(5): 1372-1388[27] Bloch A M, Leonard N E, Marsden J E. Controlled Lagrangians and the stabilization of Euler-Poincare mechanical systems. International Journal on Robust and Nonlinear Control, 2001, 11(1): 191-214[28] Viola G, Ortega R, Banavar R, Acosta J A, Astolfi A. Total energy shaping control of mechanical systems: simplifying the matching equations via coordinate changes. IEEE Transactions on Automatic Control, 2007, 52(6): 1093-1099[29] Li M Q, Huo W. Controller design for mechanical systems with underactuation degree one based on controlled Lagrangians method. International Journal of Control, 2009, 82(9): 1747-1761[30] Chang D E. The method of controlled Lagrangians: energy plus force shaping. In: Proceedings of the 48th IEEE Conference on Decision and Control Held Jointly with the 28th Chinese Control Conference. Shanghai, China, 2009. 3329-3334[31] Fax J A, Murray R M. Information flow and cooperative control of vehicle formations. IEEE Transactions on Automatic Control, 2004, 49(9): 1465-1476[32] VanDyke M C, Hall C D. Decentralized coordinated attitude control of a formation of spacecraft. Journal of Guidance, Control and Dynamics, 2006, 29(5): 1101-1109[33] Belta C, Kumar V. Motion generation for formations of robots: a geometric approach. In: Proceedings of the IEEE International Conference on Robotics and Automation. Seoul, Korea: IEEE, 2001. 1245-1250[34] Hanssmann H, Leonard N E, Smith T R. Symmetry and reduction for coordinated rigid bodies. European Journal of Control, 2006, 12(2): 176-194[35] Gharesifard B. A Geometric Approach to Energy Shaping [Ph.D. dissertation], Queen's University, Canada, 2009[36] Chang D E. Stabilizability of controlled Lagrangian systems of two degrees of freedom and one degree of under-actuation by the energy-shaping method. IEEE Transactions on Automatic Control, 2010, 55(8): 1888-1893[37] Woolsey C A, Techy L. Cross-track control of a slender, underactuated AUV using potential shaping. Ocean Engineering, 2009, 36(1): 82-91[38] Bullo F, Murray R M. Tracking for fully actuated mechanical systems: a geometric framework. Automatica, 1999, 35(1): 17-34[39] Bullo F. Nonlinear Control of Mechanical Systems: a Riemannian Geometry Approach [Ph.D. dissertation], California Institute of Technology, USA, 1999[40] Frazzoli E. Robust Hybrid Control for Autonomous Vehicle Motion Planning [Ph.D. dissertation], Massachusetts Institute of Technology, USA, 2001[41] Bhatta P. Nonlinear Stability and Control of Gliding Vehicles [Ph.D. dissertation], Princeton University, USA, 2006[42] Ortega R, Spong M W, Gomez-Estern F, Blankenstein G. Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Transactions on Automatic Control, 2002, 47(8): 1218-1233[43] Ortega R, Canseco E G. Interconnection and damping assignment passivity-based control: a survey. European Journal of Control, 2004, 10(5): 432-450[44] Yu H S, Zou Z W, Tang Y L. Speed control of PMSM based on energy-shaping and PWM signal transformation principle. In: Proceedings of the International Conference on Electrical Machines and Systems. Wuhan, China: IEEE, 2008. 3166-3170[45] Donaire A, Junco S. Energy shaping, interconnection and damping assignment, and integral control in the bond graph domain. Simulation Modelling Practice and Theory, 2009, 17(1): 152-174[46] Batlle C, Doria-Cerezo A, Espinosa-Perez G, Ortega R. Simultaneous interconnection and damping assignment passivity-based control: the induction machine case study. International Journal of Control, 2009, 82(2): 241-255[47] Chang D E. Controlled Lagrangian and Hamiltonian Systems [Ph.D. dissertation], California Institute of Technology, USA, 2002

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