留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

拟哈密顿系统非线性随机最优控制

朱位秋 应祖光

朱位秋, 应祖光. 拟哈密顿系统非线性随机最优控制[J]. 力学进展, 2013, 43(1): 39-55. doi: 10.6052/1000-0992-12-045
引用本文: 朱位秋, 应祖光. 拟哈密顿系统非线性随机最优控制[J]. 力学进展, 2013, 43(1): 39-55. doi: 10.6052/1000-0992-12-045
ZHU Weiqiu, YING Zuguang. ADVANCES IN RESEARCH ON NONLINEAR STOCHASTIC OPTIMAL CONTROL OF QUASI-HAMILTONIAN SYSTEMS[J]. Advances in Mechanics, 2013, 43(1): 39-55. doi: 10.6052/1000-0992-12-045
Citation: ZHU Weiqiu, YING Zuguang. ADVANCES IN RESEARCH ON NONLINEAR STOCHASTIC OPTIMAL CONTROL OF QUASI-HAMILTONIAN SYSTEMS[J]. Advances in Mechanics, 2013, 43(1): 39-55. doi: 10.6052/1000-0992-12-045

拟哈密顿系统非线性随机最优控制

doi: 10.6052/1000-0992-12-045
基金项目: 国家自然科学基金重点项目(10932009)和面上项目(11072212,11072215,11272279)资助
详细信息
    作者简介:

    朱位秋, 男, 汉族, 浙江义乌人. 现为浙江大学航空航天学院应用力学研究所教授, 博士生导师, 所长, 中国科学院院士. 1967s1975 年在飞机结构强度研究所工作, 1975 年调浙江大学任教. 曾先后访问美国Wisconsin Univ., MIT, Florida Atlantic Univ., New York State Univ. at Buffalo, 日本Kyoto Univ.等. 长期从事非线性随机动力学与控制研究, 他领导课题组创建了非线性随机动力学与控制的哈密顿理论体系, 2002 年获国家自然科学二等奖.

    通讯作者:

    朱位秋

  • 中图分类号: O32,O23,TB123

ADVANCES IN RESEARCH ON NONLINEAR STOCHASTIC OPTIMAL CONTROL OF QUASI-HAMILTONIAN SYSTEMS

Funds: The project was supported by the National Natural Science Foundation of China (10932009, 11072212, 11072215, 11272279).
More Information
    Corresponding author: ZHU Weiqiu
  • 摘要: 主要介绍近十几年来拟哈密顿系统非线性随机最优控制理论方法及其应用的研究成果, 包括基于拟哈密顿系统随机平均法与随机动态规划原理的非线性随机最优控制基本策略, 即响应极小化控制、随机稳定化、首次穿越损坏最小化控制、以概率密度为目标的控制, 为将它们应用于工程实际而作的部分可观测系统最优控制、有界控制、时滞控制、半主动控制、极小极大控制的进一步研究, 以及综合考虑这些实际问题的非线性随机最优控制的综合策略, 非线性随机最优控制在滞迟系统、分数维系统等中的若干应用, 介绍与这些研究有关的背景, 并指出今后有待进一步研究的问题.

     

  • 1 Stengel R F. Stochastic Optimal Control: Theory and Application. New York: Wiley, 1986
    2 Fleming W H, Soner H M. Controlled Markov Processes and Viscosity Solutions. New York: Springer-Verlag, 1992
    3 Yong J M, Zhou X Y. Stochastic Control, Hamiltonian Systems and HJB Equations. New York: Springer-Verlag,1999
    4 朱位秋. 非线性随机动力学与控制——Hamiltonian理论体 系框架. 北京: 科学出版社, 2003
    5 Soong T T. Active Structural Control: Theory and Practice. New York: John Wiley & Sons, 1990
    6 Socha L. Linearization in analysis of nonlinear stochastic systems: Recent results-part I: Theory. ASME Applied Mechanics Reviews, 2005, 58: 178-205  
    7 Socha L. Linearization in analysis of nonlinear stochastic systems: Recent results-part II: Application. ASME Applied Mechanics Reviews, 2005, 58: 303-315  
    8 Crespo L G, Sun J Q. Stochastic optimal control of nonlinear dynamical systems via Bellman's principle and cell mapping. Automatica, 2003, 39: 2109-2114  
    9 Dimentberg M F, Iourtchenko A S, Brautus A S. Optimal bounded control of steady-state random vibrations. Probabilistic Engineering Mechanics, 2000, 15: 381-386  
    10 Li J, Peng Y B, Chen J B. A physical approach to structural stochastic optimal controls. Probabilistic Engineering Mechanics, 2010, 25: 127-141  
    11 Kovaleva A. Optimal Control of Mechanical Oscillations. Berlin: Springer, 1999
    12 Zhu W Q. Nonlinear stochastic dynamics and control in Hamiltonian formulation. ASME Applied Mechanics Reviews, 2006, 59: 230-248  
    13 Tabor M. Chaos and Integrability in Nonlinear Dynamics, An Introduction. New York: Wiley & Sons, 1989
    14 李继彬, 赵晓华, 刘正荣. 广义哈密顿系统理论及其应用. 第2版. 北京: 科学出版社, 2007
    15 Stratonovich R L. Topics in the Theory of Random Noise. New York: Gordon Breach, 1963
    16 Khasminskii R Z. A limit theorem for solution of differential equations with random right-hand side. Theory Problems and Applications, 1966, 11: 390-406  
    17 Papanicolaou G C, Kohler W. Asymptotic theory of mixing stochastic ordinary differential equations. Communications in Pure and Application Mathematics, 1974, 27:641-668
    18 Blankenship G L, Papanicolaou G C. Stability and control of stochastic systems with wide-band noise disturbances. SIAM Journal of Application Mathematics, 1978, 34: 437-476  
    19 Landa P S, Stratonovich R L. Theory of stochastic transition of various systems between states. Vestnik MGU (Proc. Moscow Univ.), 1962, III: 33-45 (in Russian)
    20 Khasminskii R Z. Behavior of a conservative system with small friction and small random noise. Prikladnaya Matematika i Mechanica (Appl. Math. Mech.), 1964, 28:1126-1130 (in Russian)
    21 Roberts J B. Energy method for nonlinear systems with non-white excitation. In: Hennig K ed. Random Vibrations and Reliability, Berlin: Academic-Verlag, 1982. 285-294
    22 Red-Horse J R, Spanos P D. A generalization to stochastic averaging in random vibration. International Journal of Non-linear Mechanics, 1992, 27: 85-101  
    23 Cai G Q, Lin Y K. Random vibration of strongly nonlinear systems. Nonlinear Dynamics, 2001, 24: 3-15  
    24 Zhu W Q, Huang Z L, Suzuke Y. Response and stability of strongly nonlinear oscillators under wide-band random excitation. International Journal of Non-Linear Mechanics, 2001, 36: 1235-1250  
    25 Huang Z L, Zhu W Q. Stochastic averaging of strongly nonlinear oscillators under combined harmonic and white noise excitations. Journal of Sound and Vibration, 2000,238: 233-256  
    26 Huang Z L, Zhu W Q, Ni Y Q, et al. Stochastic averaging of strongly nonlinear oscillator under bounded noise excitation. Journal of Sound and Vibration, 2002, 254:245-267  
    27 Ibrahim R A. Parametric Random Vibration. Taunton: Research Studies Press Ltd, 1985
    28 Dimentberg M F. Statistical Dynamics of Nonlinear and Time-Varying Systems. Taunton: Research Studies Press Ltd, 1988
    29 朱位秋. 随机振动. 北京: 科学出版社, 1992
    30 Lin Y K, Cai G Q. Probabilistic Structural Dynamics, Advanced Theory and Applications. New York: McGrawHill, 1995
    31 Roberts J B, Spanos P D. Stochastic averaging: An approximate method of solving random vibration problems. International Journal of Non-Linear Mechanics, 1986, 21:111-134  
    32 Zhu W Q. Stochastic averaging methods in random vibration. ASME Applied Mechanics Reviews, 1988, 41:189-199  
    33 Zhu W Q. Recent developments and applications of the stochastic averaging method in random vibration. ASME Applied Mechanics Reviews, 1996, 49: s72-s82  
    34 Zhu W Q, Cai G Q. Nonlinear stochastic dynamics: A survey of recent developments. Acta Mechanica Sinica,2002, 18: 551-566  
    35 Zhu W Q, Yang Y Q. Stochastic averaging of quasinonintegrableHamiltonian systems. ASME Journal of Applied Mechanics, 1997, 64: 157-164  
    36 Zhu W Q, Huang Z L, Yang Y Q. Stochastic averaging of quasi integrable Hamiltonian systems. ASME Journal of Applied Mechanics, 1997, 64: 975-984  
    37 Zhu W Q, Huang ZL, Suzuki Y. Stochastic averaging and Lyapunov exponent of quasi partially integrable Hamiltonian systems. International Journal of Non-Linear Mechanics, 2002, 37: 419-437  
    38 Huang Z L, Zhu W Q. Stochastic averaging of quasigeneralized Hamiltonian systems. International Journal of Non-Linear Mechanics, 2009, 44: 71-80  
    39 Deng M L, Zhu W Q. Stochastic averaging of mdof quasiintegrable Hamiltonian systems under wide-band random excitation. Journal of Sound and Vibration, 2007, 305:783-794  
    40 Zhu W Q, Deng M L, Huang Z L. Optimal bounded control of first-passage failure of quasi integrable Hamiltonian systems with wide-band random excitation. Nonlinear Dynamics, 2003, 33: 189-207  
    41 Huang Z L, Zhu W Q. Exact stationary solutions of averaged equations of stochastically and harmonically excited MDOF quasi-linear systems with internal and/or external resonance. Journal of Sound and Vibration, 1997, 204:249-258  
    42 Huang Z L, Zhu W Q. Stochastic averaging of quasi integrable Hamiltonian Systems under combined harmonic and white noise excitations. International Journal of Non-Linear Mechanics, 2004, 39: 1421-1434  
    43 Huang Z L, Zhu W Q. Stochastic averaging of quasi integrable Hamiltonian Systems under bounded noise excitation. Probabilistic Engineering Mechanics, 2004, 19:219-228  
    44 Zeng Y, Zhu W Q. Stochastic averaging of n-dimensional non-linear dynamical systems subject to non-Gaussian wide-band random excitations. International Journal of Non-Linear Mechanics, 2010, 45: 572-586  
    45 Zeng Y, Zhu W Q. Stochastic averaging of quasinonintegrableHamiltonian systems under Poisson white noise excitation. ASME Journal of Applied Mechanics,2011, 78: 021002  
    46 Liu Z H, Zhu W Q. Stochastic averaging of quasiintegrable Hamiltonian systems with delayed feedback control. Journal of Sound and Vibration, 2007, 299: 178-195  
    47 Zhu W Q, Liu Z H. Response of quasi-integrable Hamiltonian systems with delayed feedback bang-bang control. Nonlinear Dynamics, 2007, 49: 31-47  
    48 Chen L C, ZhuWQ. Stochastic averaging of strongly nonlinear oscillators with small fractional derivative damping under combined harmonic and white noise excitations. Nonlinear Dynamics, 2009, 56: 231-241  
    49 Huang Z L, Jin X L, Lim C W, et al. Statistical analysis for stochastic systems including fractional derivatives. Nonlinear Dynamics, 2010, 59: 339-349  
    50 Hu F, Chen L C, Zhu W Q. Stationary response of strongly non-linear oscillator with fractional derivative damping under bounded noise excitation. International Journal of Non-Linear Mechanics, 2012, 47: 1081-1087  
    51 Housner G W, Bergman L A, Caughey T K, et al. Structural control: Past, present and future. ASCE Journal of Engineering Mechanics, 1997, 123: 897-971  
    52 Yoshida K. A method of optimal control of non-linear stochastic systems with non-quadratic criteria. International Journal of Control, 1984, 39: 279-291  
    53 Chang R J. Optimal linear feedback control for a class of nonlinear non-quadratic non-Gaussian problem. ASME Journal of Dynamic Systems, Measurement and Control,1991, 113: 569-574
    54 Liberzon D, Brockett R W. Nonlinear feedback systems perturbed by noise: Steady-state probability distribution and optimal control. IEEE Automatic Control, 2000, 45:1116-1130  
    55 Bratus A, Dimentberg M, Iourtchenko D, et al. Hybrid solution method for dynamic programming equations for MDOF stochastic systems. Dynamics and Control, 2000,10: 107-116  
    56 Crespo L G, Sun J Q. Nolinear stochastic control via stationary response design. Probabilistic Engineering Mechanics, 2003, 18: 79-86  
    57 Kushner H J. Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems. Boston: Birkhauser, 1990
    58 Kushner H J, Rungguldier. Nearly optimal state feedback control for stochastic systems with wide-band noise disturbances. SIAM Journal of Control and Optimization,1987, 25: 298  
    59 Zhu W Q, Ying Z G. Optimal nonlinear feedback control of quasi-Hamiltonian systems. Science in China, Series A, 1999, 42: 1213-1219  
    60 Zhu W Q, Ying Z G, Soong T T. An optimal nonlinear feedback control strategy for randomly excited structural systems. Nonlinear Dynamics, 2001, 24: 31-51  
    61 Hu F, ZhuW Q. Stabilization of quasi integrable Hamiltonian systems with fractional derivative damping by using fractional optimal control. submitted to IEEE Transaction on Automatic Control, 2012
    62 Zhu W Q, Lei Y. Stochastic averaging of energy envelope of bilinear hysteretic systems. In: Ziegler F, Schueller G I, eds. Nonlinear Stochastic Dynamic Engineering Systems, Proc. IUTAM Symposium, Innsbruck, Austria, 1987. Berlin: Springer-Verlag, 1988. 381-391
    63 Zhu W Q, Lin Y K. Stochastic averaging of energy envelope. ASCE Journal of Engineering Mechanics, 1991,117: 1890-1905  
    64 Ying Z G, Zhu W Q, Ni Y Q, et al. Stochastic averaging of Duhem hysteretic systems. Journal of Sound and Vibration, 2002, 254: 91-104  
    65 Ying Z G, Zhu W Q, Ni Y Q, et al. Random response of Preisach hysteretic systems. Journal of Sound and Vibration, 2002, 254: 37-49  
    66 Spanos P D, Cacciola P, Muscolino G. Stochastic averaging of Preisach hysteretic systems. ASCE Journal of Engineering Mechanics, 2004, 130: 1257-1267  
    67 Wang Y, Ying Z G, Zhu W Q. Stochastic averaging of energy envelope of Preisach hysteretic systems. Journal of Sound and Vibration, 2009, 321: 976-993  
    68 Zhu W Q, Ying Z G, Ni Y Q, et al. Optimal nonlinear stochastic control of hysteretic structures. ASCE Journal of Engineering Mechanics, 2000, 126: 1027-1032  
    69 Wang Y, Ying Z G, Zhu W Q. Nonlinear stochastic optimal control of Preisach hysteretic systems. Probabilistic Engineering Mechanics, 2009, 24: 255-264  
    70 Ying Z G, Ni Y Q, Ko J M. Non-linear stochastic optimal control for coupled-structures system of multi-degreeoffreedom. Journal of Sound and Vibration, 2004, 274:843-861  
    71 Florchinger P. Feedback stabilization of affine in the control stochastic differential systems by the control Lyapunov function method. SIAM Journal of Control and Optimization, 1997, 35: 500-511  
    72 Zhu W Q. Feedback stabilization of quasi non-integrable Hamiltonian systems by using Lyapunov exponent. Nonlinear Dynamics, 2004, 36: 455-470  
    73 Zhu W Q, Huang Z L. Feedback stabilization of quasiintegrable Hamiltonian systems. ASME Journal of Applied Mechanics, 2003, 70: 129-136  
    74 Zhu W Q, Huang Z L. Stochastic stabilization of quasi partially-integrable Hamiltonian systems by using Lyapunov exponent. Nonlinear Dynamics, 2003, 33: 209-224  
    75 Zhu W Q. Lyapunov exponent and stochastic stability of quasi non-integrable Hamiltonian systems. International Journal of Non-Linear Mechanics, 2004, 39: 645-655
    76 Zhu W Q, Huang Z L. Stochastic stabilization of quasi non-integrable Hamiltonian systems. International Journal of Non-Linear Mechanics, 2004, 39: 879-895  
    77 Zhu W Q, Huang Z L, Deng M L. First-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems. International Journal of Non-Linear Mechanics, 2003, 38: 1133-1148  
    78 Zhu W Q, Huang Z L, Deng M L. Feedback minimization of first-passage failure of quasi non-integrable Hamiltonian systems. International Journal of Non-Linear Mechanics,2002, 37: 1057-1071  
    79 Zhu W Q, Wu Y J. Optimal bounded control of firstpassage failure of strongly nonlinear oscillators under combined harmonic and white noise excitations. Journal of Sound and Vibration, 2004, 271: 83-101  
    80 Karny M. Towards fully probabilistic control design. Automatica, 1996, 32: 1719-1722  
    81 Forbes M G, Guay M, Forbes J F. Control design for firstorder processes: Shaping the probability density of the process state. Journal of Process Control, 2004, 14: 399-410  
    82 Guo L, Wang H, Wang A P. Optimal probability density function control for NARMAX stochastic systems. Automatica, 2008, 44: 1904-1911  
    83 Yang Y, Guo L, Wang H. Constrained PI tracking control for output probability distributions based on two-step neural networks. IEEE Transactions on Circuits Systems, Part I, 2009, 56: 1416-1426  
    84 Zhu C X, ZhuWQ. Feedback control of nonlinear stochastic systems for targeting a specified stationary probability density. Automatica, 2011, 47: 539-544  
    85 Zhu C X, Zhu W Q, Yang Y F. Design of feedback control of a nonlinear stochastic system for targeting a prespecified stationary probability distribution. Probabilistic Engineering Mechanics, 2012, 30: 20-26  
    86 Wonham W M. On the separation theorem of stochastic control. SIAM Journal of Control, 1968, 6: 312-326  
    87 Bensoussan A. Stochastic Control of Partially Observable Systems. UK, Cambridge: Cambridge University Press,1992
    88 Zhu W Q, Ying Z G. Nonlinear stochastic optimal control of partially observable linear structures. Engineering Structures, 2002, 24: 333-342  
    89 Zhu W Q, Luo M, Ying Z G. Nonlinear stochastic optimal control of tall buildings under wind loading. Engineering Structures, 2004, 26: 1561-1572  
    90 Luo M, Zhu W Q. Nonlinear stochastic optimal control of offshore platforms under wave loading. Journal of Sound and Vibration, 2006, 296: 734-745  
    91 Charalambous C D, Elliott R J. Classes of nonlinear partially observable stochastic optimal control problems with explicit optimal control law. SIAM Journal of Control and Optimization, 1998, 36: 542-578  
    92 Zhu W Q, Ying Z G. On stochastic optimal control of partially observable nonlinear quasi Hamiltonian systems. Journal of Zhejiang University, Science, 2004, 5: 1313-1317  
    93 Ying Z G, Zhu W Q. A stochastic optimal control strategy for partially observable nonlinear quasi-Hamiltonian systems. Journal of Sound and Vibration, 2008, 310: 184-196  
    94 Feng J, Zhu W Q, Ying Z G. Stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems. Science China, 2010, 53: 147-154  
    95 Dimentberg M F, Bratus A S. Bounded parametric control of random vibrations. Proceedings of the Royal Society of London, Series A, 2000, 456: 2351-2363  
    96 Zhu W Q, Deng M L. Optimal bounded control for minimizing the response of quasi non-integrable Hamiltonian systems. Nonlinear Dynamics, 2004, 35: 81-100  
    97 Zhu W Q, Deng M L. Optimal bounded control for minimizing the response of quasi integrable Hamiltonian systems. International Journal of Non-Linear Mechanics,2004, 39: 1535-1546  
    98 Zhu W Q, Wu Y J. Optimal bounded control of strongly nonlinear oscillator under combined harmonic and whitenoise excitations. Probabilistic Engineering Mechanics,2005, 20: 1-9  
    99 Bartolini G, Punta E. Chattering elimination with secondorder sliding modes robust to coulomb friction. ASME Journal of Dynamic Systems, Measurement and Control,2000, 122: 679-686  
    100 Bartoszewicz A. Chattering attenuation in sliding mode control systems. Control and Cybernetics, 2000, 29: 585-594
    101 Parra-Vega V, Hirzinger G. Chattering-free sliding mode control for a class of nonlinear mechanical systems. International Journal of Robust and Nonlinear Control, 2001,11: 1161-1178  
    102 Chitour Y, Liu W, Sontag E. On the continuity and incrementalgain properties of certain saturated linear feedback loops. International Journal of Robust and Nonlinear Control, 1995, 5: 413-440  
    103 Hu T, Lin Z, Chen B M. An analysis and design method for linear systems subject to actuator saturation and disturbance. Automatica, 2002, 38: 351-359  
    104 Ying Z G, Zhu W Q. A stochastically averaged optimal control strategy for quasi-Hamiltonian systems with actuator saturation. Automatica, 2006, 42: 1577-1582  
    105 Huan R H, Wu Y J, Zhu W Q. Stochastic optimal bounded control of MDOF quasi nonintegrable-Hamiltonian systems with actuator saturation. Archive of Applied Mechanics, 2009, 79: 157-168  
    106 Huan R H, Zhu W Q. Stochastic optimal control of quasi integrable Hamiltonian systems subject to actuator saturation. Journal of Vibration and Control, 2009, 15: 85-99  
    107 Feng C S, Zhu W Q. Stochastic optimal control of strongly non-linear systems under wide-band random excitation with actuator saturation. Acta Mechanica Solida Sinica,2008, 21: 116-126
    108 Di Paola M, Pirrotta A. Time delay induced effects on control of linear systems under random excitation. Probabilistic Engineering Mechanics, 2001, 16: 43-51  
    109 Bilello C, Di Paola M, Pirrotta A. Time delay induced effects on control of non-linear systems under random excitation. Mechanica, 2002, 37: 207-220  
    110 Hu H Y, Wang Z H. Dynamics of Controlled Mechanical Systems with Delayed Feedback. Berlin: Springer, 2002
    111 Yang J N, Akbarpour A, Askar G. Effect of time delay on control of seismic-excited buildings. ASCE Journal of Structural Engineering, 1990, 116: 2801-2814  
    112 Agrawal A K, Yang J N. Effect of fixed time delay on stability and performance of actively controlled civil engineering structures. Earthquake Engineering and Structural Dynamics, 1997, 26: 1169-1185  
    113 Balashevich N V, Gabasov R, Kirillova F M. Synthesis of optimal feedback and the stabilization of systems with a delay in the control. Journal of Applied Mathematics and Mechanics, 1998, 62: 133-143  
    114 Pu J P. Time delay compensation in active control of structures. ASCE Journal of Engineering Mechanics,1998, 124: 1018-1028  
    115 Agrawal A K, Yang J N. Compensation of time-delay for control of civil engineering structures. Earthquake Engineering and Structural Dynamics, 2000, 29: 37-62  
    116 Chu S Y, Soong T T, Lin C C, et al. Time-delay effect and compensation on direct output feedback controlled mass damper systems. Earthquake Engineering and Structural Dynamics, 2002, 31: 121-137  
    117 Cai G, Huang J. Optimal control method with time delay in control. Journal of Sound and Vibration, 2002, 251:383-394  
    118 Udwadia F E, Von Bremen H F, Kumar R, et al. Time delayed control of structural systems. Earthquake Engineering and Structural Dynamics, 2003, 32: 495-535  
    119 Wang Z H, Hu H Y, Wang H L. Robust stabilization to non-linear delayed systems via delayed state feedback: The averaging method. Journal of Sound and Vibration,2005, 279: 937-953  
    120 Haraguchi M, Hu H Y. Using a new discretization approach to design a delayed LQG controller. Journal of Sound and Vibration, 2008, 314: 558-570  
    121 Sun J Q. A method of continuous time approximation of delayed dynamical systems. Communications in Nonlinear Science and Numerical Simulation, 2009, 14: 998-1007  
    122 Sun J Q, Song B. Control studies of time-delayed dynamical systems with the method of continuous time approximation. Communications in Nonlinear Science and Numerical Simulation, 2009, 14: 3933-3944  
    123 Zhao P. Practical stability, controllability and optimal control of stochastic Markovian jump systems with timedelays. Automatica, 2008, 44: 3120-3125
    124 Kushner H J. Numerical approximations for nonlinear stochastic systems with delay. Stochastics An International Journal of Probability and Stochastic Processes, 2005,77: 211-240  
    125 Sun J Q. Finite dimensional Markov process approximation for stochastic time-delayed dynamical systems. Communications in Nonlinear Science and Numerical Simulation, 2009, 14: 1822-1829  
    126 Grigoriu M. Control of time delay linear systems with Gaussian white noise. Probabilistic Engineering Mechanics, 1997, 12: 89-96  
    127 Li X P, Zhu W Q, Liu Z H. Stochastic averaging of quasi linear systems subject to multitime-delayed feedback control and wide-band random excitation. Journal of Vibration and Control, 2009, 15: 1187-1205  
    128 Feng C S, Zhu W Q. Response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control. Journal of Zhejiang University, Science A, 2009, 10: 54-61  
    129 Liu Z H, Zhu W Q. Asymptotic Lyapunov stability with probability one of quasi-integrable Hamiltonian systems with delayed feedback control. Automatica, 2008, 44:1923-1928  
    130 Liu Z H, Zhu W Q. Stochastic Hopf bifurcation of quasiintegrable Hamiltonian systems with time-delayed feedback control. Journal of Theoretical and Applied Mechanics, 2008, 46: 531-550
    131 Liu Z H, ZhuWQ. First-passage failure of quasi-integrable Hamiltonian systems under time-delayed feedback control. Journal of Sound and Vibration, 2008, 315: 301-317  
    132 Li X P, Liu Z H, Zhu W Q. First-passage failure of quasi linear systems subject to multi-time-delayed feedback control and wide-band random excitation. Probabilistic Engineering Mechanics, 2009, 24: 144-150  
    133 Liu Z H, Zhu W Q. Compensation for time-delayed feedback bang-bang control of quasi-integrable Hamiltonian systems. Science in China, Series E, 2009, 52: 688-697  
    134 Ying, Z G, Zhu W Q. A stochastic optimal time-delay control for nonlinear structural systems. Structural Engineering and Mechanics, 2009, 31: 621-624
    135 Feng J, Zhu W Q, Liu Z H. Stochastic optimal time-delay control of quasi-integrable Hamiltonian systems. Communications in Nonlinear Science and Numerical Simulation, 2011, 16: 2978-2984  
    136 Liu Z H, Zhu W Q. Time-delay stochastic optimal control and stabilization of quasi-integrable Hamiltonian systems. Probabilistic Engineering Mechanics, 2012, 27: 29-34  
    137 Symans M D, Constantinon M C. Semi-active control systems for seismic protection of structures: A state-of-theart review. Engineering Structures, 1999, 21: 469-487  
    138 Gavin H P, Hanson R D, Filisko F E. Electrorheological dampers. Part II: Testing and modeling. ASME Journal of Applied Mechanics, 1996, 63: 676-682
    139 Spencer B F, Dyke S J, Sain M K, et al. Phenomenological model for magneto-rheological dampers. ASCE Journal of Engineering Mechanics, 1997, 123: 230-238  
    140 Wereley N M, Pang L, Kamath G M. Idealized hysteresis modeling of electro-rheological and magnetorheological dampers. Journal of Intelligent Material Systems and Structures, 1998, 9: 642-649  
    141 Leitmann G. Semiactive control for vibration attenuation. Journal of Intelligent Material Systems and Structures,1994, 5: 841-846  
    142 Dyke S J, Spencer B F, Sain M K, et al. Modeling and control of magnetorheological dampers for seismic response reduction. Smart Materials and Structures, 1996, 5: 565-575  
    143 Jansen L M, Dyke S J. Semi-active control strategy for MR dampers: Comparative study. ASCE Journal of Engineering Mechanics, 2000, 126: 795-803  
    144 Ying Z G, Zhu W Q, Soong T T. A stochastic optimal semi-active control strategy for ER/MR dampers. Journal of Sound and Vibration, 2003, 259: 45-62  
    145 Dong L, Ying Z G, Zhu W Q. Stochastic optimal semiactive control of nonlinear systems using MR damper. Advances in Structural Engineering, 2004, 7: 485-494  
    146 Ying Z G, Ni Y Q, Ko J M. A new stochastic optimal control strategy for hysteretic MR dampers. Acta Mechanica Solida Sinica, 2004, 17: 223-229
    147 Cheng H, Zhu W Q, Ying Z G. Stochastic optimal semiactive control of hysteretic systems by using a magnetorheological damper. Smart Materials and Structures,2006, 15: 711-718  
    148 Zhu W Q, Luo M, Dong L. Semi-active control of wind excited building structures using MR/ER dampers. Probabilistic Engineering Mechanics, 2004, 19: 279-285  
    149 Zhou K M, Doyle J C, Glover K. Robust and Optimal Control. New Jersey: Prentice-Hall, 1996
    150 Stengel R F, Ray L R, Marrison C I. Probability evaluation of control system robustness. International Journal of Systems and Science, 1995, 26: 1363-1382  
    151 Marrison C I, Stengel R F. Robust control system design using random search and genetic algorithms. IEEE Transactions on Automatic Control, 1997, 42: 835-839  
    152 Wang Q, Stengel R F. Robust control of nonlinear systems with parametric uncertainty. Automatica, 2002, 38:1591-1599  
    153 Wang Y, Ying Z G, Zhu W Q. Optimal bounded control of hysteretic systems under external and parametrical random excitations. Advances in Structural Engineering,2008, 11: 177-187  
    154 Wang Y, Ying Z G, Zhu W Q. Robustness of non-linear stochastic optimal control for quasi-Hamiltonian systems with parametric uncertainty. International Journal of Systems Science, 2009, 40: 1217-1227  
    155 Savkin A V, Petersen I R. Minimax optimal control of uncertain systems with structured uncertainty. International Journal of Robust and Nonlinear Control, 1995, 5:119-137  
    156 Petersen I R, James M R. Performance analysis and controller synthesis for nonlinear systems with stochastic uncertainty constraints. Automatica, 1996, 32: 959-972  
    157 Ugrinovskii V A, Petersen I R. Finite horizon minimax optimal control of stochastic partially observed time varying uncertain systems. Mathematics of Control, Signals, and Systems, 1999, 12: 1-23  
    158 Ugrinovskii V A, Petersen I R. Minimax LQG control of stochastic partially observed uncertain systems. SIAM Journal of Control and Optimization, 2001, 40: 1189-1226
    159 Ugrinovskii V A, Petersen I R. Absolute stabilization and minimax optimal control of uncertain systems with stochastic uncertainty. SIAM Journal of Control and Optimization, 1999, 37: 1089-1122  
    160 Wang Y, Ying Z G, Zhu W Q. A minimax optimal control strategy for uncertain quasi-Hamiltonian systems. Journal of Zhejiang University, Science A, 2008, 9: 950-954  
    161 Wang Y, Ying Z G, Zhu, W Q. Stochastic minimax control for stabilization uncertain quasi-integrable Hamiltonian systems. Automatica, 2009, 45: 1847-1853  
    162 Huan R H, Chen L C, Jin W L, et al. Stochastic optimal vibration control of partially observable nonlinear quasi Hamiltonian systems with actuator saturation. Acta Mechanica Solida Sinica, 2009, 22: 143-151
    163 Feng J, Ying Z G, Zhu W Q, et al. A minimax stochastic optimal semi-active control strategy for uncertain quasiintegrable Hamiltonian systems using magneto-rheological dampers. Journal of Vibration and Control, 2012, 18:1986-1995  
    164 Ying Z G, Ni Y Q, Ko J M. A bounded stochastic optimal semi-active control. Journal of Sound and Vibration,2007, 304: 948-956  
    165 Feng J, Ying Z G, Zhu W Q. A minimax optimal control strategy for partially observable uncertain quasiHamiltonian systems. International Journal of NonLinear Mechanics, 2012, 47: 1147-1153  
    166 Feng J, Ying Z G,Wang Y, et al. Stochastic minimax optimal time-delay state feedback control of uncertain quasiintegrable Hamiltonian systems. Acta Mechanica, 2011,222: 309-319  
    167 Huan R H, Ying Z G, Jin W L, et al. Minimax optimal control of uncertain quasi-integrable Hamiltonian systems with time-delayed bounded feedback. Probabilistic Engineering Mechanics, 2010, 25: 271-278  
  • 加载中
计量
  • 文章访问数:  1663
  • HTML全文浏览量:  19
  • PDF下载量:  2339
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-03-26
  • 修回日期:  2012-11-14
  • 刊出日期:  2013-01-24

目录

    /

    返回文章
    返回