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Probabilistic Criteria of Stochastic Optimal Control

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Stochastic Optimal Control of Structures
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Abstract

As indicated in Chap. 3, the classical LQG with specified parameters of control law just secures the structural performance in the sense of second-order moment, and cannot be applied to design a logical control system on the basis of nominal white Gaussian noise.

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References

  • Chen GP, Malik OP, Qin YH, Xu GY (1992) Optimization technique for the design of a linear optimal power system stabilizer. IEEE Trans Energy Convers 7(3):453–459

    Article  Google Scholar 

  • Chen SP, Li XJ, Zhou XY (1998) Stochastic linear quadratic regulators with indefinite control weight costs. SIAM J Control Optim 36:1685–1702

    Article  MathSciNet  MATH  Google Scholar 

  • Leondes CT, Salami MA (1980) Algorithms for the weighting matrices in sampled-data linear time-invariant optimal regulator problems. Comput Electr Eng 7:11–23

    Article  MATH  Google Scholar 

  • Li J, Chen JB, Fan WL (2007) The equivalent extreme-value event and evaluation of the structural system reliability. Struct Saf 29(2):112–131

    Article  Google Scholar 

  • Li J, Peng YB, Chen JB (2011a) Probabilistic criteria of structural stochastic optimal controls. Probab Eng Mech 26(2):240–253

    Article  Google Scholar 

  • Li J, Peng YB, Chen JB (2011b) Nonlinear stochastic optimal control strategy of hysteretic structures. Struct Eng Mech 38(1):39–63

    Article  Google Scholar 

  • Mathews JH, Fink KD (2003) Numerical methods using Matlab, 4th edn. Prentice-Hall

    Google Scholar 

  • Stengel RF, Ray LR, Marrison CI (1992) Probabilistic evaluation of control system robustness. In: IMA workshop on control systems design for advanced engineering systems: complexity, uncertainty, information and organization, Minneapolis, MN

    Google Scholar 

  • Sun JQ (2006) Stochastic Dynamics and Control. Elsevier, Amsterdam

    Book  Google Scholar 

  • Tsay SC, Fong IK, Kuo TS (1991) Robust linear quadratic optimal–control for systems with linear uncertainties. Int J Control 53(1):81–96

    Article  MathSciNet  MATH  Google Scholar 

  • Yang JN, Li Z, Liu SC (1992a) Stable controllers for instantaneous optimal control. ASCE J Eng Mech 118(8):1612–1630

    Article  Google Scholar 

  • Yang JN, Li Z, Liu SC (1992b) Control of hysteretic system using velocity and acceleration feedbacks. ASCE J Eng Mech 118(11):2227–2245

    Article  Google Scholar 

  • Zhang WS, Xu YL (2001) Closed form solution for along-wind response of actively controlled tall buildings with LQG controllers. J Wind Eng Ind Aerodyn 89:785–807

    Article  Google Scholar 

  • Zhu WQ, Ying ZG, Soong TT (2001) An optimal nonlinear feedback control strategy for randomly excited structural systems. Nonlinear Dyn 24:31–51

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Yongbo Peng .

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Peng, Y., Li, J. (2019). Probabilistic Criteria of Stochastic Optimal Control. In: Stochastic Optimal Control of Structures. Springer, Singapore. https://doi.org/10.1007/978-981-13-6764-9_4

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  • DOI: https://doi.org/10.1007/978-981-13-6764-9_4

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-6763-2

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