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Stochastic Maximum Principle

Encyclopedia of Systems and Control

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Abstract

The stochastic maximum principle (SMP) gives some necessary conditions for optimality for a stochastic optimal control problem. We give a summary of well-known results concerning stochastic maximum principle in finite-dimensional state space as well as some recent developments in infinite-dimensional state space.

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References

  • Bensoussan A (1983) Stochastic maximum principle for distributed parameter systems. J Frankl Inst 315(5–6):387–406

    Article  MATH  MathSciNet  Google Scholar 

  • Bismut JM (1976) Linear quadratic optimal stochastic control with random coefficients. SIAM J Control Optim 14(3):419–444

    Article  MATH  MathSciNet  Google Scholar 

  • Bismut JM (1978) An introductory approach to duality in optimal stochastic control. SIAM Rev 20(1):62–78

    Article  MATH  MathSciNet  Google Scholar 

  • Du K, Meng Q (2012) Stochastic maximum principle for infinite dimensional control systems. arXiv:1208.0529

    Google Scholar 

  • Du K, Meng Q (2013) A maximum principle for optimal control of stochastic evolution equations. SIAM J Control Option 51(4):4343–4362

    Article  MathSciNet  Google Scholar 

  • Fuhrman M, Hu Y, Tessitore G (2012) Stochastic maximum principle for optimal control of SPDEs. C R Math Acad Sci Paris 350(13–14):683–688

    Article  MATH  MathSciNet  Google Scholar 

  • Fuhrman M, Hu Y, Tessitore G (2013) Stochastic maximum principle for optimal control of SPDEs. Appl Math Optim 68(2):181–217

    Article  MATH  MathSciNet  Google Scholar 

  • Haussmann UG (1986) A stochastic maximum principle for optimal control of diffusions. Pitman research notes in mathematics series, vol 151. Longman Scientific & Technical, Harlow/Wiley, New York

    Google Scholar 

  • Hu Y, Peng S (1990) Maximum principle for semilinear stochastic evolution control systems. Stoch Stoch Rep 33(3–4):159–180

    Article  MATH  MathSciNet  Google Scholar 

  • Kushner HJ (1972) Necessary conditions for continuous parameter stochastic optimization problems. SIAM J Control 10:550–565

    Article  MATH  MathSciNet  Google Scholar 

  • Lü Q, Zhang X (2012) General Pontryagin-type stochastic maximum principle and backward stochastic evolution equations in infinite dimensions. arXiv:1204.3275

    Google Scholar 

  • Pardoux E, Peng S (1990) Adapted solution of a backward stochastic differential equation. Syst Control Lett 14(1):55–61

    Article  MATH  MathSciNet  Google Scholar 

  • Peng S (1990) A general stochastic maximum principle for optimal control problems. SIAM J Control Optim 28(4):966–979

    Article  MATH  MathSciNet  Google Scholar 

  • Tang S, Li X (1994) Maximum principle for optimal control of distributed parameter stochastic systems with random jumps. In: Markus L, Elworthy KD, Everitt WN, Lee EB (eds) Differential equations, dynamical systems, and control science. Lecture notes in pure and applied mathematics, vol 152. Dekker, New York, pp 867–890

    Google Scholar 

  • Yong J, Zhou XY (1999) Stochastic controls: Hamiltonian systems and HJB equations. Applications of mathematics, vol 43. Springer, New York

    Google Scholar 

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Authors and Affiliations

  1. IRMAR, Université Rennes 1, Rennes Cedex, France

    Ying Hu

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  1. Ying Hu
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Correspondence to Ying Hu .

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Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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© 2014 Springer-Verlag London

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Hu, Y. (2014). Stochastic Maximum Principle. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_229-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_229-1

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  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

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Chapter history

  1. Latest

    Stochastic Maximum Principle
    Published:
    06 November 2019

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_229-2

  2. Original

    Stochastic Maximum Principle
    Published:
    21 March 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_229-1