Optimal control for linear discrete systems with respect to probabilistic criteria

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• 作者：V. M. Azanov (1)
  
• 刊名：Automation and Remote Control
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：75
• 期：10
• 页码：1743-1753
• 全文大小：180 KB
• 参考文献：1. Malyshev, V.V. and Kibzun, A.I., / Analiz i sintez vysokotochnogo upravleniya letatel鈥檔ymi apparatami (Analysis and Synthesis of High Accuracy Control for Flying Vehicles), Moscow: Mashinostroenie, 1987.
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  4. Krasovskii, N.N., On Optimal Control under Random Perturbations, / Prikl. Mat. Mekh., 1960, vol. 24, no. 1, pp. 64鈥?9.
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  6. Vishnaykov, V.B. and Kibzun, A.I., Deterministic Equivalents for the Problems of Stochastic Programming with Probabilistic Criteria, / Autom. Remote Control, 2006, vol. 67, no. 6, pp. 945鈥?61. CrossRef
  7. Kan, Yu.S. and Kibzun, A.I., / Zadachi stokhasticheskogo programmirovaniya s veroyatnostnymi kriteriyami (Stochastic Programming Problems with Probabilistic Criteria), Moscow: Fizmatlit, 2009.
  
• 作者单位：V. M. Azanov (1)
  
  1. Moscow Aviation Institute, Moscow, Russia
  
• ISSN：1608-3032

文摘

We consider the optimal control problem for a linear discrete stochastic system. The optimality criterion is the probability for the first coordinate of the system to fall into a given neighborhood of zero in time not exceeding a predefined value. The problem reduces to an equivalent stochastic optimal control problem with probabilistic terminal criterion. The latter can be solved analytically with dynamical programming. We give sufficient conditions for which the resulting optimal control turns out to be also optimal with respect to the quantile criterion.