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Control optimization in bilinear systems

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Abstract

We consider optimization problems for continuous systems linear with respect to state and control. Due to the specifics of such problems (degeneracy, turnpike character of solutions), we propose to use nonlocal Krotov’s iterative method together with the Gurman-Dykhta transformation into a regular derivative problem, which significantly improves the efficiency of this method. The proposed procedure is illustrated with an example.

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References

  1. Krotov, V.F., Control of the Quantum Systems and Some Ideas of the Optimal Control Theory, Autom. Remote Control, 2009, vol. 70, no. 3, pp. 357–365.

    Article  MathSciNet  MATH  Google Scholar 

  2. Krotov, V.F., Bulatov, A.V., and Baturina, O.V., Optimization of Linear Systems with Controllable Coefficients, Autom. Remote Control, 2011, vol. 72, no. 6, pp. 1199–1212.

    Article  MathSciNet  MATH  Google Scholar 

  3. Krotov, V.F. and Fel’dman, I.N., Iterative Method for Solving Optimal Control Problems, Tekh. Kibern., 1983, no. 2, pp. 160–168.

    Google Scholar 

  4. Krotov, V.F., Global Methods in Optimal Control Theory, New York: Marcel Dekker, 1996.

    MATH  Google Scholar 

  5. Gurman, V.I., Turnpike Solutions in Optimal Control Problems for Quantum-mechanical Systems, Autom. Remote Control, 2011, vol. 72, no. 6, pp. 1248–1257.

    Article  MathSciNet  MATH  Google Scholar 

  6. Gurman, V.I., Printsip rasshireniya v zadachakh upravleniya (The Extension Principle in Control Problems), Moscow: Nauka, 1985.

    MATH  Google Scholar 

  7. Gurman, V.I., Turnpike Solutions in the Procedures Seeking Optimal Controls, Autom. Remote Control, 2003, vol. 64, no. 3, pp. 399–408.

    Article  MathSciNet  MATH  Google Scholar 

  8. Gaishun, I.V., Vpolne razreshimye mnogomernye differentsial’nye uravneniya (Completely Resolvable Multidimensional Differential Equations), Minsk: Nauka i Tekhnika, 1983.

    Google Scholar 

  9. Abgaryan, K.A., Matrichnoe ischislenie s prilozheniyami v teorii dinamicheskikh sistem (Matrix Calculus with Applications to Dynamical Systems Theory), Moscow: Vuzovskaya Kniga, 2006.

    Google Scholar 

  10. Gurman, V.I. and Rasina, I.V., Discrete-continuous Representations of Impulsive Processes in the Controllable Systems, Autom. Remote Control, 2012, vol. 73, no. 8, pp. 1290–1300.

    Article  Google Scholar 

  11. Rasina, I.V., Iterative Optimization Algorithms for Discrete-Continuous Processes, Autom. Remote Control, 2012, vol. 73, no. 10, pp. 1591–1603.

    Article  Google Scholar 

  12. Rasina, I.V. and Baturina, O.V., Optimizing Discrete-Continuous Systems Linear with Respect to State, Autom. Remote Control, 2013, vol. 74, no. 4, pp. 604–612.

    Article  Google Scholar 

  13. Caneva, T., Murphy, M., Calarco, T., Fazio, R., et al., Optimal Control at the Quantum Speed Limit, Phys. Rev. Lett., 2009, vol. 103, no. 24, 240501, http://arxiv.org/abs/0902.4193v2.

    Article  Google Scholar 

  14. Gurman, V.I. and Blinov, A.O., Optimal Control Synthesis with a Quantum Mechanical System, Programmnye sistemy: teoriya i prilozheniya. Elektr. nauch. zhurn. IPS im. A.K. Ailamazyana RAN, 2011, no. 1, pp. 9–18, http//psta/priras/ru/read/psta2011_1_9-18/pdf.

    Google Scholar 

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Authors and Affiliations

  1. Siberian Academy of Law, Economics, and Management, Irkutsk, Russia

    I. V. Rasina

  2. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    O. V. Baturina

Authors
  1. I. V. Rasina
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  2. O. V. Baturina
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Original Russian Text © I.V. Rasina, O.V. Baturina, 2013, published in Avtomatika i Telemekhanika, 2013, No. 5, pp. 102–113.

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Rasina, I.V., Baturina, O.V. Control optimization in bilinear systems. Autom Remote Control 74, 802–810 (2013). https://doi.org/10.1134/S0005117913050056

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  • DOI: https://doi.org/10.1134/S0005117913050056

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