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On one problem of optimal control at the impact phase and unification of the interaction end instants

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Abstract

Consideration was given to the problem of optimal control of a mechanical system at the impact phase and the influence of different instants of phase end on the performance criterion.

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References

  1. Kozlov, V.V. and Treshchev, D.V. Billiardy (Geneticheskoe vvedenie v dinamiku sistem s udarami) (Billiards (A Genetic Introduction to the Dynamics of Systems with Impacts)), Moscow: Mosk. Gos. Univ., 1991.

    MATH  Google Scholar 

  2. Ivanov, A.P., Dinamika sistem s mekhanicheskimi soudareniyami (Dynamics of Systems with Mechanical Collisions), Moscow: Intern. Education Program, 1997.

    Google Scholar 

  3. Miller, B.M. and Rubinovich, E.Ya., Optimizatsiya dinamicheskikh sistem s impul’snymi upravleniyami (Optimization of the Dynamic Systems with Pulse Controls), Moscow: Nauka, 2005.

    Google Scholar 

  4. Bentsman, J. and Miller, B.M., Dynamical Systems with Active Singularities of Elastic Type: A Modeling and Controller Synthesis Framework, IEEE Trans. Automat. Control, 2007, vol. 52, no. 1, pp. 39–55.

    Article  MathSciNet  Google Scholar 

  5. Miller, B.M. and Bentsman, J., Optimal Control Problems in Hybrid Systems with Active Singularities, Nonlinear Anal., 2006, vol. 65, pp. 999–1017.

    Article  MATH  MathSciNet  Google Scholar 

  6. Miller, B.M. and Bentsman, J., Generalized Solutions in Systems with Active Unilateral Constraints, Nonlinear Anal.: Hybrid Syst., 2007, vol. 1, pp. 510–526.

    Article  MATH  MathSciNet  Google Scholar 

  7. Bentsman, J., Miller, B., Rubinovich, E.Ya., et al., Optimal Control of Dynamical Systems with Active Singularities Under Single- and Multi-Impact Sequences: A Ball/Racket Systems Example, in Proc. Joint 48th IEEE Conf. Decision and Control and 28th Chinese Control Conf., Shanghai, December 16–18, 2009, pp. 5033–5038.

  8. Galyaev, A.A., Optimal Pulse Control of Dynamic Systems in the Shock Phase, Autom. Remote Control, 2006, no. 1, pp. 65–77.

  9. Galyaev, A.A., Miller, B.M., and Rubinovich, E.Ya., Optimal Impulsive Control of Dynamical System in an Impact Phase, in Lecture Notes Appl. Comput. Mechanics, 2006. vol. 27, pp. 385–386.

    Article  Google Scholar 

  10. Bentsman, J., Galyaev, A.A., Miller, B.M., and Rubinovich, E.Ya., On Control of Dynamical Systems in a Singular Motion Phase, in Abstr. Int. Symp. on Generalized Solutions in the Control Problems, GSCP-06, Ulan-Ude, July 5–7, 2006.

  11. Bentsman, J., Miller, B., and Rubinovich, E.Ya., Dynamical Systems with Active Singularities: Input/State/Output Modeling and Control, Automatica, July 2008, pp. 1741–1752.

  12. Miller, B. and Bentsman, J., The Singularity Opening Approach to Control of Mechanical Systems with Constraints, in Proc. 2nd IFAC Workshop Lagrangian and Hamilton. Methods for Nonlinear Control. LHMNLC’03, Seville, April 3–5, 2003.

  13. Arutyunov, A.V., Magaril-Il’yaev, G.G., and Tikhomirov, V.M., Printsip maksimuma Pontryagina: dokazatel’stvo i prilozheniya (Pontryagin Principle of Maximum: Proof and Applications), Moscow: Faktorial, 2006.

    Google Scholar 

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Authors and Affiliations

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

    A. A. Galyaev

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  1. A. A. Galyaev
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Original Russian Text © A.A. Galyaev, 2010, published in Avtomatika i Telemekhanika, 2010, No. 12, pp. 11–24.

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Galyaev, A.A. On one problem of optimal control at the impact phase and unification of the interaction end instants. Autom Remote Control 71, 2505–2517 (2010). https://doi.org/10.1134/S0005117910120027

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  • DOI: https://doi.org/10.1134/S0005117910120027

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