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On control synthesis for uncertain dynamical discrete-time systems through polyhedral techniques
1. | N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16, S.Kovalevskaja street, Ekaterinburg, 620990, Russian Federation |
References:
[1] |
I. M. Anan'evskii, N. V. Anokhin and A. I. Ovseevich, Synthesis of a bounded control for linear dynamical systems using the general Lyapunov function,, Dokl. Akad. Nauk, 434 (2010), 319.
|
[2] |
R. Baier and F. Lempio, Computing Aumann's integral,, in Modeling Techniques for Uncertain Systems (Sopron, 18 (1994), 71.
|
[3] |
N. S. Bakhvalov, N. P. Zhidkov and G. M. Kobel'kov, Numerical Methods,, Nauka, (1987).
|
[4] |
B. R. Barmish and J. Sankaran, The propagation of parametric uncertainty via polytopes,, IEEE Trans. Automat. Control., 24 (1979), 346.
|
[5] |
F. L. Chernousko, State Estimation for Dynamic Systems,, CRC Press, (1994). Google Scholar |
[6] |
A. N. Daryin and A. B. Kurzhanski, Parallel algorithm for calculating the invariant sets of high-dimensional linear systems under uncertainty,, Zh. Vychisl. Mat. Mat. Fiz., 53 (2013), 47.
|
[7] |
T. Filippova, Differential equations of ellipsoidal state estimates in nonlinear control problems under uncertainty,, Discrete Contin. Dyn. Syst. 2011, (2011), 410.
|
[8] |
M. I. Gusev, External estimates of the reachability sets of nonlinear controlled systems,, Avtomat. i Telemekh., 73 (2012), 39.
|
[9] |
E. K. Kostousova, Control synthesis via parallelotopes: optimization and parallel computations,, Optim. Methods Softw., 14 (2001), 267.
|
[10] |
E. K. Kostousova, Polyhedral estimates for attainability sets of linear multistage systems with integral constraints on the control,, Computational Technologies, 8 (2003), 55. Google Scholar |
[11] |
E. K. Kostousova, On polyhedral estimates in problems of the synthesis of control strategies in linear multistep systems,, Algorithms and Software for Parallel Computations, 9 (2006), 84.
|
[12] |
E. K. Kostousova, On polyhedral estimates for trajectory tubes of dynamical discrete-time systems with multiplicative uncertainty,, Discrete Contin. Dyn. Syst. 2011, II (2011), 864.
|
[13] |
E. K. Kostousova, On tight polyhedral estimates for reachable sets of linear differential systems,, AIP Conf. Proc., 1493 (2012), 579. Google Scholar |
[14] |
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games,, Nauka, (1974).
|
[15] |
V. M. Kuntsevich and A. B. Kurzhanski, Attainability domains for linear and some classes of nonlinear discrete systems and their control,, Problemy Upravlen. Inform., 42 (2010), 5.
|
[16] |
A. B. Kurzhanskii and N. B. Mel'nikov, On the problem of the synthesis of controls: the Pontryagin alternative integral and the Hamilton-Jacobi equation,, Mat. Sb. 191, 191 (2000), 69.
|
[17] |
A. B. Kurzhanski and O. I. Nikonov, On the problem of synthesizing control strategies. Evolution equations and set-valued integration,, Dokl. Akad. Nauk SSSR, 311 (1990), 788.
|
[18] |
A. B. Kurzhanski and I. Vályi, Ellipsoidal Calculus for Estimation and Control,, Birkhäuser, (1997).
|
[19] |
A. B. Kurzhanski and P. Varaiya, Dynamics and Control of Trajectory Tubes. Theory and Computation (Systems & Control: Foundations & Applications, Book 85),, Birkhäuser Basel, (2014).
|
[20] |
J. C. Lagarias, J. A. Reeds, M. H. Wright and P. E. Wright, Convergence properties of the Nelder-Mead simplex method in low dimensions,, SIAM Journal of Optimization, 9 (1998), 112.
|
[21] |
B. T. Polyak and P. S. Scherbakov, Robust Stability and Control,, Nauka, (2002). Google Scholar |
[22] |
R. G. Schneider, Convex Bodies: The Brunn-Minkowski Theory,, Cambridge Univ. Press, (1993).
|
[23] |
A. M. Taras'yev, A. A. Uspenskiy and V. N. Ushakov, Approximation schemas and finite-difference operators for constructing generalized solutions of Hamilton-Jacobi equations,, Izv. Ross. Akad. Nauk Tekhn. Kibernet., 33 (1994), 173.
|
[24] |
V. V. Vasin and I. I. Eremin, Operators and Iterative Processes of Fejér Type. Theory and Applications,, Ross. Akad. Nauk Ural. Otdel., (2005).
|
[25] |
A. Yu. Vazhentsev, Internal ellipsoidal approximations for problems of the synthesis of a control with bounded coordinates,, Izv. Akad. Nauk Teor. Sist. Upr., (2000), 70.
|
[26] |
V. M. Veliov, Second order discrete approximations to strongly convex differential inclusions,, Systems Control Lett., 13 (1989), 263.
|
show all references
References:
[1] |
I. M. Anan'evskii, N. V. Anokhin and A. I. Ovseevich, Synthesis of a bounded control for linear dynamical systems using the general Lyapunov function,, Dokl. Akad. Nauk, 434 (2010), 319.
|
[2] |
R. Baier and F. Lempio, Computing Aumann's integral,, in Modeling Techniques for Uncertain Systems (Sopron, 18 (1994), 71.
|
[3] |
N. S. Bakhvalov, N. P. Zhidkov and G. M. Kobel'kov, Numerical Methods,, Nauka, (1987).
|
[4] |
B. R. Barmish and J. Sankaran, The propagation of parametric uncertainty via polytopes,, IEEE Trans. Automat. Control., 24 (1979), 346.
|
[5] |
F. L. Chernousko, State Estimation for Dynamic Systems,, CRC Press, (1994). Google Scholar |
[6] |
A. N. Daryin and A. B. Kurzhanski, Parallel algorithm for calculating the invariant sets of high-dimensional linear systems under uncertainty,, Zh. Vychisl. Mat. Mat. Fiz., 53 (2013), 47.
|
[7] |
T. Filippova, Differential equations of ellipsoidal state estimates in nonlinear control problems under uncertainty,, Discrete Contin. Dyn. Syst. 2011, (2011), 410.
|
[8] |
M. I. Gusev, External estimates of the reachability sets of nonlinear controlled systems,, Avtomat. i Telemekh., 73 (2012), 39.
|
[9] |
E. K. Kostousova, Control synthesis via parallelotopes: optimization and parallel computations,, Optim. Methods Softw., 14 (2001), 267.
|
[10] |
E. K. Kostousova, Polyhedral estimates for attainability sets of linear multistage systems with integral constraints on the control,, Computational Technologies, 8 (2003), 55. Google Scholar |
[11] |
E. K. Kostousova, On polyhedral estimates in problems of the synthesis of control strategies in linear multistep systems,, Algorithms and Software for Parallel Computations, 9 (2006), 84.
|
[12] |
E. K. Kostousova, On polyhedral estimates for trajectory tubes of dynamical discrete-time systems with multiplicative uncertainty,, Discrete Contin. Dyn. Syst. 2011, II (2011), 864.
|
[13] |
E. K. Kostousova, On tight polyhedral estimates for reachable sets of linear differential systems,, AIP Conf. Proc., 1493 (2012), 579. Google Scholar |
[14] |
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games,, Nauka, (1974).
|
[15] |
V. M. Kuntsevich and A. B. Kurzhanski, Attainability domains for linear and some classes of nonlinear discrete systems and their control,, Problemy Upravlen. Inform., 42 (2010), 5.
|
[16] |
A. B. Kurzhanskii and N. B. Mel'nikov, On the problem of the synthesis of controls: the Pontryagin alternative integral and the Hamilton-Jacobi equation,, Mat. Sb. 191, 191 (2000), 69.
|
[17] |
A. B. Kurzhanski and O. I. Nikonov, On the problem of synthesizing control strategies. Evolution equations and set-valued integration,, Dokl. Akad. Nauk SSSR, 311 (1990), 788.
|
[18] |
A. B. Kurzhanski and I. Vályi, Ellipsoidal Calculus for Estimation and Control,, Birkhäuser, (1997).
|
[19] |
A. B. Kurzhanski and P. Varaiya, Dynamics and Control of Trajectory Tubes. Theory and Computation (Systems & Control: Foundations & Applications, Book 85),, Birkhäuser Basel, (2014).
|
[20] |
J. C. Lagarias, J. A. Reeds, M. H. Wright and P. E. Wright, Convergence properties of the Nelder-Mead simplex method in low dimensions,, SIAM Journal of Optimization, 9 (1998), 112.
|
[21] |
B. T. Polyak and P. S. Scherbakov, Robust Stability and Control,, Nauka, (2002). Google Scholar |
[22] |
R. G. Schneider, Convex Bodies: The Brunn-Minkowski Theory,, Cambridge Univ. Press, (1993).
|
[23] |
A. M. Taras'yev, A. A. Uspenskiy and V. N. Ushakov, Approximation schemas and finite-difference operators for constructing generalized solutions of Hamilton-Jacobi equations,, Izv. Ross. Akad. Nauk Tekhn. Kibernet., 33 (1994), 173.
|
[24] |
V. V. Vasin and I. I. Eremin, Operators and Iterative Processes of Fejér Type. Theory and Applications,, Ross. Akad. Nauk Ural. Otdel., (2005).
|
[25] |
A. Yu. Vazhentsev, Internal ellipsoidal approximations for problems of the synthesis of a control with bounded coordinates,, Izv. Akad. Nauk Teor. Sist. Upr., (2000), 70.
|
[26] |
V. M. Veliov, Second order discrete approximations to strongly convex differential inclusions,, Systems Control Lett., 13 (1989), 263.
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