
Previous Article
Global existence and asymptotic behaviour of solutions for nonlinear evolution equations related to a tumour invasion model
 PROC Home
 This Issue

Next Article
Reduction of a kinetic model of active export of importins
On control synthesis for uncertain dynamical discretetime 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, no. 3 (2010), 319323 [Russian], Transl. as Dokl. Math., 82 (2010), 831834. 
[2] 
R. Baier and F. Lempio, Computing Aumann's integral, in Modeling Techniques for Uncertain Systems (Sopron, 1992), (eds. A. B. Kurzhanski and V. M. Veliov), Progr. Systems Control Theory, vol. 18, Birkhäser, Boston (1994), 7192. 
[3] 
N. S. Bakhvalov, N. P. Zhidkov and G. M. Kobel'kov, Numerical Methods, Nauka, Moscow, 1987 [Russian]. 
[4] 
B. R. Barmish and J. Sankaran, The propagation of parametric uncertainty via polytopes, IEEE Trans. Automat. Control., AC24 (1979), 346349. 
[5] 
F. L. Chernousko, State Estimation for Dynamic Systems, CRC Press, Boca Raton, 1994. 
[6] 
A. N. Daryin and A. B. Kurzhanski, Parallel algorithm for calculating the invariant sets of highdimensional linear systems under uncertainty, Zh. Vychisl. Mat. Mat. Fiz., 53, no.1 (2013), 4757 [Russian], Transl. as Comput. Math. Math. Phys., 53, no.1 (2013), 3443. 
[7] 
T. Filippova, Differential equations of ellipsoidal state estimates in nonlinear control problems under uncertainty, Discrete Contin. Dyn. Syst. 2011, Dynamical systems, differential equations and applications, 8th AIMS Conference, Suppl. vol. I (2011), 410419. 
[8] 
M. I. Gusev, External estimates of the reachability sets of nonlinear controlled systems, Avtomat. i Telemekh., no. 3 (2012), 3951 [Russian], Transl. as Autom. Remote Control, 73 (2012), 450461. 
[9] 
E. K. Kostousova, Control synthesis via parallelotopes: optimization and parallel computations, Optim. Methods Softw., 14 (2001), 267310. 
[10] 
E. K. Kostousova, Polyhedral estimates for attainability sets of linear multistage systems with integral constraints on the control, Computational Technologies, 8 (2003), 5574 [Russian; also available from: http://www.ict.nsc.ru/jct/search/article?l=eng]. 
[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, Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg, vol.9, (2006), 84105 [Russian]. 
[12] 
E. K. Kostousova, On polyhedral estimates for trajectory tubes of dynamical discretetime systems with multiplicative uncertainty, Discrete Contin. Dyn. Syst. 2011, Dynamical systems, differential equations and applications, 8th AIMS Conference, Suppl. vol. II (2011), 864873. 
[13] 
E. K. Kostousova, On tight polyhedral estimates for reachable sets of linear differential systems, AIP Conf. Proc., 1493 (2012), 579586; doi: http://dx.doi.org/10.1063/1.4765545. 
[14] 
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games, Nauka, Moscow, 1974 [Russian]. 
[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., no.1 (2010), 521 [Russian], Transl. as J. Automation and Inform. Sci., 42 (2010), 118. 
[16] 
A. B. Kurzhanskii and N. B. Mel'nikov, On the problem of the synthesis of controls: the Pontryagin alternative integral and the HamiltonJacobi equation, Mat. Sb. 191, no. 6 (2000), 69100 [Russian], Transl. as Sb. Math., 191 (2000), 849881. 
[17] 
A. B. Kurzhanski and O. I. Nikonov, On the problem of synthesizing control strategies. Evolution equations and setvalued integration, Dokl. Akad. Nauk SSSR, 311, no. 4 (1990), 788793 [Russian], Transl. as Soviet Math. Doklady, 41 (1990), 300305. 
[18] 
A. B. Kurzhanski and I. Vályi, Ellipsoidal Calculus for Estimation and Control, Birkhäuser, Boston, 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 NelderMead simplex method in low dimensions, SIAM Journal of Optimization, 9 (1998), 112147. 
[21] 
B. T. Polyak and P. S. Scherbakov, Robust Stability and Control, Nauka, Moscow, 2002 [Russian]. 
[22] 
R. G. Schneider, Convex Bodies: The BrunnMinkowski Theory, Cambridge Univ. Press, Cambridge, 1993. 
[23] 
A. M. Taras'yev, A. A. Uspenskiy and V. N. Ushakov, Approximation schemas and finitedifference operators for constructing generalized solutions of HamiltonJacobi equations, Izv. Ross. Akad. Nauk Tekhn. Kibernet., no. 3 (1994) 173185 [Russian], Transl. as J. Comput. Systems Sci. Internat., 33, no.6 (1995), 127139. 
[24] 
V. V. Vasin and I. I. Eremin, Operators and Iterative Processes of Fejér Type. Theory and Applications, Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg, 2005 [Russian]. 
[25] 
A. Yu. Vazhentsev, Internal ellipsoidal approximations for problems of the synthesis of a control with bounded coordinates, Izv. Akad. Nauk Teor. Sist. Upr., no.3 (2000), 7077 [Russian]. 
[26] 
V. M. Veliov, Second order discrete approximations to strongly convex differential inclusions, Systems Control Lett., 13, no.3 (1989), 263269. 
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, no. 3 (2010), 319323 [Russian], Transl. as Dokl. Math., 82 (2010), 831834. 
[2] 
R. Baier and F. Lempio, Computing Aumann's integral, in Modeling Techniques for Uncertain Systems (Sopron, 1992), (eds. A. B. Kurzhanski and V. M. Veliov), Progr. Systems Control Theory, vol. 18, Birkhäser, Boston (1994), 7192. 
[3] 
N. S. Bakhvalov, N. P. Zhidkov and G. M. Kobel'kov, Numerical Methods, Nauka, Moscow, 1987 [Russian]. 
[4] 
B. R. Barmish and J. Sankaran, The propagation of parametric uncertainty via polytopes, IEEE Trans. Automat. Control., AC24 (1979), 346349. 
[5] 
F. L. Chernousko, State Estimation for Dynamic Systems, CRC Press, Boca Raton, 1994. 
[6] 
A. N. Daryin and A. B. Kurzhanski, Parallel algorithm for calculating the invariant sets of highdimensional linear systems under uncertainty, Zh. Vychisl. Mat. Mat. Fiz., 53, no.1 (2013), 4757 [Russian], Transl. as Comput. Math. Math. Phys., 53, no.1 (2013), 3443. 
[7] 
T. Filippova, Differential equations of ellipsoidal state estimates in nonlinear control problems under uncertainty, Discrete Contin. Dyn. Syst. 2011, Dynamical systems, differential equations and applications, 8th AIMS Conference, Suppl. vol. I (2011), 410419. 
[8] 
M. I. Gusev, External estimates of the reachability sets of nonlinear controlled systems, Avtomat. i Telemekh., no. 3 (2012), 3951 [Russian], Transl. as Autom. Remote Control, 73 (2012), 450461. 
[9] 
E. K. Kostousova, Control synthesis via parallelotopes: optimization and parallel computations, Optim. Methods Softw., 14 (2001), 267310. 
[10] 
E. K. Kostousova, Polyhedral estimates for attainability sets of linear multistage systems with integral constraints on the control, Computational Technologies, 8 (2003), 5574 [Russian; also available from: http://www.ict.nsc.ru/jct/search/article?l=eng]. 
[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, Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg, vol.9, (2006), 84105 [Russian]. 
[12] 
E. K. Kostousova, On polyhedral estimates for trajectory tubes of dynamical discretetime systems with multiplicative uncertainty, Discrete Contin. Dyn. Syst. 2011, Dynamical systems, differential equations and applications, 8th AIMS Conference, Suppl. vol. II (2011), 864873. 
[13] 
E. K. Kostousova, On tight polyhedral estimates for reachable sets of linear differential systems, AIP Conf. Proc., 1493 (2012), 579586; doi: http://dx.doi.org/10.1063/1.4765545. 
[14] 
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games, Nauka, Moscow, 1974 [Russian]. 
[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., no.1 (2010), 521 [Russian], Transl. as J. Automation and Inform. Sci., 42 (2010), 118. 
[16] 
A. B. Kurzhanskii and N. B. Mel'nikov, On the problem of the synthesis of controls: the Pontryagin alternative integral and the HamiltonJacobi equation, Mat. Sb. 191, no. 6 (2000), 69100 [Russian], Transl. as Sb. Math., 191 (2000), 849881. 
[17] 
A. B. Kurzhanski and O. I. Nikonov, On the problem of synthesizing control strategies. Evolution equations and setvalued integration, Dokl. Akad. Nauk SSSR, 311, no. 4 (1990), 788793 [Russian], Transl. as Soviet Math. Doklady, 41 (1990), 300305. 
[18] 
A. B. Kurzhanski and I. Vályi, Ellipsoidal Calculus for Estimation and Control, Birkhäuser, Boston, 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 NelderMead simplex method in low dimensions, SIAM Journal of Optimization, 9 (1998), 112147. 
[21] 
B. T. Polyak and P. S. Scherbakov, Robust Stability and Control, Nauka, Moscow, 2002 [Russian]. 
[22] 
R. G. Schneider, Convex Bodies: The BrunnMinkowski Theory, Cambridge Univ. Press, Cambridge, 1993. 
[23] 
A. M. Taras'yev, A. A. Uspenskiy and V. N. Ushakov, Approximation schemas and finitedifference operators for constructing generalized solutions of HamiltonJacobi equations, Izv. Ross. Akad. Nauk Tekhn. Kibernet., no. 3 (1994) 173185 [Russian], Transl. as J. Comput. Systems Sci. Internat., 33, no.6 (1995), 127139. 
[24] 
V. V. Vasin and I. I. Eremin, Operators and Iterative Processes of Fejér Type. Theory and Applications, Ross. Akad. Nauk Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg, 2005 [Russian]. 
[25] 
A. Yu. Vazhentsev, Internal ellipsoidal approximations for problems of the synthesis of a control with bounded coordinates, Izv. Akad. Nauk Teor. Sist. Upr., no.3 (2000), 7077 [Russian]. 
[26] 
V. M. Veliov, Second order discrete approximations to strongly convex differential inclusions, Systems Control Lett., 13, no.3 (1989), 263269. 
[1] 
Elena K. Kostousova. On polyhedral control synthesis for dynamical discretetime systems under uncertainties and state constraints. Discrete and Continuous Dynamical Systems, 2018, 38 (12) : 61496162. doi: 10.3934/dcds.2018153 
[2] 
Elena K. Kostousova. On polyhedral estimates for trajectory tubes of dynamical discretetime systems with multiplicative uncertainty. Conference Publications, 2011, 2011 (Special) : 864873. doi: 10.3934/proc.2011.2011.864 
[3] 
Elena K. Kostousova. External polyhedral estimates of reachable sets of discretetime systems with integral bounds on additive terms. Mathematical Control and Related Fields, 2021, 11 (3) : 625641. doi: 10.3934/mcrf.2021015 
[4] 
Hongyan Yan, Yun Sun, Yuanguo Zhu. A linearquadratic control problem of uncertain discretetime switched systems. Journal of Industrial and Management Optimization, 2017, 13 (1) : 267282. doi: 10.3934/jimo.2016016 
[5] 
Yuefen Chen, Yuanguo Zhu. Indefinite LQ optimal control with process state inequality constraints for discretetime uncertain systems. Journal of Industrial and Management Optimization, 2018, 14 (3) : 913930. doi: 10.3934/jimo.2017082 
[6] 
Chuandong Li, Fali Ma, Tingwen Huang. 2D analysis based iterative learning control for linear discretetime systems with time delay. Journal of Industrial and Management Optimization, 2011, 7 (1) : 175181. doi: 10.3934/jimo.2011.7.175 
[7] 
Haijun Sun, Xinquan Zhang. Guaranteed cost control of discretetime switched saturated systems. Discrete and Continuous Dynamical Systems  B, 2021, 26 (8) : 45154522. doi: 10.3934/dcdsb.2020300 
[8] 
Xi Zhu, Meixia Li, Chunfa Li. Consensus in discretetime multiagent systems with uncertain topologies and random delays governed by a Markov chain. Discrete and Continuous Dynamical Systems  B, 2020, 25 (12) : 45354551. doi: 10.3934/dcdsb.2020111 
[9] 
Aleksandar Zatezalo, Dušan M. Stipanović. Control of dynamical systems with discrete and uncertain observations. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 46654681. doi: 10.3934/dcds.2015.35.4665 
[10] 
Ran Dong, Xuerong Mao. Asymptotic stabilization of continuoustime periodic stochastic systems by feedback control based on periodic discretetime observations. Mathematical Control and Related Fields, 2020, 10 (4) : 715734. doi: 10.3934/mcrf.2020017 
[11] 
Huan Su, Pengfei Wang, Xiaohua Ding. Stability analysis for discretetime coupled systems with multidiffusion by graphtheoretic approach and its application. Discrete and Continuous Dynamical Systems  B, 2016, 21 (1) : 253269. doi: 10.3934/dcdsb.2016.21.253 
[12] 
Tadeusz Kaczorek, Andrzej Ruszewski. Analysis of the fractional descriptor discretetime linear systems by the use of the shuffle algorithm. Journal of Computational Dynamics, 2021, 8 (2) : 153163. doi: 10.3934/jcd.2021007 
[13] 
Byungik Kahng, Miguel Mendes. The characterization of maximal invariant sets of nonlinear discretetime control dynamical systems. Conference Publications, 2013, 2013 (special) : 393406. doi: 10.3934/proc.2013.2013.393 
[14] 
Victor Kozyakin. Minimax joint spectral radius and stabilizability of discretetime linear switching control systems. Discrete and Continuous Dynamical Systems  B, 2019, 24 (8) : 35373556. doi: 10.3934/dcdsb.2018277 
[15] 
Yueyuan Zhang, Yanyan Yin, Fei Liu. Robust observerbased control for discretetime semiMarkov jump systems with actuator saturation. Journal of Industrial and Management Optimization, 2021, 17 (6) : 30133026. doi: 10.3934/jimo.2020105 
[16] 
Yadong Shu, Bo Li. Linearquadratic optimal control for discretetime stochastic descriptor systems. Journal of Industrial and Management Optimization, 2022, 18 (3) : 15831602. doi: 10.3934/jimo.2021034 
[17] 
Qiying Hu, Chen Xu, Wuyi Yue. A unified model for state feedback of discrete event systems II: Control synthesis problems. Journal of Industrial and Management Optimization, 2008, 4 (4) : 713726. doi: 10.3934/jimo.2008.4.713 
[18] 
Peter Giesl, Zachary Langhorne, Carlos Argáez, Sigurdur Hafstein. Computing complete Lyapunov functions for discretetime dynamical systems. Discrete and Continuous Dynamical Systems  B, 2021, 26 (1) : 299336. doi: 10.3934/dcdsb.2020331 
[19] 
Vladimir Răsvan. On the central stability zone for linear discretetime Hamiltonian systems. Conference Publications, 2003, 2003 (Special) : 734741. doi: 10.3934/proc.2003.2003.734 
[20] 
Sofian De Clercq, Koen De Turck, Bart Steyaert, Herwig Bruneel. Framebound priority scheduling in discretetime queueing systems. Journal of Industrial and Management Optimization, 2011, 7 (3) : 767788. doi: 10.3934/jimo.2011.7.767 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]