-
Previous Article
Unique global solution of an initial-boundary value problem to a diffusion approximation model in radiation hydrodynamics
- DCDS Home
- This Issue
-
Next Article
Fixed point indices of planar continuous maps
Steplength thresholds for invariance preserving of discretization methods of dynamical systems on a polyhedron
1. | Department of Mathematics and Computational Sciences, Széchenyi István University, 9026 Győr, Egyetem tér 1, Hungary |
2. | Department of Industrial and Systems Engineering, Lehigh University, 200 West Packer Avenue, Bethlehem, PA, 18015-1582, United States, United States |
References:
[1] |
D. Bertsimas and J. Tsitsiklis, Introduction to Linear Optimization, Athena Scientific, Nashua, 1998. |
[2] |
G. Bitsoris, On the positive invariance of polyhedral sets for discrete-time systems, System and Control Letters, 11 (1998), 243-248.
doi: 10.1016/0167-6911(88)90065-5. |
[3] |
F. Blanchini, Set invariance in control, Automatica, 35 (1999), 1747-1767.
doi: 10.1016/S0005-1098(99)00113-2. |
[4] |
F. Blanchini and S. Miani, Constrained stabilization of continuous-time linear systems, Systems and Control Letters, 28 (1996), 95-102.
doi: 10.1016/0167-6911(96)00013-8. |
[5] |
F. Blanchini, S. Miani, C. E. T. Dórea and J. C. Hennet, Discussion on: '(A, B)- invariance conditions of polyhedral domains for continuous-time systems by C. E. T. Dórea and J.-C. Hennet', European Journal of Control, 5 (1999), 82-86.
doi: 10.1016/S0947-3580(99)70142-1. |
[6] |
S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, Philadelphia, 1994.
doi: 10.1137/1.9781611970777. |
[7] |
E. B. Castelan and J. C. Hennet, On invariant polyhedra of continuous-time linear systems, IEEE Transactions on Automatic Control, 38 (1993), 1680-1685.
doi: 10.1109/9.262058. |
[8] |
C. E. T. Dórea and J. C. Hennet, (A, B)-invariance conditions of polyhedral domains for continuous-time systems, European Journal of Control, 5 (1999), 70-81. |
[9] |
C. E. T. Dórea and J. C. Hennet, (A,B)-invariant polyhedral sets of linear discrete time systems, Journal of Optimization Theory and Applications, 103 (1999), 521-542.
doi: 10.1023/A:1021727806358. |
[10] |
E. Hairer, S. P. Nørsett and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, Springer-Verlag, New York, 1993. |
[11] |
N. J. Higham, Functions of Matrices: Theory and Computation, Society for Industrial and Applied Mathematics, Philadelphia, 2008.
doi: 10.1137/1.9780898717778. |
[12] |
R. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1990. |
[13] |
Z. Horváth, Invariant cones and polyhedra for dynamical systems, in Proceeding of the International Conference in Memoriam Gyula Farkas, Cluj Univ. Press, Cluj-Napoca, 2006, 65-74. |
[14] |
Z. Horváth, On the positivity step size threshold of Runge-Kutta methods, Applied Numerical Mathematics, 53 (2005), 341-356.
doi: 10.1016/j.apnum.2004.08.026. |
[15] |
Z. Horváth, Y. Song and T. Terlaky, Invariance Preserving Discretization Methods of Dynamical Systems, Lehigh University, Department of Industrial and Systems Engineering, Technical Report 14T-009, 2014. |
[16] |
Z. Horváth, Y. Song and T. Terlaky, A Novel Unified Approach to Invariance in Control, Lehigh University, Department of Industrial and Systems Engineering, Technical Report 14T-003, 2014. |
[17] |
J. F. B. M. Kraaijevanger, Absolute monotonicity of polynomials occurring in the numerical solution of initial value problems, Numerische Mathematik, 48 (1986), 303-322.
doi: 10.1007/BF01389477. |
[18] |
R. Loewy and H. Schneider, Positive operators on the $n$-dimensional ice cream cone, Journal of Mathematical Analysis and Applications, 49 (1975), 375-392.
doi: 10.1016/0022-247X(75)90186-9. |
[19] |
C. Roos, T. Terlaky and J.-Ph. Vial, Interior Point Methods for Linear Optimization, Springer Science, Heidelberg, 2006. |
[20] |
M. N. Spijker, Contractivity in the numerical solution of initial value problems, Numerische Mathematik, 42 (1983), 271-290.
doi: 10.1007/BF01389573. |
[21] |
R. Stern and H. Wolkowicz, Exponential nonnegativity on the ice cream cone, SIAM Journal on Matrix Analysis and Applications, 12 (1991), 160-165.
doi: 10.1137/0612012. |
[22] |
B. Sturmfels, Solving Systems of Polynomial Equations, CBMS Lectures Series, American Mathematical Society, 2002. |
[23] |
J. Vandergraft, Spectral properties of matrices which have invariant cones, SIAM Journal on Applied Mathematics, 16 (1968), 1208-1222.
doi: 10.1137/0116101. |
show all references
References:
[1] |
D. Bertsimas and J. Tsitsiklis, Introduction to Linear Optimization, Athena Scientific, Nashua, 1998. |
[2] |
G. Bitsoris, On the positive invariance of polyhedral sets for discrete-time systems, System and Control Letters, 11 (1998), 243-248.
doi: 10.1016/0167-6911(88)90065-5. |
[3] |
F. Blanchini, Set invariance in control, Automatica, 35 (1999), 1747-1767.
doi: 10.1016/S0005-1098(99)00113-2. |
[4] |
F. Blanchini and S. Miani, Constrained stabilization of continuous-time linear systems, Systems and Control Letters, 28 (1996), 95-102.
doi: 10.1016/0167-6911(96)00013-8. |
[5] |
F. Blanchini, S. Miani, C. E. T. Dórea and J. C. Hennet, Discussion on: '(A, B)- invariance conditions of polyhedral domains for continuous-time systems by C. E. T. Dórea and J.-C. Hennet', European Journal of Control, 5 (1999), 82-86.
doi: 10.1016/S0947-3580(99)70142-1. |
[6] |
S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, Philadelphia, 1994.
doi: 10.1137/1.9781611970777. |
[7] |
E. B. Castelan and J. C. Hennet, On invariant polyhedra of continuous-time linear systems, IEEE Transactions on Automatic Control, 38 (1993), 1680-1685.
doi: 10.1109/9.262058. |
[8] |
C. E. T. Dórea and J. C. Hennet, (A, B)-invariance conditions of polyhedral domains for continuous-time systems, European Journal of Control, 5 (1999), 70-81. |
[9] |
C. E. T. Dórea and J. C. Hennet, (A,B)-invariant polyhedral sets of linear discrete time systems, Journal of Optimization Theory and Applications, 103 (1999), 521-542.
doi: 10.1023/A:1021727806358. |
[10] |
E. Hairer, S. P. Nørsett and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, Springer-Verlag, New York, 1993. |
[11] |
N. J. Higham, Functions of Matrices: Theory and Computation, Society for Industrial and Applied Mathematics, Philadelphia, 2008.
doi: 10.1137/1.9780898717778. |
[12] |
R. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1990. |
[13] |
Z. Horváth, Invariant cones and polyhedra for dynamical systems, in Proceeding of the International Conference in Memoriam Gyula Farkas, Cluj Univ. Press, Cluj-Napoca, 2006, 65-74. |
[14] |
Z. Horváth, On the positivity step size threshold of Runge-Kutta methods, Applied Numerical Mathematics, 53 (2005), 341-356.
doi: 10.1016/j.apnum.2004.08.026. |
[15] |
Z. Horváth, Y. Song and T. Terlaky, Invariance Preserving Discretization Methods of Dynamical Systems, Lehigh University, Department of Industrial and Systems Engineering, Technical Report 14T-009, 2014. |
[16] |
Z. Horváth, Y. Song and T. Terlaky, A Novel Unified Approach to Invariance in Control, Lehigh University, Department of Industrial and Systems Engineering, Technical Report 14T-003, 2014. |
[17] |
J. F. B. M. Kraaijevanger, Absolute monotonicity of polynomials occurring in the numerical solution of initial value problems, Numerische Mathematik, 48 (1986), 303-322.
doi: 10.1007/BF01389477. |
[18] |
R. Loewy and H. Schneider, Positive operators on the $n$-dimensional ice cream cone, Journal of Mathematical Analysis and Applications, 49 (1975), 375-392.
doi: 10.1016/0022-247X(75)90186-9. |
[19] |
C. Roos, T. Terlaky and J.-Ph. Vial, Interior Point Methods for Linear Optimization, Springer Science, Heidelberg, 2006. |
[20] |
M. N. Spijker, Contractivity in the numerical solution of initial value problems, Numerische Mathematik, 42 (1983), 271-290.
doi: 10.1007/BF01389573. |
[21] |
R. Stern and H. Wolkowicz, Exponential nonnegativity on the ice cream cone, SIAM Journal on Matrix Analysis and Applications, 12 (1991), 160-165.
doi: 10.1137/0612012. |
[22] |
B. Sturmfels, Solving Systems of Polynomial Equations, CBMS Lectures Series, American Mathematical Society, 2002. |
[23] |
J. Vandergraft, Spectral properties of matrices which have invariant cones, SIAM Journal on Applied Mathematics, 16 (1968), 1208-1222.
doi: 10.1137/0116101. |
[1] |
Michal Fečkan, Michal Pospíšil. Discretization of dynamical systems with first integrals. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3543-3554. doi: 10.3934/dcds.2013.33.3543 |
[2] |
Fanni M. Sélley. A self-consistent dynamical system with multiple absolutely continuous invariant measures. Journal of Computational Dynamics, 2021, 8 (1) : 9-32. doi: 10.3934/jcd.2021002 |
[3] |
Rui Kuang, Xiangdong Ye. The return times set and mixing for measure preserving transformations. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 817-827. doi: 10.3934/dcds.2007.18.817 |
[4] |
Mikhail B. Sevryuk. Invariant tori in quasi-periodic non-autonomous dynamical systems via Herman's method. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 569-595. doi: 10.3934/dcds.2007.18.569 |
[5] |
Zeng-Zhen Tan, Rong Hu, Ming Zhu, Ya-Ping Fang. A dynamical system method for solving the split convex feasibility problem. Journal of Industrial and Management Optimization, 2021, 17 (6) : 2989-3011. doi: 10.3934/jimo.2020104 |
[6] |
Matti Lassas, Eero Saksman, Samuli Siltanen. Discretization-invariant Bayesian inversion and Besov space priors. Inverse Problems and Imaging, 2009, 3 (1) : 87-122. doi: 10.3934/ipi.2009.3.87 |
[7] |
Sho Matsumoto, Jonathan Novak. A moment method for invariant ensembles. Electronic Research Announcements, 2018, 25: 60-71. doi: 10.3934/era.2018.25.007 |
[8] |
Michihiro Hirayama. Periodic probability measures are dense in the set of invariant measures. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 1185-1192. doi: 10.3934/dcds.2003.9.1185 |
[9] |
Ji Li, Kening Lu, Peter W. Bates. Invariant foliations for random dynamical systems. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3639-3666. doi: 10.3934/dcds.2014.34.3639 |
[10] |
Luca Dieci, Timo Eirola, Cinzia Elia. Periodic orbits of planar discontinuous system under discretization. Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : 2743-2762. doi: 10.3934/dcdsb.2018103 |
[11] |
Luis C. García-Naranjo, Mats Vermeeren. Structure preserving discretization of time-reparametrized Hamiltonian systems with application to nonholonomic mechanics. Journal of Computational Dynamics, 2021, 8 (3) : 241-271. doi: 10.3934/jcd.2021011 |
[12] |
Rafael de la Llave, Jason D. Mireles James. Parameterization of invariant manifolds by reducibility for volume preserving and symplectic maps. Discrete and Continuous Dynamical Systems, 2012, 32 (12) : 4321-4360. doi: 10.3934/dcds.2012.32.4321 |
[13] |
Burcu Özçam, Hao Cheng. A discretization based smoothing method for solving semi-infinite variational inequalities. Journal of Industrial and Management Optimization, 2005, 1 (2) : 219-233. doi: 10.3934/jimo.2005.1.219 |
[14] |
Chui-Jie Wu, Hongliang Zhao. Generalized HWD-POD method and coupling low-dimensional dynamical system of turbulence. Conference Publications, 2001, 2001 (Special) : 371-379. doi: 10.3934/proc.2001.2001.371 |
[15] |
Ivan Werner. Equilibrium states and invariant measures for random dynamical systems. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 1285-1326. doi: 10.3934/dcds.2015.35.1285 |
[16] |
Toshiko Ogiwara, Danielle Hilhorst, Hiroshi Matano. Convergence and structure theorems for order-preserving dynamical systems with mass conservation. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3883-3907. doi: 10.3934/dcds.2020129 |
[17] |
Nasab Yassine. Quantitative recurrence of some dynamical systems preserving an infinite measure in dimension one. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 343-361. doi: 10.3934/dcds.2018017 |
[18] |
Nils Ackermann, Thomas Bartsch, Petr Kaplický. An invariant set generated by the domain topology for parabolic semiflows with small diffusion. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 613-626. doi: 10.3934/dcds.2007.18.613 |
[19] |
Yaofeng Su. Almost surely invariance principle for non-stationary and random intermittent dynamical systems. Discrete and Continuous Dynamical Systems, 2019, 39 (11) : 6585-6597. doi: 10.3934/dcds.2019286 |
[20] |
Tan Bui-Thanh, Quoc P. Nguyen. FEM-based discretization-invariant MCMC methods for PDE-constrained Bayesian inverse problems. Inverse Problems and Imaging, 2016, 10 (4) : 943-975. doi: 10.3934/ipi.2016028 |
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]