-
Previous Article
Dynamic programming using radial basis functions
- DCDS Home
- This Issue
-
Next Article
Robustness of performance and stability for multistep and updated multistep MPC schemes
Stratified discontinuous differential equations and sufficient conditions for robustness
1. | Project Commands INRIA Saclay & ENSTA ParisTech, 828, Boulevard des Maréchaux, 91762 Palaiseau, France |
References:
[1] |
J.-P. Aubin and A. Cellina, Differential Inclusions: Set-Valued Maps and Viability Theory,, Springer-Verlag New York, (1984).
doi: 10.1007/978-3-642-69512-4. |
[2] |
R. C. Barnard and P. R. Wolenski, Flow invariance on stratified domains,, Set-Valued and Variational Analysis, 21 (2013), 377.
doi: 10.1007/s11228-013-0230-y. |
[3] |
U. Boscain and B. Piccoli, Optimal Syntheses for Control Systems on 2-D Manifolds, vol. 43,, Springer, (2004).
|
[4] |
A. Bressan and Y. Hong, Optimal control problems on stratified domains,, Network and Heterogeneous Media, 2 (2007), 313.
doi: 10.3934/nhm.2007.2.313. |
[5] |
P. Brunovskỳ, The closed-loop time-optimal control. I: Optimality,, SIAM Journal on Control, 12 (1974), 624.
doi: 10.1137/0312046. |
[6] |
P. Brunovskỳ, The closed-loop time optimal control. II: Stability,, SIAM Journal on Control and Optimization, 14 (1976), 156.
doi: 10.1137/0314013. |
[7] |
P. Brunovskỳ, Every normal linear system has a regular time-optimal synthesis,, Mathematica Slovaca, 28 (1978), 81.
|
[8] |
P. Brunovskỳ, Regular synthesis for the linear-quadratic optimal control problem with linear control constraints,, J. Differential Equations, 38 (1980), 344.
doi: 10.1016/0022-0396(80)90012-1. |
[9] |
F. Clarke, Discontinuous feedback and nonlinear systems,, in 8th IFAC Symposium on Nonlinear Control Systems, (2010), 1. Google Scholar |
[10] |
F. Clarke, Y. Ledyaev, R. Stern and P. Wolenski, Nonsmooth Analysis and Control Theory, vol. 178,, Springer, (1998).
|
[11] |
A. F. Filippov and F. M. Arscott, Differential Equations with Discontinuous Righthand Sides: Control Systems, vol. 18,, Springer, (1988).
doi: 10.1007/978-94-015-7793-9. |
[12] |
O. Hájek, Terminal manifolds and switching locus,, Mathematical systems theory, 6 (1972), 289.
doi: 10.1007/BF01740720. |
[13] |
O. Hájek, Discontinuous differential equations, I,, J. Differential Equations, 32 (1979), 149.
doi: 10.1016/0022-0396(79)90056-1. |
[14] |
O. Hájek, Discontinuous differential equations, II,, J. Differential Equations, 32 (1979), 171. Google Scholar |
[15] |
C. Hermosilla and H. Zidani, Infinite horizon problem on stratifiable state-constraints set,, J. Differential Equations, 258 (2015), 1430.
doi: 10.1016/j.jde.2014.11.001. |
[16] |
S. Honkapohja and T. Ito, Stability with regime switching,, Journal of Economic Theory, 29 (1983), 22.
doi: 10.1016/0022-0531(83)90121-7. |
[17] |
M. R. Jeffrey and A. Colombo, The two-fold singularity of discontinuous vector fields,, SIAM Journal on Applied Dynamical Systems, 8 (2009), 624.
doi: 10.1137/08073113X. |
[18] |
V. Y. Kaloshin, A geometric proof of the existence of whitney stratifications,, Mosc. Math. J, 5 (2005), 125.
|
[19] |
A. Marigo and B. Piccoli, Regular syntheses and solutions to discontinuous odes,, ESAIM: Control, 7 (2002), 291.
doi: 10.1051/cocv:2002013. |
[20] |
J. Mather, Notes on topological stability,, Bull. Amer. Math. Soc., 49 (2012), 475.
doi: 10.1090/S0273-0979-2012-01383-6. |
[21] |
L. D. Meeker, Local time-optimal feedback control of strictly normal two-input linear systems,, SIAM journal on control and optimization, 27 (1989), 53.
doi: 10.1137/0327005. |
[22] |
Z. Rao and H. Zidani, Hamilton-jacobi-bellman equations on multi-domains,, in Control and Optimization with PDE Constraints, 164 (2013), 93.
doi: 10.1007/978-3-0348-0631-2_6. |
[23] |
E. D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, vol. 6,, Springer, (1998).
doi: 10.1007/978-1-4612-0577-7. |
[24] |
H. Sussmann, Regular synthesis for time-optimal control of single-input real analytic systems in the plane,, SIAM journal on control and optimization, 25 (1987), 1145.
doi: 10.1137/0325062. |
[25] |
M. A. Teixeira, Stability conditions for discontinuous vector fields,, J. Differential Equations, 88 (1990), 15.
doi: 10.1016/0022-0396(90)90106-Y. |
[26] |
L. Van den Dries and C. Miller, Geometric categories and o-minimal structures,, Duke Mathematical Journal, 84 (1996), 497.
doi: 10.1215/S0012-7094-96-08416-1. |
show all references
References:
[1] |
J.-P. Aubin and A. Cellina, Differential Inclusions: Set-Valued Maps and Viability Theory,, Springer-Verlag New York, (1984).
doi: 10.1007/978-3-642-69512-4. |
[2] |
R. C. Barnard and P. R. Wolenski, Flow invariance on stratified domains,, Set-Valued and Variational Analysis, 21 (2013), 377.
doi: 10.1007/s11228-013-0230-y. |
[3] |
U. Boscain and B. Piccoli, Optimal Syntheses for Control Systems on 2-D Manifolds, vol. 43,, Springer, (2004).
|
[4] |
A. Bressan and Y. Hong, Optimal control problems on stratified domains,, Network and Heterogeneous Media, 2 (2007), 313.
doi: 10.3934/nhm.2007.2.313. |
[5] |
P. Brunovskỳ, The closed-loop time-optimal control. I: Optimality,, SIAM Journal on Control, 12 (1974), 624.
doi: 10.1137/0312046. |
[6] |
P. Brunovskỳ, The closed-loop time optimal control. II: Stability,, SIAM Journal on Control and Optimization, 14 (1976), 156.
doi: 10.1137/0314013. |
[7] |
P. Brunovskỳ, Every normal linear system has a regular time-optimal synthesis,, Mathematica Slovaca, 28 (1978), 81.
|
[8] |
P. Brunovskỳ, Regular synthesis for the linear-quadratic optimal control problem with linear control constraints,, J. Differential Equations, 38 (1980), 344.
doi: 10.1016/0022-0396(80)90012-1. |
[9] |
F. Clarke, Discontinuous feedback and nonlinear systems,, in 8th IFAC Symposium on Nonlinear Control Systems, (2010), 1. Google Scholar |
[10] |
F. Clarke, Y. Ledyaev, R. Stern and P. Wolenski, Nonsmooth Analysis and Control Theory, vol. 178,, Springer, (1998).
|
[11] |
A. F. Filippov and F. M. Arscott, Differential Equations with Discontinuous Righthand Sides: Control Systems, vol. 18,, Springer, (1988).
doi: 10.1007/978-94-015-7793-9. |
[12] |
O. Hájek, Terminal manifolds and switching locus,, Mathematical systems theory, 6 (1972), 289.
doi: 10.1007/BF01740720. |
[13] |
O. Hájek, Discontinuous differential equations, I,, J. Differential Equations, 32 (1979), 149.
doi: 10.1016/0022-0396(79)90056-1. |
[14] |
O. Hájek, Discontinuous differential equations, II,, J. Differential Equations, 32 (1979), 171. Google Scholar |
[15] |
C. Hermosilla and H. Zidani, Infinite horizon problem on stratifiable state-constraints set,, J. Differential Equations, 258 (2015), 1430.
doi: 10.1016/j.jde.2014.11.001. |
[16] |
S. Honkapohja and T. Ito, Stability with regime switching,, Journal of Economic Theory, 29 (1983), 22.
doi: 10.1016/0022-0531(83)90121-7. |
[17] |
M. R. Jeffrey and A. Colombo, The two-fold singularity of discontinuous vector fields,, SIAM Journal on Applied Dynamical Systems, 8 (2009), 624.
doi: 10.1137/08073113X. |
[18] |
V. Y. Kaloshin, A geometric proof of the existence of whitney stratifications,, Mosc. Math. J, 5 (2005), 125.
|
[19] |
A. Marigo and B. Piccoli, Regular syntheses and solutions to discontinuous odes,, ESAIM: Control, 7 (2002), 291.
doi: 10.1051/cocv:2002013. |
[20] |
J. Mather, Notes on topological stability,, Bull. Amer. Math. Soc., 49 (2012), 475.
doi: 10.1090/S0273-0979-2012-01383-6. |
[21] |
L. D. Meeker, Local time-optimal feedback control of strictly normal two-input linear systems,, SIAM journal on control and optimization, 27 (1989), 53.
doi: 10.1137/0327005. |
[22] |
Z. Rao and H. Zidani, Hamilton-jacobi-bellman equations on multi-domains,, in Control and Optimization with PDE Constraints, 164 (2013), 93.
doi: 10.1007/978-3-0348-0631-2_6. |
[23] |
E. D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, vol. 6,, Springer, (1998).
doi: 10.1007/978-1-4612-0577-7. |
[24] |
H. Sussmann, Regular synthesis for time-optimal control of single-input real analytic systems in the plane,, SIAM journal on control and optimization, 25 (1987), 1145.
doi: 10.1137/0325062. |
[25] |
M. A. Teixeira, Stability conditions for discontinuous vector fields,, J. Differential Equations, 88 (1990), 15.
doi: 10.1016/0022-0396(90)90106-Y. |
[26] |
L. Van den Dries and C. Miller, Geometric categories and o-minimal structures,, Duke Mathematical Journal, 84 (1996), 497.
doi: 10.1215/S0012-7094-96-08416-1. |
[1] |
Haiyan Wang. Existence and nonexistence of positive radial solutions for quasilinear systems. Conference Publications, 2009, 2009 (Special) : 810-817. doi: 10.3934/proc.2009.2009.810 |
[2] |
Graziano Crasta, Philippe G. LeFloch. Existence result for a class of nonconservative and nonstrictly hyperbolic systems. Communications on Pure & Applied Analysis, 2002, 1 (4) : 513-530. doi: 10.3934/cpaa.2002.1.513 |
[3] |
Shu-Yu Hsu. Existence and properties of ancient solutions of the Yamabe flow. Discrete & Continuous Dynamical Systems - A, 2018, 38 (1) : 91-129. doi: 10.3934/dcds.2018005 |
[4] |
Lucas C. F. Ferreira, Jhean E. Pérez-López, Élder J. Villamizar-Roa. On the product in Besov-Lorentz-Morrey spaces and existence of solutions for the stationary Boussinesq equations. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2423-2439. doi: 10.3934/cpaa.2018115 |
[5] |
Yves Dumont, Frederic Chiroleu. Vector control for the Chikungunya disease. Mathematical Biosciences & Engineering, 2010, 7 (2) : 313-345. doi: 10.3934/mbe.2010.7.313 |
[6] |
Wei-Jian Bo, Guo Lin, Shigui Ruan. Traveling wave solutions for time periodic reaction-diffusion systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4329-4351. doi: 10.3934/dcds.2018189 |
[7] |
Jean-François Biasse. Improvements in the computation of ideal class groups of imaginary quadratic number fields. Advances in Mathematics of Communications, 2010, 4 (2) : 141-154. doi: 10.3934/amc.2010.4.141 |
[8] |
A. K. Misra, Anupama Sharma, Jia Li. A mathematical model for control of vector borne diseases through media campaigns. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1909-1927. doi: 10.3934/dcdsb.2013.18.1909 |
[9] |
Ardeshir Ahmadi, Hamed Davari-Ardakani. A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 359-377. doi: 10.3934/naco.2017023 |
[10] |
Murat Uzunca, Ayşe Sarıaydın-Filibelioǧlu. Adaptive discontinuous galerkin finite elements for advective Allen-Cahn equation. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 269-281. doi: 10.3934/naco.2020025 |
[11] |
Guirong Jiang, Qishao Lu. The dynamics of a Prey-Predator model with impulsive state feedback control. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1301-1320. doi: 10.3934/dcdsb.2006.6.1301 |
[12] |
Yunfei Lv, Rong Yuan, Yuan He. Wavefronts of a stage structured model with state--dependent delay. Discrete & Continuous Dynamical Systems - A, 2015, 35 (10) : 4931-4954. doi: 10.3934/dcds.2015.35.4931 |
[13] |
Daoyuan Fang, Ting Zhang. Compressible Navier-Stokes equations with vacuum state in one dimension. Communications on Pure & Applied Analysis, 2004, 3 (4) : 675-694. doi: 10.3934/cpaa.2004.3.675 |
[14] |
Chin-Chin Wu. Existence of traveling wavefront for discrete bistable competition model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 973-984. doi: 10.3934/dcdsb.2011.16.973 |
[15] |
Mohsen Abdolhosseinzadeh, Mir Mohammad Alipour. Design of experiment for tuning parameters of an ant colony optimization method for the constrained shortest Hamiltonian path problem in the grid networks. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 321-332. doi: 10.3934/naco.2020028 |
[16] |
Zengyun Wang, Jinde Cao, Zuowei Cai, Lihong Huang. Finite-time stability of impulsive differential inclusion: Applications to discontinuous impulsive neural networks. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2677-2692. doi: 10.3934/dcdsb.2020200 |
[17] |
Wenmin Gong, Guangcun Lu. On coupled Dirac systems. Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4329-4346. doi: 10.3934/dcds.2017185 |
[18] |
José Raúl Quintero, Juan Carlos Muñoz Grajales. On the existence and computation of periodic travelling waves for a 2D water wave model. Communications on Pure & Applied Analysis, 2018, 17 (2) : 557-578. doi: 10.3934/cpaa.2018030 |
[19] |
Tuvi Etzion, Alexander Vardy. On $q$-analogs of Steiner systems and covering designs. Advances in Mathematics of Communications, 2011, 5 (2) : 161-176. doi: 10.3934/amc.2011.5.161 |
[20] |
Alberto Bressan, Ke Han, Franco Rampazzo. On the control of non holonomic systems by active constraints. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3329-3353. doi: 10.3934/dcds.2013.33.3329 |
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]