-
Previous Article
A spectral PRP conjugate gradient methods for nonconvex optimization problem based on modified line search
- DCDS-B Home
- This Issue
-
Next Article
Determination of effective diffusion coefficients of drug delivery devices by a state observer approach
A class of nonlinear impulsive differential equation and optimal controls on time scales
1. | Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025 |
2. | Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025 |
References:
[1] |
M. U. Akhmet and M. Turan, The differential equations on time scales through impulsive differential equations,, Nonlinear Analysis, 65 (2006), 2043.
doi: 10.1016/j.na.2005.12.042. |
[2] |
M. Benchohra, J. Henderson and S. Ntouyas, "Impulsive Differential Equations and Inclusion,", Contemporary Mathematics and its Applications, 2 (2006).
|
[3] |
Rui A. C. Ferreira and Delfim F. M. Torres, Higher-order calculus of variations on time scales,, in, (2008), 149.
|
[4] |
P. Gajardo, H. Ramirez and A. Rapaport, Minimal time sequential Banach reactors with bounded and impulse controls for one or more species,, SIAM J. Control Optim., 47 (2008), 2827.
doi: 10.1137/070695204. |
[5] |
Y. Gong and X. Xiang, A class of optimal control problems of systems governed by the first order linear dynamic equations on time scales,, J. Industrial and Management Optimization, 5 (2009), 1.
|
[6] |
S. Hu and N. S. Papageorgiou, "Handbook of Multivalued Analysis. Vol. I. Theory," Mathematics and its Applications, 419,, Kluwer Academic Publishers, (1997).
|
[7] |
Roman Hilscher and Vera Zeidan, Weak maximum principle and accessory problem for control problems on time scales,, Nonlinear Analysis, 70 (2009), 3209.
doi: 10.1016/j.na.2008.04.025. |
[8] |
V. Lakshmikantham and S. Sivasundaram, B. Kaymakcalan, "Dynamical Systems on Measure Chains,'', Kluwer Acadamic Publishers, (1996). Google Scholar |
[9] |
G. Liu, X. Xiang and Y. Peng, Nonlinear integro-differential equation and optimal controls on time scales,, Computers and Mathematics with Applications, 61 (2011), 155.
doi: 10.1016/j.camwa.2010.10.013. |
[10] |
H. Liu and X. Xiang, A class of the first order impulsive dynamic equations on time scales,, Nonlinear Analysis, 69 (2008), 2803.
doi: 10.1016/j.na.2007.08.052. |
[11] |
Yajun Ma and Jitao Sun, Uniform eventual Lipschitz stability of impulsive systems on time scales,, Applied Mathematics and Computation, 211 (2009), 246.
doi: 10.1016/j.amc.2009.01.033. |
[12] |
Agnieszka B. Malinowska and Delfim F. M. Torres, Strong minimizers of the calculus of variations on time scales and the Weierstrass condition,, Proceedings of the Estonian Academy of Sciences, 58 (2009), 205.
doi: 10.3176/proc.2009.4.02. |
[13] |
Agnieszka B. Malinowska and Delfim F. M. Torres, Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales,, Applied Mathematics and Computation, 217 (2010), 1158.
doi: 10.1016/j.amc.2010.01.015. |
[14] |
Y. Peng and X. Xiang, Second order nonlinear impulsive time-variant systems with unbounded perturbation and optimal controls,, J. Industrial and Management Optimization, 4 (2008), 17.
|
[15] |
Y. Peng, X. Xiang, Y. Gong and G. Liu, Necessary conditions of optimality for a class of optimal control problems on time scales,, Computers and Mathematics with Applications, 58 (2009), 2035.
doi: 10.1016/j.camwa.2009.08.032. |
[16] |
Y. Peng, X. Xiang and Yang Jiang, Nonliear dynaminc systems and optimal control problems on time scales,, ESAIM Control, 17 (2011), 654.
doi: 10.1051/cocv/2010022. |
[17] |
E. Zeidler, "Nonlinear Functional Analysis and Its Applications III, Variational Methods and Optimization,", Springer-Verlag, (1985).
|
[18] |
Z. Zhan and W. Wei, On existence of optimal control governed by a class of the first-order linear dynamic systems on time scales,, Applied Mathematics and Computation, 215 (2009), 2070.
doi: 10.1016/j.amc.2009.08.009. |
[19] |
Z. Zhan and W. Wei, Necessary conditions for a class of optimal control problems on time scales,, Abstract and Applied Analysis, 2009 (9743).
|
show all references
References:
[1] |
M. U. Akhmet and M. Turan, The differential equations on time scales through impulsive differential equations,, Nonlinear Analysis, 65 (2006), 2043.
doi: 10.1016/j.na.2005.12.042. |
[2] |
M. Benchohra, J. Henderson and S. Ntouyas, "Impulsive Differential Equations and Inclusion,", Contemporary Mathematics and its Applications, 2 (2006).
|
[3] |
Rui A. C. Ferreira and Delfim F. M. Torres, Higher-order calculus of variations on time scales,, in, (2008), 149.
|
[4] |
P. Gajardo, H. Ramirez and A. Rapaport, Minimal time sequential Banach reactors with bounded and impulse controls for one or more species,, SIAM J. Control Optim., 47 (2008), 2827.
doi: 10.1137/070695204. |
[5] |
Y. Gong and X. Xiang, A class of optimal control problems of systems governed by the first order linear dynamic equations on time scales,, J. Industrial and Management Optimization, 5 (2009), 1.
|
[6] |
S. Hu and N. S. Papageorgiou, "Handbook of Multivalued Analysis. Vol. I. Theory," Mathematics and its Applications, 419,, Kluwer Academic Publishers, (1997).
|
[7] |
Roman Hilscher and Vera Zeidan, Weak maximum principle and accessory problem for control problems on time scales,, Nonlinear Analysis, 70 (2009), 3209.
doi: 10.1016/j.na.2008.04.025. |
[8] |
V. Lakshmikantham and S. Sivasundaram, B. Kaymakcalan, "Dynamical Systems on Measure Chains,'', Kluwer Acadamic Publishers, (1996). Google Scholar |
[9] |
G. Liu, X. Xiang and Y. Peng, Nonlinear integro-differential equation and optimal controls on time scales,, Computers and Mathematics with Applications, 61 (2011), 155.
doi: 10.1016/j.camwa.2010.10.013. |
[10] |
H. Liu and X. Xiang, A class of the first order impulsive dynamic equations on time scales,, Nonlinear Analysis, 69 (2008), 2803.
doi: 10.1016/j.na.2007.08.052. |
[11] |
Yajun Ma and Jitao Sun, Uniform eventual Lipschitz stability of impulsive systems on time scales,, Applied Mathematics and Computation, 211 (2009), 246.
doi: 10.1016/j.amc.2009.01.033. |
[12] |
Agnieszka B. Malinowska and Delfim F. M. Torres, Strong minimizers of the calculus of variations on time scales and the Weierstrass condition,, Proceedings of the Estonian Academy of Sciences, 58 (2009), 205.
doi: 10.3176/proc.2009.4.02. |
[13] |
Agnieszka B. Malinowska and Delfim F. M. Torres, Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales,, Applied Mathematics and Computation, 217 (2010), 1158.
doi: 10.1016/j.amc.2010.01.015. |
[14] |
Y. Peng and X. Xiang, Second order nonlinear impulsive time-variant systems with unbounded perturbation and optimal controls,, J. Industrial and Management Optimization, 4 (2008), 17.
|
[15] |
Y. Peng, X. Xiang, Y. Gong and G. Liu, Necessary conditions of optimality for a class of optimal control problems on time scales,, Computers and Mathematics with Applications, 58 (2009), 2035.
doi: 10.1016/j.camwa.2009.08.032. |
[16] |
Y. Peng, X. Xiang and Yang Jiang, Nonliear dynaminc systems and optimal control problems on time scales,, ESAIM Control, 17 (2011), 654.
doi: 10.1051/cocv/2010022. |
[17] |
E. Zeidler, "Nonlinear Functional Analysis and Its Applications III, Variational Methods and Optimization,", Springer-Verlag, (1985).
|
[18] |
Z. Zhan and W. Wei, On existence of optimal control governed by a class of the first-order linear dynamic systems on time scales,, Applied Mathematics and Computation, 215 (2009), 2070.
doi: 10.1016/j.amc.2009.08.009. |
[19] |
Z. Zhan and W. Wei, Necessary conditions for a class of optimal control problems on time scales,, Abstract and Applied Analysis, 2009 (9743).
|
[1] |
Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 183-197. doi: 10.3934/mbe.2011.8.183 |
[2] |
Shanjian Tang, Fu Zhang. Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5521-5553. doi: 10.3934/dcds.2015.35.5521 |
[3] |
Marita Holtmannspötter, Arnd Rösch, Boris Vexler. A priori error estimates for the space-time finite element discretization of an optimal control problem governed by a coupled linear PDE-ODE system. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021014 |
[4] |
Tobias Geiger, Daniel Wachsmuth, Gerd Wachsmuth. Optimal control of ODEs with state suprema. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021012 |
[5] |
Hong Seng Sim, Wah June Leong, Chuei Yee Chen, Siti Nur Iqmal Ibrahim. Multi-step spectral gradient methods with modified weak secant relation for large scale unconstrained optimization. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 377-387. doi: 10.3934/naco.2018024 |
[6] |
Diana Keller. Optimal control of a linear stochastic Schrödinger equation. Conference Publications, 2013, 2013 (special) : 437-446. doi: 10.3934/proc.2013.2013.437 |
[7] |
Lorenzo Freddi. Optimal control of the transmission rate in compartmental epidemics. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021007 |
[8] |
Zhiming Guo, Zhi-Chun Yang, Xingfu Zou. Existence and uniqueness of positive solution to a non-local differential equation with homogeneous Dirichlet boundary condition---A non-monotone case. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1825-1838. doi: 10.3934/cpaa.2012.11.1825 |
[9] |
Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399 |
[10] |
Xiaohong Li, Mingxin Sun, Zhaohua Gong, Enmin Feng. Multistage optimal control for microbial fed-batch fermentation process. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021040 |
[11] |
John T. Betts, Stephen Campbell, Claire Digirolamo. Examination of solving optimal control problems with delays using GPOPS-Ⅱ. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 283-305. doi: 10.3934/naco.2020026 |
[12] |
Livia Betz, Irwin Yousept. Optimal control of elliptic variational inequalities with bounded and unbounded operators. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021009 |
[13] |
Madalina Petcu, Roger Temam. The one dimensional shallow water equations with Dirichlet boundary conditions on the velocity. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 209-222. doi: 10.3934/dcdss.2011.4.209 |
[14] |
Boris Kramer, John R. Singler. A POD projection method for large-scale algebraic Riccati equations. Numerical Algebra, Control & Optimization, 2016, 6 (4) : 413-435. doi: 10.3934/naco.2016018 |
[15] |
Samir Adly, Oanh Chau, Mohamed Rochdi. Solvability of a class of thermal dynamical contact problems with subdifferential conditions. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 91-104. doi: 10.3934/naco.2012.2.91 |
[16] |
Elvise Berchio, Filippo Gazzola, Dario Pierotti. Nodal solutions to critical growth elliptic problems under Steklov boundary conditions. Communications on Pure & Applied Analysis, 2009, 8 (2) : 533-557. doi: 10.3934/cpaa.2009.8.533 |
[17] |
Valery Y. Glizer. Novel Conditions of Euclidean space controllability for singularly perturbed systems with input delay. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 307-320. doi: 10.3934/naco.2020027 |
[18] |
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 |
[19] |
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 |
[20] |
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 |
2019 Impact Factor: 1.27
Tools
Metrics
Other articles
by authors
[Back to Top]