
Previous Article
Error bounds for Euler approximation of linearquadratic control problems with bangbang solutions
 NACO Home
 This Issue

Next Article
Optimal control strategies for tuberculosis treatment: A case study in Angola
Control parameterization for optimal control problems with continuous inequality constraints: New convergence results
1.  Department of Mathematics and Statistics, Curtin University, GPO Box U1987 Perth, Western Australia 6845 
2.  Department of Mathematics and Statistics, Curtin University, GPO Box U1987, Perth, Western Australia 6845, Australia 
References:
[1] 
B. Açikmeşe and L. Blackmore, Lossless convexification of a class of optimal control problems with nonconvex control constraints,, Automatica, 47 (2011), 341. doi: 10.1016/j.automatica.2010.10.037. 
[2] 
N. U. Ahmed, "Dynamic Systems and Control with Applications,", World Scientific, (2006). doi: 10.1142/6262. 
[3] 
C. Büskens and H. Maurer, SQPmethods for solving optimal control problems with control and state constraints: Adjoint variables, sensitivity analysis and realtime control,, Journal of Computational and Applied Mathematics, 120 (2000), 85. doi: 10.1016/S03770427(00)003058. 
[4] 
M. Gerdts and M. Kunkel, A nonsmooth Newton's method for discretized optimal control problems with state and control constraints,, Journal of Industrial and Management Optimization, 4 (2008), 247. 
[5] 
C. J. Goh and K. L. Teo, Control parametrization: A unified approach to optimal control problems with general constraints,, Automatica, 24 (1988), 3. doi: 10.1016/00051098(88)900039. 
[6] 
L. S. Jennings and K. L. Teo, A computational algorithm for functional inequality constrained optimization problems,, Automatica, 26 (1990), 371. doi: 10.1016/00051098(90)90131Z. 
[7] 
A. N. Kolmogorov and S. V. Fomin, "Introductory Real Analysis,", Dover edition, (1975). 
[8] 
B. Li, C. J. Yu, K. L. Teo and G. R. Duan, An exact penalty function method for continuous inequality constrained optimal control problem,, Journal of Optimization Theory and Applications, 151 (2011), 260. doi: 10.1007/s1095701199045. 
[9] 
Q. Lin, R. Loxton, K. L. Teo and Y. H. Wu, A new computational method for a class of free terminal time optimal control problems,, Pacific Journal of Optimization, 7 (2011), 63. 
[10] 
R. Loxton, K. L. Teo and V. Rehbock, Optimal control problems with multiple characteristic time points in the objective and constraints,, Automatica, 44 (2008), 2923. doi: 10.1016/j.automatica.2008.04.011. 
[11] 
R. Loxton, K. L. Teo, V. Rehbock and W. K. Ling, Optimal switching instants for a switchedcapacitor DC/DC power converter,, Automatica, 45 (2009), 973. doi: 10.1016/j.automatica.2008.10.031. 
[12] 
R. Loxton, K. L. Teo, V. Rehbock and K. F. C. Yiu, Optimal control problems with a continuous inequality constraint on the state and the control,, Automatica, 45 (2009), 2250. doi: 10.1016/j.automatica.2009.05.029. 
[13] 
D. G. Luenberger and Y. Ye, "Linear and Nonlinear Programming,", 3rd edition, (2008). 
[14] 
J. Nocedal and S. J. Wright, "Numerical Optimization,", 2nd edition, (2006). 
[15] 
H. L. Royden and P. M. Fitzpatrick, "Real Analysis,", 4th edition, (2010). 
[16] 
W. Rudin, "Principles of Mathematical Analysis,", 3rd edition, (1976). 
[17] 
K. L. Teo, C. J. Goh and K. H. Wong, "A Unified Computational Approach to Optimal Control Problems,", Longman Scientific and Technical, (1991). 
[18] 
K. L. Teo and L. S. Jennings, Optimal control with a cost on changing control,, Journal of Optimization Theory and Applications, 68 (1991), 335. doi: 10.1007/BF00941572. 
[19] 
K. L. Teo, V. Rehbock and L. S. Jennings, A new computational algorithm for functional inequality constrained optimization problems,, Automatica, 29 (1993), 789. doi: 10.1016/00051098(93)900766. 
[20] 
L. Y. Wang, W. H. Gui, K. L. Teo, R. Loxton and C. H. Yang, Time delayed optimal control problems with multiple characteristic time points: Computation and industrial applications,, Journal of Industrial and Management Optimization, 5 (2009), 705. doi: 10.3934/jimo.2009.5.705. 
[21] 
C. Yu, K. L. Teo, L. Zhang and Y. Bai, A new exact penalty method for semiinfinite programming problems,, Journal of Industrial and Management Optimization, 6 (2010), 895. doi: 10.3934/jimo.2010.6.895. 
[22] 
Y. Zhao and M. A. Stadtherr, Rigorous global optimization method for dynamic systems subject to inequality path constraints,, Industrial and Engineering Chemistry Research, 50 (2011), 12678. doi: http://dx.doi.org/10.1021/ie200996f. 
show all references
References:
[1] 
B. Açikmeşe and L. Blackmore, Lossless convexification of a class of optimal control problems with nonconvex control constraints,, Automatica, 47 (2011), 341. doi: 10.1016/j.automatica.2010.10.037. 
[2] 
N. U. Ahmed, "Dynamic Systems and Control with Applications,", World Scientific, (2006). doi: 10.1142/6262. 
[3] 
C. Büskens and H. Maurer, SQPmethods for solving optimal control problems with control and state constraints: Adjoint variables, sensitivity analysis and realtime control,, Journal of Computational and Applied Mathematics, 120 (2000), 85. doi: 10.1016/S03770427(00)003058. 
[4] 
M. Gerdts and M. Kunkel, A nonsmooth Newton's method for discretized optimal control problems with state and control constraints,, Journal of Industrial and Management Optimization, 4 (2008), 247. 
[5] 
C. J. Goh and K. L. Teo, Control parametrization: A unified approach to optimal control problems with general constraints,, Automatica, 24 (1988), 3. doi: 10.1016/00051098(88)900039. 
[6] 
L. S. Jennings and K. L. Teo, A computational algorithm for functional inequality constrained optimization problems,, Automatica, 26 (1990), 371. doi: 10.1016/00051098(90)90131Z. 
[7] 
A. N. Kolmogorov and S. V. Fomin, "Introductory Real Analysis,", Dover edition, (1975). 
[8] 
B. Li, C. J. Yu, K. L. Teo and G. R. Duan, An exact penalty function method for continuous inequality constrained optimal control problem,, Journal of Optimization Theory and Applications, 151 (2011), 260. doi: 10.1007/s1095701199045. 
[9] 
Q. Lin, R. Loxton, K. L. Teo and Y. H. Wu, A new computational method for a class of free terminal time optimal control problems,, Pacific Journal of Optimization, 7 (2011), 63. 
[10] 
R. Loxton, K. L. Teo and V. Rehbock, Optimal control problems with multiple characteristic time points in the objective and constraints,, Automatica, 44 (2008), 2923. doi: 10.1016/j.automatica.2008.04.011. 
[11] 
R. Loxton, K. L. Teo, V. Rehbock and W. K. Ling, Optimal switching instants for a switchedcapacitor DC/DC power converter,, Automatica, 45 (2009), 973. doi: 10.1016/j.automatica.2008.10.031. 
[12] 
R. Loxton, K. L. Teo, V. Rehbock and K. F. C. Yiu, Optimal control problems with a continuous inequality constraint on the state and the control,, Automatica, 45 (2009), 2250. doi: 10.1016/j.automatica.2009.05.029. 
[13] 
D. G. Luenberger and Y. Ye, "Linear and Nonlinear Programming,", 3rd edition, (2008). 
[14] 
J. Nocedal and S. J. Wright, "Numerical Optimization,", 2nd edition, (2006). 
[15] 
H. L. Royden and P. M. Fitzpatrick, "Real Analysis,", 4th edition, (2010). 
[16] 
W. Rudin, "Principles of Mathematical Analysis,", 3rd edition, (1976). 
[17] 
K. L. Teo, C. J. Goh and K. H. Wong, "A Unified Computational Approach to Optimal Control Problems,", Longman Scientific and Technical, (1991). 
[18] 
K. L. Teo and L. S. Jennings, Optimal control with a cost on changing control,, Journal of Optimization Theory and Applications, 68 (1991), 335. doi: 10.1007/BF00941572. 
[19] 
K. L. Teo, V. Rehbock and L. S. Jennings, A new computational algorithm for functional inequality constrained optimization problems,, Automatica, 29 (1993), 789. doi: 10.1016/00051098(93)900766. 
[20] 
L. Y. Wang, W. H. Gui, K. L. Teo, R. Loxton and C. H. Yang, Time delayed optimal control problems with multiple characteristic time points: Computation and industrial applications,, Journal of Industrial and Management Optimization, 5 (2009), 705. doi: 10.3934/jimo.2009.5.705. 
[21] 
C. Yu, K. L. Teo, L. Zhang and Y. Bai, A new exact penalty method for semiinfinite programming problems,, Journal of Industrial and Management Optimization, 6 (2010), 895. doi: 10.3934/jimo.2010.6.895. 
[22] 
Y. Zhao and M. A. Stadtherr, Rigorous global optimization method for dynamic systems subject to inequality path constraints,, Industrial and Engineering Chemistry Research, 50 (2011), 12678. doi: http://dx.doi.org/10.1021/ie200996f. 
[1] 
Qun Lin, Ryan Loxton, Kok Lay Teo. The control parameterization method for nonlinear optimal control: A survey. Journal of Industrial & Management Optimization, 2014, 10 (1) : 275309. doi: 10.3934/jimo.2014.10.275 
[2] 
Yuefen Chen, Yuanguo Zhu. Indefinite LQ optimal control with process state inequality constraints for discretetime uncertain systems. Journal of Industrial & Management Optimization, 2018, 14 (3) : 913930. doi: 10.3934/jimo.2017082 
[3] 
Piermarco Cannarsa, Hélène Frankowska, Elsa M. Marchini. On Bolza optimal control problems with constraints. Discrete & Continuous Dynamical Systems  B, 2009, 11 (3) : 629653. doi: 10.3934/dcdsb.2009.11.629 
[4] 
IvÁn Area, FaÏÇal NdaÏrou, Juan J. Nieto, Cristiana J. Silva, Delfim F. M. Torres. Ebola model and optimal control with vaccination constraints. Journal of Industrial & Management Optimization, 2018, 14 (2) : 427446. doi: 10.3934/jimo.2017054 
[5] 
Claus Kirchner, Michael Herty, Simone Göttlich, Axel Klar. Optimal control for continuous supply network models. Networks & Heterogeneous Media, 2006, 1 (4) : 675688. doi: 10.3934/nhm.2006.1.675 
[6] 
Stanisław Migórski. A note on optimal control problem for a hemivariational inequality modeling fluid flow. Conference Publications, 2013, 2013 (special) : 545554. doi: 10.3934/proc.2013.2013.545 
[7] 
Martin Brokate, Pavel Krejčí. Optimal control of ODE systems involving a rate independent variational inequality. Discrete & Continuous Dynamical Systems  B, 2013, 18 (2) : 331348. doi: 10.3934/dcdsb.2013.18.331 
[8] 
Leszek Gasiński. Optimal control problem of Bolzatype for evolution hemivariational inequality. Conference Publications, 2003, 2003 (Special) : 320326. doi: 10.3934/proc.2003.2003.320 
[9] 
Luís Tiago Paiva, Fernando A. C. C. Fontes. Adaptive timemesh refinement in optimal control problems with state constraints. Discrete & Continuous Dynamical Systems  A, 2015, 35 (9) : 45534572. doi: 10.3934/dcds.2015.35.4553 
[10] 
Theodore TachimMedjo. Optimal control of a twophase flow model with state constraints. Mathematical Control & Related Fields, 2016, 6 (2) : 335362. doi: 10.3934/mcrf.2016006 
[11] 
Alexander Tyatyushkin, Tatiana Zarodnyuk. Numerical method for solving optimal control problems with phase constraints. Numerical Algebra, Control & Optimization, 2017, 7 (4) : 481492. doi: 10.3934/naco.2017030 
[12] 
Anthony M. Bloch, Peter E. Crouch, Nikolaj Nordkvist. Continuous and discrete embedded optimal control problems and their application to the analysis of Clebsch optimal control problems and mechanical systems. Journal of Geometric Mechanics, 2013, 5 (1) : 138. doi: 10.3934/jgm.2013.5.1 
[13] 
Zaidong Zhan, Shuping Chen, Wei Wei. A unified theory of maximum principle for continuous and discrete time optimal control problems. Mathematical Control & Related Fields, 2012, 2 (2) : 195215. doi: 10.3934/mcrf.2012.2.195 
[14] 
Heinz Schättler, Urszula Ledzewicz, Helmut Maurer. Sufficient conditions for strong local optimality in optimal control problems with $L_{2}$type objectives and control constraints. Discrete & Continuous Dynamical Systems  B, 2014, 19 (8) : 26572679. doi: 10.3934/dcdsb.2014.19.2657 
[15] 
Matthias Gerdts, Martin Kunkel. A nonsmooth Newton's method for discretized optimal control problems with state and control constraints. Journal of Industrial & Management Optimization, 2008, 4 (2) : 247270. doi: 10.3934/jimo.2008.4.247 
[16] 
Changjie Fang, Weimin Han. Wellposedness and optimal control of a hemivariational inequality for nonstationary Stokes fluid flow. Discrete & Continuous Dynamical Systems  A, 2016, 36 (10) : 53695386. doi: 10.3934/dcds.2016036 
[17] 
Huaiqiang Yu, Bin Liu. Pontryagin's principle for local solutions of optimal control governed by the 2D NavierStokes equations with mixed controlstate constraints. Mathematical Control & Related Fields, 2012, 2 (1) : 6180. doi: 10.3934/mcrf.2012.2.61 
[18] 
Andrei V. Dmitruk, Alexander M. Kaganovich. Quadratic order conditions for an extended weak minimum in optimal control problems with intermediate and mixed constraints. Discrete & Continuous Dynamical Systems  A, 2011, 29 (2) : 523545. doi: 10.3934/dcds.2011.29.523 
[19] 
Georg Vossen, Torsten Hermanns. On an optimal control problem in laser cutting with mixed finite/infinitedimensional constraints. Journal of Industrial & Management Optimization, 2014, 10 (2) : 503519. doi: 10.3934/jimo.2014.10.503 
[20] 
Maria do Rosário de Pinho, Ilya Shvartsman. Lipschitz continuity of optimal control and Lagrange multipliers in a problem with mixed and pure state constraints. Discrete & Continuous Dynamical Systems  A, 2011, 29 (2) : 505522. doi: 10.3934/dcds.2011.29.505 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]