Citation: |
[1] |
B. Açikmeşe and L. Blackmore, Lossless convexification of a class of optimal control problems with non-convex control constraints, Automatica J. IFAC, 47 (2011), 341-347.doi: 10.1016/j.automatica.2010.10.037. |
[2] |
N. U. Ahmed, "Elements of Finite-Dimensional Systems and Control Theory,'' Longman Scientific and Technical, Essex, 1988. |
[3] |
N. U. Ahmed, "Dynamic Systems and Control with Applications,'' World Scientific, Singapore, 2006. |
[4] |
Z. Benayache, G. Besançon and D. Georges, A new nonlinear control methodology for irrigation canals based on a delayed input model, in "Proceedings of the 17th World Congress of the International Federation of Automatic Control,'' 2008. |
[5] |
J. M. Blatt, Optimal control with a cost of switching control, Journal of the Australian Mathematical Society - Series B: Applied Mathematics, 19 (1976), 316-332. |
[6] |
M. Boccadoro, Y. Wardi, M. Egerstedt and E. Verriest, Optimal control of switching surfaces in hybrid dynamical systems, Discrete Event Dynamic Systems: Theory and Applications, 15 (2005), 433-448.doi: 10.1007/s10626-005-4060-4. |
[7] |
C. Büskens and H. Maurer, SQP-methods for solving optimal control problems with control and state constraints: Adjoint variables, sensitivity analysis and real-time control, Journal of Computational and Applied Mathematics, 120 (2000), 85-108.doi: 10.1016/S0377-0427(00)00305-8. |
[8] |
L. Caccetta, I. Loosen and V. Rehbock, Computational aspects of the optimal transit path problem, Journal of Industrial and Management Optimization, 4 (2008), 95-105.doi: 10.3934/jimo.2008.4.95. |
[9] |
Q. Chai, R. Loxton, K. L. Teo and C. Yang, A max-min control problem arising in gradient elution chromatography, Industrial and Engineering Chemistry Research, 51 (2012), 6137-6144.doi: 10.1021/ie202475p. |
[10] |
Q. Chai, R. Loxton, K. L. Teo and C. Yang, A unified parameter identification method for nonlinear time-delay systems, Journal of Industrial and Management Optimization, 9 (2013), 471-486.doi: 10.3934/jimo.2013.9.471. |
[11] |
Q. Chai, R. Loxton, K. L. Teo and C. Yang, A class of optimal state-delay control problems, Nonlinear Analysis: Real World Applications, 14 (2013), 1536-1550.doi: 10.1016/j.nonrwa.2012.10.017. |
[12] |
Q. Chai, R. Loxton, K. L. Teo and C. Yang, Time-delay estimation for nonlinear systems with piecewise-constant input, Applied Mathematics and Computation, 219 (2013), 9543-9560.doi: 10.1016/j.amc.2013.03.015. |
[13] |
Q. Q. Chai, C. H. Yang, K. L. Teo and W. H. Gui, Optimal control of an industrial-scale evaporation process: Sodium aluminate solution, Control Engineering Practice, 20 (2012), 618-628.doi: 10.1016/j.conengprac.2012.03.001. |
[14] |
B. Christiansen, H. Maurer and O. Zirn, Optimal control of a voice-coil-motor with Coulombic friction, in "Proceedings of the 47th IEEE Conference on Decision and Control,'' 2008.doi: 10.1109/CDC.2008.4739025. |
[15] |
M. Chyba, T. Haberkorn, R. N. Smith and S. K. Choi, Design and implementation of time efficient trajectories for autonomous underwater vehicles, Ocean Engineering, 35 (2008), 63-76.doi: 10.1016/j.oceaneng.2007.07.007. |
[16] |
J. Y. Dieulot and J. P. Richard, Tracking control of a nonlinear system with input-dependent delay, in "Proceedings of the 40th IEEE Conference on Decision and Control,'' 2001. |
[17] |
B. Farhadinia, K. L. Teo and R. Loxton, A computational method for a class of non-standard time optimal control problems involving multiple time horizons, Mathematical and Computer Modelling, 49 (2009), 1682-1691.doi: 10.1016/j.mcm.2008.08.019. |
[18] |
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), 247-270.doi: 10.3934/jimo.2008.4.247. |
[19] |
C. J. Goh and K. L. Teo, Control parametrization: A unified approach to optimal control problems with general constraints, Automatica J. IFAC, 24 (1988), 3-18.doi: 10.1016/0005-1098(88)90003-9. |
[20] |
P. G. Howlett, P. J. Pudney and X. Vu, Local energy minimization in optimal train control, Automatica J. IFAC, 45 (2009), 2692-2698.doi: 10.1016/j.automatica.2009.07.028. |
[21] |
L. S. Jennings, M. E. Fisher, K. L. Teo and C. J. Goh, "MISER3 Optimal Control Software: Theory and User Manual,'' University of Western Australia, Perth, 2004. |
[22] |
L. S. Jennings and K. L. Teo, A computational algorithm for functional inequality constrained optimization problems, Automatica J. IFAC, 26 (1990), 371-375.doi: 10.1016/0005-1098(90)90131-Z. |
[23] |
C. Jiang, Q. Lin, C. Yu, K. L. Teo and G. R. Duan, An exact penalty method for free terminal time optimal control problem with continuous inequality constraints, Journal of Optimization Theory and Applications, 154 (2012), 30-53.doi: 10.1007/s10957-012-0006-9. |
[24] |
C. Jiang, K. L. Teo, R. Loxton and G. R. Duan, A neighboring extremal solution for an optimal switched impulsive control problem, Journal of Industrial and Management Optimization, 8 (2012), 591-609.doi: 10.3934/jimo.2012.8.591. |
[25] |
K. Kaji and K. H. Wong, Nonlinearly constrained time-delayed optimal control problems, Journal of Optimization Theory and Applications, 82 (1994), 295-313.doi: 10.1007/BF02191855. |
[26] |
C. Y. Kaya and J. L. Noakes, Computational method for time-optimal switching control, Journal of Optimization Theory and Applications, 117 (2003), 69-92.doi: 10.1023/A:1023600422807. |
[27] |
H. W. J. Lee, K. L. Teo and X. Q. Cai, An optimal control approach to nonlinear mixed integer programming problems, Computers and Mathematics with Applications, 36 (1998), 87-105.doi: 10.1016/S0898-1221(98)00131-X. |
[28] |
H. W. J. Lee, K. L. Teo and A. E. B. Lim, Sensor scheduling in continuous time, Automatica J. IFAC, 37 (2001), 2017-2023.doi: 10.1016/S0005-1098(01)00159-5. |
[29] |
H. W. J. Lee, K. L. Teo, V. Rehbock and L. S. Jennings, Control parametrization enhancing technique for time optimal control problems, Dynamic Systems and Applications, 6 (1997), 243-261. |
[30] |
H. W. J. Lee, K. L. Teo, V. Rehbock and L. S. Jennings, Control parametrization enhancing technique for optimal discrete-valued control problems, Automatica J. IFAC, 35 (1999), 1401-1407.doi: 10.1016/S0005-1098(99)00050-3. |
[31] |
H. W. J. Lee and K. L. Teo, Control parametrization enhancing technique for solving a special ODE class with state dependent switch, Journal of Optimization Theory and Applications, 118 (2003), 55-66.doi: 10.1023/A:1024735407694. |
[32] |
H. W. J. Lee and K. H. Wong, Semi-infinite programming approach to nonlinear time-delayed optimal control problems with linear continuous constraints, Optimization Methods and Software, 21 (2006), 679-691.doi: 10.1080/10556780500142306. |
[33] |
R. Li, K. L. Teo, K. H. Wong and G. R. Duan, Control parameterization enhancing transform for optimal control of switched systems, Mathematical and Computer Modelling, 43 (2006), 1393-1403.doi: 10.1016/j.mcm.2005.08.012. |
[34] |
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), 260-291.doi: 10.1007/s10957-011-9904-5. |
[35] |
B. Li, K. L. Teo, C. C. Lim and G. R. Duan, An optimal PID controller design for nonlinear constrained optimal control problems, Discrete and Continuous Dynamical Systems: Series B, 16 (2011), 1101-1117.doi: 10.3934/dcdsb.2011.16.1101. |
[36] |
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), 63-81. |
[37] |
Q. Lin, R. Loxton, K. L. Teo and Y. H. Wu, A new computational method for optimizing nonlinear impulsive systems, Dynamics of Continuous, Discrete and Impulsive Systems - Series B: Applications and Algorithms, 18 (2011), 59-76. |
[38] |
Q. Lin, R. Loxton, K. L. Teo and Y. H. Wu, Optimal control computation for nonlinear systems with state-dependent stopping criteria, Automatica J. IFAC, 48 (2012), 2116-2129.doi: 10.1016/j.automatica.2012.06.055. |
[39] |
Y. Liu, A. Eberhard and K. L. Teo, A numerical method for a class of mixed switching and impulsive optimal control problems, Computers and Mathematics with Applications, 52 (2006), 625-636.doi: 10.1016/j.camwa.2006.10.001. |
[40] |
C. Liu, Z. Gong, E. Feng and H. Yin, Modelling and optimal control for nonlinear multistage dynamical system of microbial fed-batch culture, Journal of Industrial and Management Optimization, 5 (2009), 835-850.doi: 10.3934/jimo.2009.5.835. |
[41] |
Y. Liu, K. L. Teo, L. S. Jennings and S. Wang, On a class of optimal control problems with state jumps, Journal of Optimization Theory and Applications, 98 (1998), 65-82.doi: 10.1023/A:1022684730236. |
[42] |
R. Loxton, Q. Lin and K. L. Teo, Minimizing control variation in nonlinear optimal control, Automatica J. IFAC, 49 (2013), 2652-2664.doi: 10.1016/j.automatica.2013.05.027. |
[43] |
R. Loxton, Q. Lin, V. Rehbock and K. L. Teo, Control parameterization for optimal control problems with continuous inequality constraints: New convergence results, Numerical Algebra, Control and Optimization, 2 (2012), 571-599.doi: 10.3934/naco.2012.2.571. |
[44] |
R. Loxton, K. L. Teo and V. Rehbock, Optimal control problems with multiple characteristic time points in the objective and constraints, Automatica J. IFAC, 44 (2008), 2923-2929.doi: 10.1016/j.automatica.2008.04.011. |
[45] |
R. Loxton, K. L. Teo and V. Rehbock, Computational method for a class of switched system optimal control problems, IEEE Transactions on Automatic Control, 54 (2009), 2455-2460.doi: 10.1109/TAC.2009.2029310. |
[46] |
R. Loxton, K. L. Teo and V. Rehbock, An optimization approach to state-delay identification, IEEE Transactions on Automatic Control, 55 (2010), 2113-2119.doi: 10.1109/TAC.2010.2050710. |
[47] |
R. Loxton, K. L. Teo and V. Rehbock, Robust suboptimal control of nonlinear systems, Applied Mathematics and Computation, 217 (2011), 6566-6576.doi: 10.1016/j.amc.2011.01.039. |
[48] |
R. Loxton, K. L. Teo, V. Rehbock and W. K. Ling, Optimal switching instants for a switched-capacitor DC/DC power converter, Automatica J. IFAC, 45 (2009), 973-980.doi: 10.1016/j.automatica.2008.10.031. |
[49] |
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 J. IFAC, 45 (2009), 2250-2257.doi: 10.1016/j.automatica.2009.05.029. |
[50] |
D. G. Luenberger and Y. Ye, "Linear and Nonlinear Programming,'' 3rd Edition, Springer, New York, 2008. |
[51] |
R. B. Martin, Optimal control drug scheduling of cancer chemotherapy, Automatica J. IFAC, 28 (1992), 1113-1123.doi: 10.1016/0005-1098(92)90054-J. |
[52] |
J. Matula, On an extremum problem, Journal of the Australian Mathematical Society - Series B: Applied Mathematics, 28 (1987), 376-392.doi: 10.1017/S0334270000005464. |
[53] |
J. Nocedal and S. J. Wright, "Numerical Optimization,'' 2nd Edition, Springer, New York, 2006. |
[54] |
V. Rehbock, "Tracking Control and Optimal Control,'' PhD thesis, University of Western Australia, Perth, 1994. |
[55] |
V. Rehbock and L. Caccetta, Two defence applications involving discrete valued optimal control, ANZIAM Journal, 44 (2002), E33-E54.doi: 10.1017/S1446181100007884. |
[56] |
V. Rehbock, K. L. Teo, L. S. Jennings and H. W. J. Lee, A survey of the control parametrization and control parametrization enhancing methods for constrained optimal control problems, in "Progress in Optimization: Contributions from Australasia,'' Kluwer Academic Publishers, Dordrecht, 1999.doi: 10.1007/978-1-4613-3285-5_13. |
[57] |
J. P. Richard, Time-delay systems: An overview of some recent advances and open problems, Automatica J. IFAC, 39 (2003), 1667-1694.doi: 10.1016/S0005-1098(03)00167-5. |
[58] |
T. Ruby and V. Rehbock, Numerical solutions of optimal switching control problems, in "Optimization and Control with Applications,'' Springer, New York, 2005.doi: 10.1007/0-387-24255-4_21. |
[59] |
T. Ruby, V. Rehbock and W. B. Lawrance, Optimal control of hybrid power systems, Dynamics of Continuous, Discrete and Impulsive Systems - Series B: Applications and Algorithms, 10 (2003), 429-439. |
[60] |
A. Siburian and V. Rehbock, Numerical procedure for solving a class of singular optimal control problems, Optimization Methods and Software, 19 (2004), 413-426.doi: 10.1080/10556780310001656637. |
[61] |
D. E. Stewart, A numerical algorithm for optimal control problems with switching costs, Journal of the Australian Mathematical Society - Series B: Applied Mathematics, 34 (1992), 212-228.doi: 10.1017/S0334270000008730. |
[62] |
K. L. Teo, Control parametrization enhancing transform to optimal control problems, Nonlinear Analysis: Theory, Methods and Applications, 63 (2005), e2223-e2236.doi: 10.1016/j.na.2005.03.066. |
[63] |
K. L. Teo and C. J. Goh, A simple computational procedure for optimization problems with functional inequality constraints, IEEE Transactions on Automatic Control, 32 (1987), 940-941.doi: 10.1109/TAC.1987.1104471. |
[64] |
K. L. Teo, C. J. Goh and C. C. Lim, A computational method for a class of dynamical optimization problems in which the terminal time is conditionally free, IMA Journal of Mathematical Control and Information, 6 (1989), 81-95.doi: 10.1093/imamci/6.1.81. |
[65] |
K. L. Teo, C. J. Goh and K. H. Wong, "A Unified Computational Approach to Optimal Control Problems,'' Longman Scientific and Technical, Essex, 1991. |
[66] |
K. L. Teo and L. S. Jennings, Nonlinear optimal control problems with continuous state inequality constraints, Journal of Optimization Theory and Applications, 63 (1989), 1-22.doi: 10.1007/BF00940727. |
[67] |
K. L. Teo and L. S. Jennings, Optimal control with a cost on changing control, Journal of Optimization Theory and Applications, 68 (1991), 335-357.doi: 10.1007/BF00941572. |
[68] |
K. L. Teo, L. S. Jennings, H. W. J. Lee and V. Rehbock, The control parameterization enhancing transform for constrained optimal control problems, Journal of the Australian Mathematical Society - Series B: Applied Mathematics, 40 (1999), 314-335.doi: 10.1017/S0334270000010936. |
[69] |
K. L. Teo, G. Jepps, E. J. Moore and S. Hayes, A computational method for free time optimal control problems, with application to maximizing the range of an aircraft-like projectile, Journal of the Australian Mathematical Society - Series B: Applied Mathematics, 28 (1987), 393-413.doi: 10.1017/S0334270000005476. |
[70] |
K. L. Teo, W. R. Lee, L. S. Jennings, S. Wang and Y. Liu, Numerical solution of an optimal control problem with variable time points in the objective function, ANZIAM Journal, 43 (2002), 463-478. |
[71] |
K. L. Teo, V. Rehbock and L. S. Jennings, A new computational algorithm for functional inequality constrained optimization problems, Automatica J. IFAC, 29 (1993), 789-792.doi: 10.1016/0005-1098(93)90076-6. |
[72] |
T. L. Vincent and W. J. Grantham, "Optimality in Parametric Systems,'' John Wiley, New York, 1981. |
[73] |
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), 705-718.doi: 10.3934/jimo.2009.5.705. |
[74] |
L. Y. Wang, W. H. Gui, K. L. Teo, R. Loxton and C. H. Yang, Optimal control problems arising in the zinc sulphate electrolyte purification process, Journal of Global Optimization, 54 (2012), 307-323.doi: 10.1007/s10898-012-9863-x. |
[75] |
K. H. Wong, L. S. Jennings and F. Benyah, The control parametrization enhancing transform for constrained time-delayed optimal control problems, ANZIAM Journal, 43 (2002), E154-E185. |
[76] |
S. F. Woon, V. Rehbock and R. Loxton, Global optimization method for continuous-time sensor scheduling, Nonlinear Dynamics and Systems Theory, 10 (2010), 175-188. |
[77] |
S. F. Woon, V. Rehbock and R. Loxton, Towards global solutions of optimal discrete-valued control problems, Optimal Control Applications and Methods, 33 (2012), 576-594.doi: 10.1002/oca.1015. |
[78] |
C. Z. Wu and K. L. Teo, Global impulsive optimal control computation, Journal of Industrial and Management Optimization, 2 (2006), 435-450.doi: 10.3934/jimo.2006.2.435. |
[79] |
C. Z. Wu, K. L. Teo and V. Rehbock, A filled function method for optimal discrete-valued control problems, Journal of Global Optimization, 44 (2009), 213-225.doi: 10.1007/s10898-008-9319-5. |
[80] |
R. Yu and P. Leung, Optimal partial harvesting schedule for aquaculture operations, Marine Resource Economics, 21 (2006), 301-315. |
[81] |
C. Yu, B. Li, R. Loxton and K. L. Teo, Optimal discrete-valued control computation, Journal of Global Optimization, 56 (2013), 503-518.doi: 10.1007/s10898-012-9858-7. |
[82] |
Y. Zhao and M. A. Stadtherr, Rigorous global optimization for dynamic systems subject to inequality path constraints, Industrial and Engineering Chemistry Research, 50 (2011), 12678-12693.doi: 10.1021/ie200996f. |