Discrete optimal control with multiple constraints. I: Constraint separation and transformation technique. II: The batch crystallisation of sugar. (English) Zbl 0256.49034

Automatica 9, 415-429, 431-440 (1973).


49K99 Optimality conditions
49M99 Numerical methods in optimal control


[1] Valentine, F. A.: Contibutions to the calculus of variations 1933-1937. The problem of Lagrange with differential inequalities as added side conditions, 407-448 (1937)
[2] Berkovitz, L. D.: Variational methods in problems of control and programming. J. math. Anal. appl. 3, 145-169 (1961) · Zbl 0100.31005
[3] Berkovitz, L. D.: On control problems with bounded state variables. J. math. Anal. appl. 5, 488-498 (1962) · Zbl 0116.08102
[4] Dreyfus, S.: Variational problems with inequality constraints. J. math. Anal. appl. 4, 297-308 (1962) · Zbl 0119.16005
[5] Jr., A. E. Bryson; Denham, W. F.; Dreyfus, S. E.: Optimal programming problems with inequality constraints I: Necessary conditions for extremal solutions. Aiaa j. 1, 2544-2550 (1963) · Zbl 0142.35902
[6] Berkovitz, L. D.; Dreyfus, S. E.: The equivalence of some necessary conditions for optimal control in problems with bounded state variables. J. math. Anal. appl. 10, 275-283 (1965) · Zbl 0132.34403
[7] Mcintyre, J.; Paiewonsky, B.: On optimal control with bounded state variables. Advances in control systems 5, 389-419 (1967) · Zbl 0155.15401
[8] Jacobson, D. H.; Lele, M. M.; Speyer, J. L.: New necessary conditions of optimality for control problems with state-variable inequality constraints. J. math. Anal. appl. 35, 255-284 (1971) · Zbl 0188.47203
[9] Dreyfus, S.: The numerical solution of variational problems. J. math. Anal. appl. 5, 30-45 (1962) · Zbl 0111.12803
[10] Ho, Y. C.; Brentani, P. B.: On computing optimal control with inequality constraints. J. SIAM control 1, 319-348 (1963)
[11] Denham, W. F.; Jr., A. E. Bryson: Optimal programming problems with inequality constraints II: Solution by steepest-ascent. Aiaa j. 2, 25-34 (1964)
[12] Denham, W. F.: On numerical optimization with state variable inequality constraints. Aiaa j. 4, 550-552 (1966)
[13] Lastman, G. J.: Optimization of nonlinear systems with inequality constraints, ph.d. Dissertation. (1967)
[14] Kelley, H. J.: Method of gradients. Optimization techniques (1962)
[15] Mcgill, R.: Optimal control, inequality state constraints, and the generalized Newton-raphson algorithm. J. SIAM control 3, 291-298 (1965) · Zbl 0133.38901
[16] Lasdon, L. S.; Waren, A. D.; Rice, R. K.: An interior penalty method for inequality constrained optimal control problems. IEEE trans. Aut. control 12, 388-395 (1967)
[17] Dyer, D. A. J.: Convergence rate of optimal control computation for systems with constraints described by penalty functions, ph.d. Dissertation. (1970)
[18] Bellman, R.: Dynamic programming. (1957) · Zbl 0077.13605
[19] Tabak, D.; Kuo, B. J.: Optimal control by mathematical programming. (1971) · Zbl 0176.39401
[20] Canon, M. D.; Cullum, C. D.; Polak, E.: Theory of optimal control and mathematical programming. (1970) · Zbl 0264.49001
[21] Jacobson, D. H.; Lele, M. M.: A transformation technique for optimal control problems with a state variable inequality constraint. IEEE trans. Aut. control 14, 457-464 (1969)
[22] Pagurek, B.; Woodside, C. M.: The conjugate gradient method for optimal control problems with bounded control variables. Automatica 4, 337-349 (1968) · Zbl 0206.16501
[23] Speedy, C. B.; Bell, R. D.; Goodwin, G. C.: Paper presented at joint automatic control conference. Dynamic modelling of a steam generator using lest squares analysis (1970)
[24] Pontryagin, L. S.; Boltyanskii, V. G.; Gamkrelidze, R. V.; Mischenko, E. F.: The mathematical theory of optimal processes. (1962)
[25] Kuhn, H. W.; Tucker, A. W.: Proc. second Berkeley symp. Math. stat. Probability. Nonlinear programming, 481-492 (1951)
[26] Pearson, J. B.; Sridhar, R.: A discrete optimal control problem. IEEE trans. Aut. control 11, 171-174 (1966)
[27] Holtzman, J. M.: On the maximum principle for nonlinear discrete-time systems. IEEE trans. Aut. control 11, 273-274 (1966) · Zbl 0152.09302
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.