Geometric optimal control techniques to optimize the production of chemical reactors using temperature control

Agrachev, 2004, Control theory from the geometric viewpoint Anderson, 2008, Global asymptotic stability for a class of nonlinear chemical equations, SIAM Journal on Applied Mathematics, 5, 1464, 10.1137/070698282 Boltyanskii, 1966, Sufficient conditions for optimality and the justification of the dynamic programming method, SIAM Journal on Applied Mathematics, 4, 326 Bonnard, 1991, Feedback equivalence for nonlinear systems and the time optimal control problem, SIAM Journal on Control and Optimization, 29, 1300, 10.1137/0329067 Bonnard, 2007, Second order optimality conditions in the smooth case and applications in optimal control, ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV), 13, 207, 10.1051/cocv:2007012 Bonnard, 2003, Singular trajectories and their role in control theory Bonnard, 1993, Théorie des singularités de l’application entrée/sortie et optimalité des trajectoires singulières dans le problème du temps minimal, Forum Mathematicum, 5, 111 Bonnard, 1998, Time minimal control of batch reactors, ESAIM: Control, Optimisation and Calculus of Variations, 3, 407 Bonnard, 1997, Classification générique de synthèses temps minimales avec cible de codimension un et applications, Annales de l’I.H.P. Analyse non linéaire, 14, 55, 10.1016/S0294-1449(97)80149-7 Bonnard, 1995, Towards a geometric theory in the time minimal control of chemical batch reactors, SIAM J. Contr. Opt., 33, 1279, 10.1137/S0363012992241338 Bonnard, 1995, Time minimal synthesis for planar systems in the neighborhood of a terminal manifold of codimension one, 5, 379 Bonnard, 2012, Optimal control with applications in space and quantum dynamics, AIMS Series on Applied Mathematics, 5 Boscain, 2004, Optimal syntheses for control systems on 2-d manifolds, vol. 43 Brunovsky, 1980, Existence of regular syntheses for general problems, Journal of Differential Equations, 38, 317, 10.1016/0022-0396(80)90011-X Cots, 2012, Contrôle optimal géométrique : méthodes homotopiques et applications, Phd thesis, Institut Mathématiques de Bourgogne, Dijon, France Ekeland, 1977, Discontinuité des champs hamiltoniens et existence des solutions optimales en calcul des variations, Inst. Hautes Études Sci. Publ. Math., 47, 5, 10.1007/BF02684338 Feinberg, 1972, On chemical kinetics of a certain class, Rational Mech. Anal., 46, 10.1007/BF00251866 Fuller, 1963, Study of an optimum non linear system, Journal of Electronics and Control, 15, 63, 10.1080/00207216308937555 Horn, 1972, General mass action kinetics, Archive for Rational Mechanics and Analysis, 47, 81, 10.1007/BF00251225 Jurdjevic, 1997, Geometric control theory, vol. 52 Krener, 1977, The high order maximal principle and its application to singular extremals, SIAM Journal on Control and Optimization,, 15, 256, 10.1137/0315019 Kupka, 1987, Geometric theory of extremals in optimal control problems. i. the fold and maxwell case, Transactions of the American Mathematical Society, 299, 225 Kupka, 1990, The ubiquity of Fuller’s phenomenon, Nonlinear controllability and optimal control, 133, 313 Launay, 1997, The generic local structure of time-optimal synthesis with a target of codimension one in dimension greater than two, Journal of Dynamical and Control Systems, 3, 165, 10.1007/BF02465893 Ledzewicz, 2009, Singular controls and chattering arcs in optimal control problems arising in biomedicine, Control & Cybernetics, 38, 1501 Martinet, 1982, Singularities of smooth functions and maps, 10.1007/BFb0092655 McKeithan, 1995, Kinetic proofreading in t-cell receptor signal transduction, Proceedings of the National Academy of Sciences of the United States of America, 92, 5042, 10.1073/pnas.92.11.5042 Pontryagin, 1964 Schättler, 2012, Geometric optimal control. theory, methods and examples, 10.1007/978-1-4614-3834-2 Sontag, 2001, Structure and stability of certain chemical networks and applications to the kinetic proofreading model of t-cell receptor signal transduction, IEEE Transactions on Automatic Control, 46, 1028, 10.1109/9.935056 Sussmann, 1990, Synthesis, presynthesis, sufficient conditions for optimality and subanalytic sets Tóth, 2018