Time minimal synthesis with target of codimension one under generic conditions

• Autorzy: B. Bonnard , M. Pelletier
• Języki publikacji: EN

Abstrakty

EN

We consider the problem of constructing the optimal closed loop control in the time minimal control problem, with terminal constraint belonging to a manifold of codimension one, for systems of the form $v̇ = X + uY$, $|u| ≤ 1$ and $v ∈ R^2$ or $R^3$, under generic assumptions. The analysis is localized near the terminal manifold and is developed to control a class of chemical systems.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1995
• Tom: 32
• Numer: 1
• Strony: 95-109

Daty

wydano

1995

Twórcy

autor

B. Bonnard

• Département de Mathématiques, Laboratoire de Topologie, Université de Bourgogne, BP 138, 21004 Dijon Cedex, France

autor

M. Pelletier

• Département de Mathématiques, Laboratoire de Topologie, Université de Bourgogne, BP 138, 21004 Dijon Cedex, France

Bibliografia

• [1] R. Benedetti and J. J. Risler, Real Algebraic and Semi-Algebraic Sets, Hermann, Paris, 1990.
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• [3] B. Bonnard and J. de Morant, Towards a geometric theory in the time minimal control of chemical batch reactors, to appear in SIAM J. Control Optim.
• [4] B. Bonnard and M. Pelletier, Time minimal synthesis for planar systems in the neighborhood of a terminal manifold of codimension one, preprint, Laboratoire de Topologie de Dijon, 1992, to appear in JMSEC.
• [5] I. Kupka, Geometric theory of extremals in optimal control problems. I. The fold and Maxwell cases, Trans. Amer. Math. Soc. 299 (1977), 225-243.
• [6] E. B. Lee and L. Markus, Foundations of Optimal Control Theory, Wiley, New York, 1967.
• [7] H. Poincaré, Sur les lignes géodésiques des surfaces convexes, Trans. Amer. Math. Soc. 6 (1905), 237-274.
• [8] H. Schättler, The local structure of time optimal trajectories under generic conditions, SIAM J. Control Optim. 26 (1988), 899-918.
• [9] H. J. Sussmann, The structure of time optimal trajectories for single-input systems in the plane: the $C^∞$ non singular case, ibid. 25 (1987), 433-465.
• [10] H. J. Sussmann, Regular synthesis for time optimal control single-input real analytic systems in the plane, ibid. 25 (1987), 1145-1162.