Classification of generic singularities for the planar time-optimal synthesis

SIAM Journal on Control and Optimization

Volumn 34, Issue 6, 1996, Pages 1914-1946

  Piccoli, B ^a  

^a SISSA   (Italy)

Author keywords

Regular synthesis; Time optimal control; Two dimensional system

Indexed keywords

CONTROL SYSTEM SYNTHESIS; CONTROL THEORY; DIFFERENTIAL EQUATIONS; FEEDBACK; OPTIMAL CONTROL SYSTEMS;

EMBEDDED SUBMANIFOLDS; GENERIC SINGULARITIES;

CONTROL;

EID: 0030289481     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012993256149     Document Type: Article

References (14)

1. V. I. ARNOLD, Geometrical Method in the Theory of ODE, Springer-Verlag, New York, 1983.
2. V. G. BOLTIANSKII, Sufficient conditions for optimality and the justification of the dynamic programming principle, SIAM J. Control Optim., 4 (1966), pp. 326-361.
3. P. BRUNOVSKY, Every normal linear system has a regular time-optimal synthesis, Math. Slovaca, 28 (1978), pp. 81-100.
4. _, Existence of regular syntheses for general problems, J. Differential Equations, 38 (1980), pp. 317-343.
5. H. HERMES AND J. P. LASALLE, Functional Analysis and Time Optimal Control, Academic Press, New York, 1969.
6. E. B. LEE AND L. MARKUS, Foundations of Optimal Control Theory, Wiley, New York, 1967.
7. M. M. PEIXOTO, Generic properties of ordinary differential equations, in Studies in Ordinary Differentials Equations, J. Hale, ed., Studies in Mathematics 14, Mathematical Association of America, Washington, 1977, pp. 52-92.
8. B. PICCOLI, Regular time-optimal syntheses for smooth planar systems. Rend. Sem. Mat. Univ. Padova, 95 (1996), to appear.
9. ∞ nonsingular case, SIAM J. Control Optim., 25 (1987), pp. 433-465.
10. _, The structure of time-optimal trajectories for single-input systems in the plane: The general real analytic case, SIAM J. Control Optim., 25 (1987), pp. 868-904.
11. _, Regular synthesis for time-optimal control of single-input real-analytic systems in the plane, SIAM J. Control Optim., 25 (1987), pp. 1145-1162.
12. _, Envelopes, conjugate points, and optimal bang-bang extremals, in Algebraic and Geometric Methods in Nonlinear Control Theory, M. Fliess and M. Hazewinkel, eds., D. Reidel Publishing Company, Dordrecht, 1986, pp. 325-346.
13. _, Envelopes, higher-order optimality conditions, and lie brackets, in Proc. 1989 I.E.E.E. Conf. Decision and Control.
14. _, Synthesis, presynthesis, sufficient conditions for optimality and subanalytic sets, in Nonlinear Controllability and Optimal Control, H. J. Sussmann, ed., Marcel Dekker, New York, 1990, pp. 1-18.