First- and second-order sufficient optimality conditions for bang-bang controls

SIAM Journal on Control and Optimization

Volumn 35, Issue 1, 1997, Pages 315-340

  Sarychev, Andrei V ^a  

^a UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

Bang bang extremals; Optimal control problem; Pontryagin maximum principle; Sufficient optimality conditions

Indexed keywords

BANG BANG CONTROL SYSTEMS; CONTROL THEORY; NONLINEAR CONTROL SYSTEMS; OPTIMIZATION; PIECEWISE LINEAR TECHNIQUES; VECTORS;

AFFINE CONTROL SYSTEMS; NONLINEAR TIME OPTIMAL CONTROL PROBLEM; PONTRYAGIN MAXIMUM PRINCIPLE;

OPTIMAL CONTROL SYSTEMS;

EID: 0030826051     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012993246191     Document Type: Article

References (21)

1. A. A. AGRACHEV AND R. V. GAMKRELIDZE, Exponential representation of flows and chronological calculus, Mat. Sb., 107 (1978), pp. 467-532 (in Russian). English translation in Math. USSR-Sb., 35 (1979), pp. 727-785.
2. A. A. AGRACHEV AND R. V. GAMKRELIDZE, Exponential representation of flows and chronological calculus, Mat. Sb., 107 (1978), pp. 467-532 (in Russian). English translation in Math. USSR-Sb., 35 (1979), pp. 727-785.
3. A. A. AGRACHEV AND R. V. GAMKRELIDZE, Symplectic geometry and optimal control, in Nonlinear Controllability and Optimal Control, H. J. Sussmann, ed., Marcel Dekker, New York, 1990, pp. 263-277.
4. A. A. AGRACHEV, R. V. GAMKRELIDZE, AND A. V. SARYCHEV, Local invariants of smooth control systems, Acta Appl. Math., 14 (1989), pp. 191-237.
5. A. BRESSAN, A high-order test for optimality of bang-bang controls, SIAM J. Control Optim., 23 (1985), pp. 38-48.
6. R. V. GAMKRELIDZE, Principles of Optimal Control Theory, Plenum Press, New York, 1978.
7. B. S. GOH, Necessary conditions for singular extremals involving multiple control variables, SIAM J. Control, 4 (1966), pp. 716-731.
8. L. S. PONTRYAGIN, V. G. BOLTYANSKII, R. V. GAMKRELIDZE, AND E. F. MISCHENKO, The Mathematical Theory of Optimal Processes, Pergamon Press, Oxford, 1964.
9. A. V. SARYCHEV, Index of the second variation of control system, Mat. Sb., 113 (1980), pp. 464-486 (in Russian). English translation in Math. USSR-Sb., 41 (1982), pp. 383-401.
10. A. V. SARYCHEV, Index of the second variation of control system, Mat. Sb., 113 (1980), pp. 464-486 (in Russian). English translation in Math. USSR-Sb., 41 (1982), pp. 383-401.
11. A. V. SARYCHEV, Integral representation for the trajectories of control system with generalized right-hand side, Differentsialnye Uravnenia, 24 (1988), pp. 1551-1564 (in Russian). English translation in Differential Equations, 24 (1988), pp. 1021-1031.
12. A. V. SARYCHEV, Integral representation for the trajectories of control system with generalized right-hand side, Differentsialnye Uravnenia, 24 (1988), pp. 1551-1564 (in Russian). English translation in Differential Equations, 24 (1988), pp. 1021-1031.
13. A. V. SARYCHEV, Nonlinear systems with impulsive and generalized function controls, in Nonlinear Synthesis, C. I. Byrnes and A. B. Kurzhansky, eds., Birkhauser, Boston, MA, 1991, pp. 244-257.
14. A. V. SARYCHEV, On optimality of generalized (impulsive) controls in time-optimal problem, Differentsialnye Uravnenia, 27 (1991), pp. 788-801 (in Russian). English translation in Differential Equations, 27 (1991), pp. 539-550.
15. A. V. SARYCHEV, On optimality of generalized (impulsive) controls in time-optimal problem, Differentsialnye Uravnenia, 27 (1991), pp. 788-801 (in Russian). English translation in Differential Equations, 27 (1991), pp. 539-550.
16. A. V. SARYCHEV, Morse index and sufficient optimality conditions for bang-bang Pontryagin extremals, in System Modelling and Optimization, Lecture Notes in Control and Information Sci. 180, P. Kall, ed., Springer-Verlag, Berlin, 1992, pp. 440-448.
17. A. V. SARYCHEV, On Legendre-Jacobi-Morse-Type Theory of Second Variation for Optimal Control Problems, Report 382, Schwerpunktprogramm der Deutschen Forschungsgemein-Schaft "Anwendungsbezogene Optimierung und Steuerung," Würzburg, 1992.
18. A. V. SARYCHEV, Sufficient optimality conditions for Pontryagin extremals, Systems Control Lett., 19 (1992), pp. 451-460.
19. H. SCHAETTLER, On the local structure of time-optimal bang-bang trajectories, SIAM J. Control Optim., 26 (1988), pp. 186-204.
20. ∞ nonsingular case, SIAM J. Control Optim., 25 (1987), pp. 433-465.
21. H. J. SUSSMANN, Envelopes, conjugate points and optimal bang-bang extremals, in Proc. 1985 Paris Conf. on Nonlinear Systems, M. Fliess and M. Hazewinkel, eds., Reidel Publishers, Dordrecht, the Netherlands, 1987.