Local fields of extremals for optimal control problems with state constraints of relative degree 1

Journal of Dynamical and Control Systems

Volumn 12, Issue 4, 2006, Pages 563-599

  Schattler H ^a  

^a WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

Author keywords

Field of extremals; Optimal control; State space constraints

Indexed keywords

BOUNDARY CONDITIONS; CONSTRAINT THEORY; OPTIMIZATION; STATE SPACE METHODS;

BOUNDARY ARC; CONTROL-INVARIANT MANIFOLDS; RELATIVE DEGREE; STATE SPACE CONSTRAINTS;

OPTIMAL CONTROL SYSTEMS;

EID: 33749240910     PISSN: 10792724     EISSN: 15738698     Source Type: Journal    
DOI: 10.1007/s10883-006-0005-y     Document Type: Article

References (30)

1. A. Agrachev, G. Stefani, and P. L. Zezza, Strong optimality for a bangbang trajectory. SIAM J. Control Optim. 41 (2002), 991-1014.
2. L. Berkovitz, Optimal control theory. Springer-Verlag (1974).
3. V. G. Boltyanskii, Sufficient conditions for optimality and the justification of the dynamic programming principle. SIAM J. Control Optim. 4 (1966), 326-361.
4. B. Bonnard, L. Faubourg, G. Launay, and E. Trélat, Optimal control with state space constraints and the space shuttle re-entry problem. J. Dynam. Control Systems 9 (2003), 155-199.
5. A. Cernea and H. Frankowska, The connection between the maximum principle and the value function for optimal control problems under state constraints. Proc. 43 IEEE Conf. on Decision and Control, Nassau, The Bahamas (2004), pp. 893-898.
6. L. Cesari, Optimization. Theory and Applications. Springer-Verlag, New York (1983).
7. M. G. Crandall and P. L. Lions, Viscosity solutions to Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277 (1983), 1-42.
8. H. Frankowska, Regularity of minimizers and of adjoint states in optimal control under state constraints. Convex Anal. 13 (2006), No. 2.
9. K. Grasse and H. J. Sussmann, Global controllability by nice controls. In: Nonlinear Controllability and Optimal Control (H. Sussmann, ed.), Marcel Dekker, New York (1990), pp. 33-79.
10. M. d. R. de Pinho, M. M. Ferreira, U. Ledzewicz, and H. Schättler, A model for cancer chemotherapy with state constraints. Nonlinear Anal. 63 (2005), 2591-2602.
11. W. H. Fleming and R. W. Rishel, Deterministic and stochastic optimal control. Springer-Verlag, New York (1975).
12. R. F. Hartl, S. P. Sethi, and R. G. Vickson, A survey of the maximum principles for optimal control problems with state constraints. SIAM Rev. 37 (1995), 181-218.
13. A. D. Ioffe and V. M. Tihomirov, Theory of extremal problems. North-Holland, Amsterdam (1979).
14. U. Ledzewicz and H. Schättler, Optimal bang-bang controls for a 2-compartment model in cancer chemotherapy. J. Optim. Theory Appl. 114 (2002), 609-637.
15. U. Ledzewicz and H. Schättler, Controlling a model for bone marrow dynamics in cancer chemotherapy. Math. Biosci. Engineering 1 (2004), 95-110.
16. U. Ledzewicz and H. Schättler, A local field of extremals for single-input systems with state space constraints. Proc. 43 IEEE Conf. on Decision and Control, Nassau, The Bahamas (2004), pp. 923-928.
17. K. Malanowski, On normality of Lagrange multipliers for state constrained optimal control problems. Optimization 52 (2003), 75-91.
18. H. Maurer, On optimal control problems with bounded state variables and control appearing linearly. SIAM J. Control Optim. 15 (1977), 345-362.
19. H. Maurer, On the minimum principle for optimal control problems with state constraints. Schriftenreihe des Rechenzentrums der Universität Münster (1979).
20. H. Maurer and N. Osmolovskii, Quadratic sufficient optimality conditions for bang-bang control problems. Control Cybernet. 33 (2003), 555-584.
21. J. Noble and H. Schättler, Sufficient conditions for relative minima of broken extremals in optimal control theory. J. Math. Anal. Appl. 269, (2002), 98-128.
22. B. Piccoli and H. Sussmann, Regular synthesis and sufficient conditions for optimality. SIAM J. Control Optim. 39 (2000), 359-410.
23. L. S. Pontryagin, V. G. Boltyanskii, V. G. Gamkrelidze, and R. V. Mishchenko, Mathematical theory of optimal processes. Wiley-Interscience (1962).
24. F. Rampazzo and R. Vinter, A theorem on existence of neighbouring trajectories satisfying a state constraint, with applications to optimal control. IMA J. Math. Control Inform. 16 (1999), 335-351.
25. P. Rinaldi and H. Schättler, On optimal control problems with state space constraints arising in the design of bipolar transistors. In: Proc. 41 IEEE Conf. Decision and Control, Las Vegas (2002), pp. 4722-4727.
26. H. Schättler, A local field of extremals near boundary-arc interior-arc junctions. Proc. 44 IEEE Conf. Decision and Control, Sevilla (2005), pp. 945-950.
27. H. M. Soner, Optimal control with state-space constraints, I. SIAM J. Control Optim. 24 (1986), 552-561.
28. H. Stalford, Sufficient conditions for optimal control with state and control constraints. J. Optim. Theory Appl. 7 (1971), 118-135.
29. K. Suzuki, Optimum base-doping profile for minimum base transit time considering velocity saturation at base-collector junction and dependence of mobility and bandgap narrowing on doping concentration. IEEE Trans. Electron. Devices 48 (2001), No. 9, 2102-2107.
30. R. B. Vinter, Optimal control. Birkhäuser, Boston (2000).