Lipschitzian regularity of minimizers for optimal control problems with control-affine dynamics

Applied Mathematics and Optimization

Volumn 41, Issue 2, 2000, Pages 237-254

  Sarychev, A V ^a   Torres, D F M ^a  

^a UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; LAGRANGE MULTIPLIERS; NONLINEAR CONTROL SYSTEMS; STATISTICAL METHODS;

CALCULUS OF VARIATIONS; LIPSCHITZIAN REGULARITY; NONLINEAR CONTROL-AFFINE SYSTEMS; PONTRYAGIN MAXIMUM PRINCIPLES;

OPTIMAL CONTROL SYSTEMS;

EID: 0034149003     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002459911013     Document Type: Article

References (18)

1. . Ambrosio L, Ascenzi O, Buttazzo G (1989) Lipschitz regularity for minimizers of integral functionals with highly discontinuous integrands. J Math Anal Appl 142:301-316
2. Bernstein S (1912) Sur les équations du calcul des variations. Ann Sci École Norm Sup 3:431-185
3. Cesari L (1983) Optimization Theory and Applications. Springer-Verlag, New York
4. Cheng C, Mizel VJ (1996) On the Lavrentiev phenomenon for optimal control problems with second-order dynamics. SIAM J Control Optim 34:2172-2179
5. Clarke FH (1976) The Maximum Principle under minimal hypotheses. SIAM J Control Optim 14:1078-1091
6. Clarke FH (1985) Existence and regularity in the small in the Calculus of Variations. J Differential Equations 59:336-354
7. Clarke FH (1989) Methods of Dynamic and Nonsmooth Optimization. SIAM, Philadelphia, PA
8. Clarke FH, Loewen PD (1989) Variational problems with Lipschitzian minimizers. Ann Inst Poincaré Anal Non Linéaire 6:185-209
9. Clarke FH, Vinter RB (1985) Regularity properties of solutions to the basic problem in the calculus of variations. Trans Amer Math Soc 289:73-98
10. Clarke FH, Vinter RB (1986) Regularity of solutions to variational problems with polynomial Lagrangians. Bull Polish Acad Sci 34:73-81
11. Clarke FH, Vinter RB (1990) A regularity theory for variational problems with higher order derivatives. Trans Amer Math Soc 320:227-251
12. Clarke FH, Vinter RB (1990) Regularity properties of optimal controls. SIAM J Control Optim 28:980-997
13. Gamkrelidze RV (1978) Principles of Optimal Control Theory. Plenum, New York
14. Morrey CB (1966) Multiple Integrals in the Calculus of Variations. Springer-Verlag, Berlin
15. Sarychev AV (1997) First and second-order integral functionals of the calculus of variations which exhibit the Lavrentiev phenomenon. J Dynam Control Systems 3:565-588
16. Sussmann HJ (1994) A strong version of the Maximum Principle under weak hypotheses. Proc 33rd IEEE Conference on Decision and Control, Orlando, FL, pp 1950-1956
17. Tonelli L (1915) Sur une méthode directe du calcul des variations. Rend Circ Mat Palermo 39:233-264
18. Torres DM (1997) Lipschitzian regularity of minimizers in the calculus of variations and optimal control (in Portuguese). MSc thesis, Univ Aveiro, Aveiro