Variational approach to some optimization control problems

• Autorzy: R. M. Bianchini
• Języki publikacji: EN

Abstrakty

EN

This paper presents the variational approach to some optimization problems: Mayer's problem with or without constraints on the final point, local controllability of a trajectory, time-optimal problems.

Słowa kluczowe

EN

tangent vectors   variational cone   local controllability   Mayer's optimization problem  

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1995
• Tom: 32
• Numer: 1
• Strony: 83-94

Daty

wydano

1995

Twórcy

autor

R. M. Bianchini

• Department of Mathematics U. Dini, University of Florence, Viale Morgagni 67/A, 50134 Firenze, Italy

Bibliografia

• [1] M. S. Bazaraa and C. M. Shetty, Foundations of Optimization, Lecture Notes in Econom. and Math. Systems 122, Springer, Berlin, 1976.
• [2] R. M. Bianchini and G. Stefani, Controllability along a reference trajectory: a variational approach, SIAM J. Control Optim. 31 (1993), 900-927.
• [3] A. I. Dubovickiĭ and A. M. Miljutin, Extremum problems with constraints, J. Soviet Math. 4 (1963), 452-455.
• [4] K. Grasse, Controllability and accessibility in nonlinear control systems, PhD thesis, University of Illinois at Urbana-Champaign, 1979.
• [5] M. R. Hestenes, Calculus of Variations and Optimal Control Theory, Wiley, New York, 1966.
• [6] E. B. Lee and L. Markus, Foundations of Optimal Control Theory, Wiley, New York, 1967.
• [7] E. S. Polovinkin and G. V. Smirnov, An approach to the differentiation of many-valued mappings and necessary conditions for optimization of solutions of differential inclusions, Differencial'nye Uravnenija 22 (1986), 944-954.
• [8] R. T. Rockafellar, Clarke's tangent cones and the boundaries of closed convex sets in $R^n$, Nonlinear Anal. 3 (1979), 145-154.