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Warianty tytułu
Języki publikacji
Abstrakty
This paper provides an analysis of second-order necessary or sufficient optimality conditions of Pontryagin or bounded strong minima, for optimal control problems of ordinary differential equations, considered on a nonfixed time interval, with constraints on initial-final time-state as well as mixed state-control constraints of equality type satisfying condition of linear independence of gradients w.r.t. control.
Czasopismo
Rocznik
Tom
Strony
1535--1556
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
- Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warszawa, Poland, osmolovski@ap.siedlce.pl
Bibliografia
- ARUTYUNOV, A. and KARAMZIN, D. (2005) Necessary conditions for a weak minimum in optimal control problems with mixed constraints. Differential Equations 41 (11), 1532-1543.
- AUGUSTIN, D. and MAURER, H. (2001) Computational sensitivity analysis for state constrained optimal control problems. Annals of Operations Research 101, 75-99.
- BONNANS, J.F. and HERMANT, A. (2007) Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints. Annals of I.H.P. - Nonlinear Analysis. DOI: 10.1016/j.anihpc.2007.12.002.
- DONTCHEV, A.L., HAGER, W.W., POORE, A.B., and YANG, B. (1995) Optimality, stability and convergence in nonlinear control. Applied Math. and Optimization 31, 297-326.
- DUNN, J.C. (1995) Second order optimality conditions in sets of L∞ functions with range in a polyhedron. SIAM J. Control Optimization 33, 1603-1635.
- DUNN, J.C. (1996) On L2 sufficient conditions and the gradient projection method for optimal control problems. SIAM J. Control Optimization 34, 1270-1290.
- LEVITIN, E.S., MILYUTIN, A.A. and OSMOLOVSKII, N.P. (1978) Conditions of high order for a local minimum in problems with constraints. Russian Math. Surveys 33 (6), 97-168.
- MALANOWSKI, K. (1992) Second order conditions and constraint qualifications in stability and sensitivity analysis of solutions to optimization problems in Hilbert spaces. Applied Math. Optimization 25, 51-79.
- MALANOWSKI, K. (1993) Two-norm approach in stability and sensitivity analysis of optimization and optimal control problems. Advances in Math. Sciences and Applications 2, 397-443.
- MALANOWSKI, K. (1994) Stability and sensitivity of solutions to nonlinear optimal control problems. Applied Math. Optimization 32, 111-141.
- MALANOWSKI, K. (2001) Sensitivity analysis for parametric control problems with control-state constraints. Dissertationes Mathematicae CCCXCIV, 1-51.
- MALANOWSKI, K. and MAURER, H. (1996) Sensitivity analysis for parametric control problems with control-state constraints. Comput. Optim. and Applications 5, 253-283.
- MALANOWSKI, K. and MAURER, H. (1998) Sensitivity analysis for state constrained optimal control problems. Discrete and Continuous Dynamical Systems 4, 241-272.
- MALANOWSKI, K. and MAURER, H. (2001) Sensitivity analysis for optimal control problems subject to higher order state constraints. Annals of Operations Research 101, 43-74.
- MAURER, H. (1981) First and second order sufficient optimality conditions in mathematical programming and optimal control. Mathematical Programming Study 14, 163-177.
- MAURER, H. and OBERLE, H.J. (2002) Second order sufficient conditions for optimal control problems with free final time: the Riccati approach. SIAM J. on Control and Optimization 41, 380-403.
- MAURER, H. and PICKENHAIN, S. (1995) Second order sufficient conditions for optimal control problems with mixed control-state constraints. J. Optim. Theory and Applications 86, 649-667.
- MILYUTIN, A.A. and OSMOLOVSKII, N.P. (1998) Calculus of Variations and Optimal Control. Translations of Mathematical Monographs 180, American Mathematical Society, Providence.
- OSMOLOVSKII, N.P. (1988) Theory of higher order conditions in optimal control. Doctor of Science Thesis (in Russian), Moscow.
- OSMOLOVSKII, N.P. (2004) Quadratic optimality conditions for broken extremals in the general problem of calculus of variations. Journal of Math. Science 123 (3), 3987-4122.
- OSMOLOVSKII, N.P. and LEMPIO, F. (2000) Jacobi-type conditions and Riccati equation for broken extremal. Journal of Math. Science 100 (5), 2572-2592.
- OSMOLOVSKII, N.P. and LEMPIO, F. (2002) Transformation of quadratic forms to perfect squares for broken extremals. Journal of Set Valued Analysis 10, 209-232.
- PONTRYAGIN, L.S., BOLTYANSKII, V.G., GAMKRELIDZE, R.V. and MISHCHENKO, E.F. (1961) The Mathematical Theory of Optimal Processes. Fizmatgiz, Moscow; English translation: Pergamon Press, New York, 1964.
- ZEIDAN, V. (1994) The Riccati equation for optimal control problems with mixed state-control constraints: necessity and sufficiency. SIAM J. Control and Optimization 32, 1297-1321.
Typ dokumentu
Bibliografia
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