A characterization of stability and sensitivity properties for state-constrained optimal control

• Autorzy: Malanowski K.
• Języki publikacji: EN

Abstrakty

EN

In a series of the recent papers of the author, it was shown that the solutions and Lagrange multipliers of state-constrained optimal control problems are locally Lipschitz continuous and directionally differentiable functions of the parameter, under usual constraint qualifications and weakened second order conditions. In this paper, it is shown that those conditions are not only sufficient, but also necessary. Thus, they consitute a characterization of Lipschitz stability and sensitivity properties for state-constrained optimal control problems.

Słowa kluczowe

EN

optimal control; nonlinear ODEs; state constraints; parametric problems; stability and sensitivity analysis

PL

sterowanie optymalne

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2007
• Tom: Vol. 36, no 3
• Strony: 711--726
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Malanowski K.

• Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland,

Bibliografia

• DONTCHEV, A.L. and HAGER,W.W. (1998) Lipschitzian stability for state constrained nonlinear optimal control. SIAM J. Control Optim. 36, 698-718.
• HAGER, W.W. (1979) Lipschitz continuity for constrained processes. SIAM J. Control Optim. 17, 321-338.
• DONTCHEV, A.L. and MALANOWSKI, K. (2000) A characterization of Lipschitzian stability in optimal control. In: A. Ioffe, S. Reich and I. Shafrir, eds., Calculus of Variations and Optimal Control, Research Notes in Mathematics, 411, 62-76, Chapman & Hall, Boca Raton.
• HARTL, R.F., SETHI, S.P. and VICKSON, R.G. (1995) A survey of the maximum principle for optimal control problems with state constraints. SIAM Review 37, 181-218.
• MALANOWSKI, K. (1993) Two-norm approach in stability and sensitivity analysis for optimization and optimal control problems. Adv. Math. Sci. Appl. 2, 397-443.
• MALANOWSKI, K. (1995) Stability and sensitivity of solutions to nonlinear optimal control problems. Appl. Math. Optim. 32, 111-141.
• MALANOWSKI, K. (2001) Stability and sensitivity analysis for optimal control problems with control-state constraints. Dissertationes Mathematicae CCCXCIV, Polska Akademia Nauk, Instytut Matematyczny, Warszawa.
• MALANOWSKI, K. (2003) On normality of Lagrange multipliers for state constrained optimal control problems. Optimization 52, 75-91.
• MALANOWSKI, K. (2007a) Sufficient optimality conditions in stability analysis for state-constrained optimal control. Appl. Math. Optim. 55, 255-271.
• MALANOWSKI, K. (2007b) Stability and sensitivity analysis for linear-quadratic optimal control subject to state constraints. Optimization 56, 463-478.
• MALANOWSKI, K. (2007c) Stability analysis for nonlinear optimal control problems subject to state constraints. SI AM J. Optim. (to be published).
• MALANOWSKI, K. (2007d) Stability and sensitivity analysis for state-constrained optimal control problems. Research Report RB/34/2006, Systems Research Institute of the Polish Academy of Sciences (to be published).
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• NEUSTADT, L.W. (1976) Optimization: A Theory of Necessary Conditions. Princeton Univ. Press, Princeton, NJ.
• OUTRATA, J.V. and SCHINDLER, Z. (1980) An augmented Lagrangian method for a class of convex optimal control problems. Problems of Control and Information Theory 10, 67-81.
• ROBINSON, S.M. (1980) Strongly regular generalized equations. Math. Oper. Res. 5, 43-62.