Optimal Control of the Solid Fuel Ignition Model with H[sup 1]-Cost

Optimal control problems for the stationary as well as the time-dependent solid fuel ignition model are investigated. Existence of optimal controls is proved, and optimality systems are derived. The analysis is based on a closedness lemma for the exponential function in L1 and a generalization of Aubin's lemma.

[1]  G. M. Troianiello,et al.  Elliptic Differential Equations and Obstacle Problems , 1987 .

[2]  E. Casas,et al.  Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity , 1998 .

[3]  Viorel Barbu.  Necessary conditions for nonconvex distributed control problems governed by elliptic variational inequalities , 1981 .

[4]  R. Glowinski,et al.  On control problems for some advection-reaction-diffusion systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[5]  Karl Kunisch,et al.  Optimal control of the solid fuel ignition model , 2000 .

[6]  Haim Brezis,et al.  Monotonicity Methods in Hilbert Spaces and Some Applications to Nonlinear Partial Differential Equations , 1971 .

[7]  Kazufumi Ito,et al.  Augmented Lagrangian-SQP-Methods in Hilbert Spaces and Application to Control in the Coefficients Problems , 1996, SIAM J. Optim..

[8]  D. Gilbarg,et al.  Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[9]  J. Zowe,et al.  Regularity and stability for the mathematical programming problem in Banach spaces , 1979 .

[10]  Jacques-Louis Lions,et al.  Control of distributed singular systems , 1985 .

[11]  Jerrold Bebernes,et al.  Mathematical Problems from Combustion Theory , 1989 .

[12]  D. A. Frank-Kamenet︠s︡kiĭ.  Diffusion and heat transfer in chemical kinetics , 1969 .

[13]  R. Temam.  Navier-Stokes Equations , 1977 .

[14]  Gerd Grubb,et al.  PROBLÉMES AUX LIMITES NON HOMOGÉNES ET APPLICATIONS , 1969 .

[15]  V. Barbu.  Nonlinear Semigroups and di erential equations in Banach spaces , 1976 .

[16]  Ekkehard W. Sachs,et al.  Convergence Rate of the Augmented Lagrangian SQP Method , 1997, Universität Trier, Mathematik/Informatik, Forschungsbericht.

[17]  Kazufumi Ito,et al.  Newton's Method for a Class of Weakly Singular Optimal Control Problems , 2000, SIAM J. Optim..

[18]  Karl Kunisch,et al.  The Numerical Solution of the Steady State Solid Fuel Ignition Model and Its Optimal Control , 2000, SIAM J. Sci. Comput..