State-constrained optimal control governed by non-well-posed parabolic differential equations

SIAM Journal on Control and Optimization

Volumn 40, Issue 5, 2002, Pages 1517-1539

  Wang, Gengsheng ^a   Wang, Lijuan ^a  

^a CENTRAL CHINA NORMAL UNIVERSITY   (China)

Author keywords

Non well posed parabolic equation; Optimal control; State constraint

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; INTEGRAL EQUATIONS; MAXIMUM PRINCIPLE; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; SET THEORY; THEOREM PROVING;

NON WELL POSED PARABOLIC EQUATION; SEMILINEAR PARABOLIC DIFFERENTIAL EQUATIONS; SMOOTH BOUNDARY; STATE CONSTRAINT;

OPTIMAL CONTROL SYSTEMS;

EID: 0036401919     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012900377006     Document Type: Article

References (18)

1. V. Barbu, Analysis and Control of Nonlinear Infinite Dimensional System, Academic Press, New York, 1993.
2. V. Barbu, Optimal Control of Variational Inequalities, Res. Notes Math. 100, Pitman, Boston, London, Melbourne, 1984.
3. V. Barbu, Exact controllability of the superlinear heat equation. Appl. Math. Optim., 42 (2000), pp. 73-89.
4. V. Barbu and N. Pavel, Optimal control problems with two point boundary conditions, J. Optim. Theory Appl., 77 (1993), pp. 51-78.
5. V. Barbu and N. Pavel, Periodic optimal control in Hilbert space, Appl. Math. Optim., 33 (1996), pp. 169-188.
6. M. Bergounioux and F. Troltzsch, Optimal conditions and generalized bang-bang principle for a state constrained semilinear parabolic problem, Numer. Funct. Anal. Optim., 15 (1996), pp. 517-537.
7. E. Casas, Pontryagin's principle for state-constrained boundary control problems of semilinear parabolic equations, SIAM, J. Control Optim., 35 (1997), pp. 1297-1327.
8. E. Casas and J. Yong, Maximum principle for state-constrained optimal control problems governed by quasilinear equations, Differential Integral Equations, 130 (1996), pp. 179-200.
9. F. H. Clarke, Optimization and Non smooth Analysis, John Wiley, New York, 1983.
10. H. Fattorini and H. Frankowska, Necessary conditions for infinite dimensional control problems, Math. Control Signals Systems, 4 (1991), pp. 225-257.
11. H. O. Fattorini and T. Murphy, Optimal problems for nonlinear parabolic boundary control systems, SIAM J. Control Optim., 32 (1994), pp. 1577-1596.
12. X. Li and J. Yong, Necessary conditions for optimal control of distributed parameter systems, SIAM J. Control Optim., 29 (1991), pp. 895-908.
13. X. Li and J. Yong, Optimal Control Theory for Infinite Dimensional Systems, Birkhäuser Boston, Cambridge, MA, 1995.
14. J. L. Lions, Some Methods in the Mathematical Analysis of Systems and Their Control, Science Press, Beijing, China, Gordon and Breach, Science Publishers, New York, 1981.
15. J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin, Heidelberg, New York, 1971.
16. G. Wang and S. Chen, Maximum principle for optimal control of some parabolic systems with two point boundary conditions, Numer. Funct. Anal. Optim., 20 (1999), pp. 163-174.
17. G. Wang, Optimal control of parabolic differential equations with two point boundary state constraints, SIAM J. Control Optim., 38 (2000), pp. 1639-1654.
18. G. Wang, Optimal control of parabolic variational inequality involving state constraint, Nonlinear Anal., 42 (2000), pp. 789-801.