Exact controllability of semilinear evolution systems and its application

Journal of Optimization Theory and Applications

Volumn 107, Issue 2, 2000, Pages 415-432

  Zhang, X ^a,b  

^a FUDAN UNIVERSITY   (China)

^b SICHUAN UNIVERSITY   (China)

Author keywords

Exact controllability; Inequalities; Observability; Semilinear systems

Indexed keywords

CONTROLLABILITY; FIXED POINT ARITHMETIC;

CONTRACTION MAPPING PRINCIPLES; EVOLUTION SYSTEMS; EXACT CONTROLLABILITY; FIRST ORDER SYSTEMS; INEQUALITY; ITS APPLICATIONS; SEMILINEAR; SEMILINEAR EVOLUTION; SEMILINEAR SYSTEM; SYSTEM APPLICATIONS;

OBSERVABILITY;

EID: 0034348661     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026460831701     Document Type: Article

References (23)

1. 1. ZHANG, X., Exact Controllability of Semilinear Distributed Parameter Systems and Some Related Problems, Fudan University, PhD Thesis, 1998.
2. 2. PAZY, A., Semigroup of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, NY, 1983.
3. 3. BARDOS, C., LEBEAU, G., and RAUCH, J., Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary, SIAM Journal on Control and Optimization, Vol. 30, pp. 1024-1065, 1992.
4. 4. BENSOUSSAN, A., On the General Theory of Exact Controllability for Skew-Symmetric Operators, Acta Applicandae Mathematicae, Vol. 20, pp. 197-229, 1990.
5. 5. FURSIKOV, A. V., and IMANUVILOV, O. Y., Controllability of Evolution Equations, Lecture Notes, Research Institute of Mathematics, Seoul National University, Seoul, Korea, Vol. 34, 1994.
6. 6. KOMORNIK, V., Exact Controllability and Stabilization (Multiplier Method), John Wiley and Sons, Masson, Paris, France, 1995.
7. 7. LI, X., and YONG, J., Optimal Control Theory for Infinite-Dimensional Systems, Birkhäuser, Boston, Massachusetts, 1995.
8. 8. LIONS, J. L., Contrôlabilité Exacte, Perturbations et Systémes Distribués, Vol. 1, Recherches en Mathématiques Appliquées, Masson, Paris, France, Vol. 8, 1988.
9. 9. LIU, K., Locally Distributed Control and Damping for Conservative Systems, SIAM Journal on Control and Optimization, Vol. 35, pp. 1574-1590, 1997.
10. 10. RUSSELL, D. L., Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Problems, SIAM Review, Vol. 20, pp. 639-739, 1978.
11. 11. FABRE, C., PUEL, J. P., and ZUAZUA, E., Boundary Approximate Controllability for Semilinear Heat Equations, Lecture Notes on Control and Information Sciences, Springer Verlag, Berlin, Germany, Vol. 185, pp. 524-530, 1992.
12. 12. ZHOU, H., Approximate Controllability for a Class of Semilinear Abstract Equations, SIAM Journal on Control and Optimization, Vol. 21, pp. 551-555, 1983.
13. 13. CHEWNING, W. C., Controllability of the Nonlinear Wave Equation in Several Space Variables, SIAM Journal on Control and Optimization, Vol. 14, pp. 19-25, 1975.
14. 14. FATTORINI, H. O., Local Controllability of a Nonlinear Wave Equation, Mathematical System Theory, Vol. 9, pp. 340, 1975.
15. 15. HERMES, H., Controllability and Singular Problems, SIAM Journal on Control, Vol. 2, pp. 241-260, 1965.
16. 16. LUKES, D. L., Global Controllability of Nonlinear Systems, SIAM Journal on Control and Optimization, Vol. 25, pp. 715-722, 1987.
17. 17. MARKUS, L., Controllability of Semilinear Control Systems, SIAM Journal on Control, Vol. 3, pp. 78-90, 1965.
18. 18. ZUAZUA, E., Exact Controllability for the Semilinear Wave Equations, Journal de Mathématiques Pures et Appliquées, Vol. 59, pp. 1-31, 1990.
19. 19. ZUAZUA, E., Exact Boundary Controllability for the Semilinear Wave Equation, Nonlinear Partial Differential Equations and Their Applications, Edited by H. Brezis and J. L. Lions, Pitman, Vol. 10, pp. 357-391, 1991.
20. 20. ZUAZUA, E., Exact Controllability for Semilinear Wave Equations in One Space Dimension, Annales de l'Institut Henri Poincaré: Analyse Non Linéaire, Vol. 10, pp. 109-129, 1993.
21. 21. CARMICHAEL, N., and QUINN, M. D., Fixed Point Methods in Nonlinear Control, Lecture Notes in Control and Information Sciences, Springer Verlag, Berlin, Germany, Vol. 75, pp. 24-51, 1984.
22. 22. SEIDMAN, T. I., Invariance of the Reachable Set under Nonlinear Perturbations, SIAM Journal on Control and Optimization, Vol. 25, pp. 1173-1191, 1985.
23. 23. LASIECKA, I., and TRIGGIANI, R., Exact Controllability of Semilinear Abstract Systems with Applications to Waves and Plates Boundary Control Problems, Applied Mathematics and Optimization, Vol. 23, pp. 109-154, 1991.