Bilinear Optimal Control of the Velocity Term in a Kirchhoff Plate Equation

Journal of Mathematical Analysis and Applications

Volumn 238, Issue 2, 1999, Pages 451-467

  Bradley, Mary Elizabeth ^a   Lenhart, Suzanne ^b   Yong, Jiongmin ^c  

^a UNIVERSITY OF LOUISVILLE   (United States)

^b UNIVERSITY OF TENNESSEE   (United States)

^c FUDAN UNIVERSITY   (China)

Author keywords

Bilinear control; Kirchhoff plate; Optimal control

Indexed keywords

EID: 0001534477     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1999.6524     Document Type: Article

References (24)

1. J. M. Ball, J. E. Marsden, and M. Slemrod, Controllability for distributed bilinear systems, SIAM J. Control Optim. 20 (1982), 575-597.
2. J. M. Ball and M. Slemrod, Feedback stabilization of semilinear control systems, Appl. Math. Optim. 5 (1979), 169-179.
3. J. M. Ball and M. Slemrod, Nonharmonic Fourier series and the stabilization of distributed semilinear control systems, Commun. Pure Appl. Math. 32 (1979), 555-589.
4. M. E. Bradley, Global exponential decay rates for a Kirchhoff plate with boundary nonlinearities, Differential Integral Equations 7 (1994), 275-292.
5. M. E. Bradley and S. Lenhart, Bilinear optimal control of a Kirchhoff plate, Systems Control Lett. 22 (1994), 27-38.
6. M. E. Bradley and S. Lenhart, Bilinear optimal control of a Kirchhhoff plate via internal controllers, in "Modelling and Optimization of Distributed Parameter Systems: Applications to Engineering," pp. 233-240, Chapman and Hall, London, 1996.
7. W. Desch, I. Lasiecka, and W. Schappacher, Feedback boundary control problems for linear semigroups, Israel J. Math. 51, No. 3 (1985), 177-207.
8. R. Fister, Optimal control of harvesting in a predator-prey parabolic system, Houston J. Math. 23 (1997), 341-355.
9. E. Hendrickson and I. Lasiecka, Boundary control problem for a dynamic Kirchhoff plate model with partial observation, in "Modelling and Optimization in Distributed Parameter Systems: Applications to Engineering," pp. 241-253, Chapman and Hall, London, 1996.
10. M. A. Horn and I. Lasiecka, Asymptotic behavior with respect to thickness of boundary stabilizing feedback for the Kirchhoff plate, J. Differential Equations 114 (1994), 396-433.
11. V. Komornik, On the boundary stabilization of plates, in "Metz Days," (M. Chipot and J. Saint Jean Paulin, Eds.), Pitman Research Notes in Mathematics, Vol. 249, pp. 105-111, Longman, Essex, UK.
12. V. Komornik, "Exact Controllability and Stabilization: The Multiplier Method, Wiley and Masson, New York, 1994.
13. J. E. Lagnese, Uniform boundary stabilization of homogeneous isotropic plates, Lecture Notes in Control and Inform. Sci. 102 (1987), 204-215.
14. J. E. Lagnese, "Boundary Stabilization of Thin Plates," SIAM, Philadelphia, 1989.
15. J. E. Lagnese, G. Leugering, and E. J. P. G. Schmidt, "Modeling, Analysis, and Control of Dynamic Elastic MultiLink Structures," Birkhaüser, Boston, 1994.
16. J. E. Lagnese and J. L. Lions, "Modelling Analysis and Control of Thin Plates," Masson, Paris, 1988.
17. Σ and homogeneous boundary displacement, J. Differential Equations 93 (1991), 62-101.
18. I. Lasiecka and R. Triggiani, Differential and algebraic Riccati equations with applications to boundary/point control problems: Continuous theory and approximation theory, in "Lecture Notes in Control and Information Sciences," 164, Springer-Verlag, New York, 1991.
19. I. Lasiecka and R. Triggiani, Regularity theory of hyperbolic equations with non-homogeneous Neumann boundary conditions. II. General boundary data, J. Differential Equations 94 (1991), 112-164.
20. X. Li and J. Yong, "Optimal Control Theory for Infinite Dimensional Systems," Birkhaüser, Boston, 1995.
21. M. Liang, Bilinear optimal control for a wave equation, Math. Models Methods Appl. Sci. 9 (1999), 45-68.
22. J. L. Lions, "Optimal Control of Systems governed by Partial Differential Equations," Springer-Verlag, Berlin, 1971.
23. A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," Springer-Verlag, New York, 1983.
24. H. L. Royden, "Real Analysis," Macmillan, New York, 1968.