JOURNAL BROWSE
Search
Advanced SearchSearch Tips
RICCATI EQUATION IN QUADRATIC OPTIMAL CONTROL PROBLEM OF DAMPED SECOND ORDER SYSTEM
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
RICCATI EQUATION IN QUADRATIC OPTIMAL CONTROL PROBLEM OF DAMPED SECOND ORDER SYSTEM
Ha, Junhong; Nakagiri, Shin-Ichi;
  PDF(new window)
 Abstract
This paper studies the properties of solutions of the Riccati equation arising from the quadratic optimal control problem of the general damped second order system. Using the semigroup theory, we establish the weak differential characterization of the Riccati equation for a general class of the second order distributed systems with arbitrary damping terms.
 Keywords
Riccati equation;quadratic optimal control problem;hyperbolic equation with damping term;
 Language
English
 Cited by
 References
1.
N. U. Ahmed and K. L. Teo, Optimal Control of Distributed Parameter Systems, North Holland, 1981.

2.
J. M. Ball, Strongly continuous semigroups, weak solutions, and the variation of con-stants formula, Proc. Amer. Math. Soc. 63 (1977), no. 2, 370-373.

3.
H. T. Banks, K. Ito, and Y. Wang, Well Posedness for damped second order systems with unbounded input operators, Differential Integral Equations 8 (1995), no. 3, 587-606.

4.
H. T. Banks, F. Kappel, and Y. Wang, Weak solutions and differentiability for size structured population models, Estimation and control of distributed parameter systems (Vorau, 1990), 35-50, Internat. Ser. Numer. Math., 100, Birkhauser, Basel, 1991.

5.
V. Barbu, Extended algebraic Riccati equations in the abstract hyperbolic case, Nonlinear Anal. 40 (2000), no. 1-8, Ser. A: Theory Methods, 105-129. crossref(new window)

6.
F. Bucci, A Dirichlet boundary control problem for the strongly damped wave equation, SIAM J. Control Optim. 30 (1992), no. 5, 1092-1100. crossref(new window)

7.
R. W. Carroll, Abstract Methods in Partial Differential Equstions, Harper and Row, New York, 1969.

8.
R. F. Curtain and A. J. Pritchard, Infinite Dimensional Linear Systems Theory, Lecture Notes in Control and Information Sciences, Springer-Verlag, Vol. 8, 1978.

9.
R. F. Curtain and Salamon, Finite dimensional compensators for infinite dimensional systems with unbounded input operators, SIAM J. Control Optim. 24 (1986), no. 4, 797-816. crossref(new window)

10.
R. Dautray and J. L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Springer-Verlag, Vol. 5, Evolution Problems, 1992.

11.
F. Flandoli, Riccati equation arising in a boundary control problem with distributed parameters, SIAM J. Control Optim. 22 (1984), no. 1, 76-86. crossref(new window)

12.
J. Ha, Optimal control problems for hyperbolic distributed parameter systems with damp-ing terms, Doctor Thesis, The Graduate School of Science and Technology, Kobe University, 1996, August.

13.
J. Ha and S. Nakagiri, Existence and regularity of weak solutions for semilinear second order evolution equations, Funkcial. Ekvac. 41 (1998), no. 1, 1-24.

14.
J. Ha, S. Nakagiri, and H. Tanabe, Frechet differentiability of solution mappings for semilinear second order evolution equations, J. Math. Anal. Appl. 346 (2008), no. 2, 374-383. crossref(new window)

15.
A. Haraux, Linear semigroups in Banach spaces, Semigroups, theory and applications, Vol. II (Trieste, 1984), 93-135, Pitman Res. Notes Math. Ser., 152, Longman Sci. Tech., Harlow, 1986.

16.
R. E. Kalman, Contributions to the theory of optimal control, Bol. Soc. Mat. Mexicana 5 (1960), 102-119.

17.
I. Lasiecka and R. Triggiani, Differential and Algebraic Riccati Equations with Appli-cation to Boundary/Point Control Problems: Continuous Theory and Approximation Theory, Lecture Notes in Control and Information Sciences, Springer-Verlag, Vol. 164, 1991.

18.
I. Lasiecka and R. Triggiani, Dirichlet boundary control problem for parabolic equations with quadratic cost: Analyticity and Riccati's feedback synthesis, SIAM J. Control Optim. 21 (1983), no. 1, 41-67. crossref(new window)

19.
I. Lasiecka and R. Triggiani, Control theory for partial differential equations: continuous and approximation theories. II. Abstract hyperbolic-like systems over a finite time horizon, Encyclopedia of Mathematics and its Applications, Vol. 75. Cambridge University Press, Cambridge, 2000.

20.
J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag Berlin Heidelberg New York, 1971.

21.
J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications I, II, Springer-Verlag Berlin Heidelberg New York, 1972.

22.
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983.

23.
A. J. Pritchard and D. Salamon, The linear quadratic control problem for infinite dimensional systems with unbounded input and output operators, SIAM J. Control Optim. 25 (1987), no. 1, 121-144. crossref(new window)

24.
H. Tanabe, Equations of Evolution, Pitman, London, 1979.

25.
R. Triggiani, Optimal quadratic boundary control problem for wave- and wave-like equa-tions with high internal damping: An abstract approach, Lecture Notes in Pure and Appl. Math., 165, Control of partial differential equations (Trento, 1993), 215-270, Dekker, New York, 1994.