Approximation in Lqr Problems for Innnite Dimensional Systems with Unbounded Input Operators

We present a variational framework based on sesquilinear forms for Galerkin approximation techniques for state feedback control in problems governed by innnite dimensional dynamical systems. Both parabolic and second order in time, hyperbolic partial diierential equations with unbounded input and unbounded observation operators are included as special cases of our treatment.

[1]  R. Showalter.  Hilbert Space Methods for Partial Differential Equations , 1979, Electronic Journal of Differential Equations.

[2]  J. Gibson.  Linear-Quadratic Optimal Control of Hereditary Differential Systems: Infinite Dimensional Riccati Equations and Numerical Approximations , 1983 .

[3]  J. Lions,et al.  Non-homogeneous boundary value problems and applications , 1972 .

[4]  I. Lasiecka.  Unified theory for abstract parabolic boundary problems—a semigroup approach , 1980 .

[5]  Michel Sorine.  Sur le semi-groupe non lineaire associe a l'equation de Riccati , 1982 .

[6]  K. Ito,et al.  Linear quadratic optimal control problem for linear systems with unbounded input and output operators: numerical approximations , 1989 .

[7]  Chandrasekhar equations for infinite dimensional systems. II. Unbounded input and output case , 1988 .

[8]  R. Datko,et al.  Uniform Asymptotic Stability of Evolutionary Processes in a Banach Space , 1972 .

[9]  Y. Sakawa.  Feedback control of the second order evolution equations with damping , 1983, The 22nd IEEE Conference on Decision and Control.

[10]  Karl Kunisch,et al.  The linear regulator problem for parabolic systems , 1984 .

[11]  A. Aziz.  The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations , 1972 .

[12]  P. Grisvard.  Elliptic Problems in Nonsmooth Domains , 1985 .

[13]  Franco Flandoli,et al.  Algebraic Riccati equation arising in boundary control problems , 1985, 1985 24th IEEE Conference on Decision and Control.

[14]  Irena Lasiecka,et al.  Dirichlet boundary control problems for parabolic equations with quadratic cost: Analyticity and riccati's feedback synthesis , 1983 .

[15]  Kazufumi Ito,et al.  Strong convergence and convergence rates of approximating solutions for algebraic riccati equations in Hilbert spaces , 1987 .

[16]  D. Russell,et al.  A mathematical model for linear elastic systems with structural damping , 1982 .

[17]  田辺 広城,et al.  Equations of evolution , 1979 .

[18]  Tosio Kato.  Perturbation theory for linear operators , 1966 .

[19]  R. Triggiani,et al.  The regulator problem for parabolic equations with dirichlet boundary control , 1987 .