Convergence of Galerkin Approximations for Operator Riccati Equations -- A Nonlinear Evolution Equation Approach
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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An approximation and convergence theory is developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation is treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result is proved for quasi-autonomous nonlinear evolution accretive operators which is then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of these results are illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.
- Numerical Mathematics