Solution to the Algebraic Riccati Equation for Parabolic Systems

Résumé du livre

This paper presents an analytical solution to the operator algebraic Riccati equation (ARE) for selfadjoint parabolic systems. The solution to the operator ARE is important in the design of the steady state, on line filter for estimating the system's states. This analytical solution is derived by considering the operator analog of Potter's method of using the Hamiltonian system's eigenvectors and eigenvalues to solve a finite dimensional ARE. As an example of using this analytical solution, the steady state filtering error covariance for the 2D heat equation is studied.