Convergence of Galerkin approximations for operator Riccati equations - a nonlinear evolution equation approach

DOI10.1016/0022-247X(91)90035-XzbMath0717.65064OpenAlexW2162465589MaRDI QIDQ2638737

I. G. Rosen

Publication date: 1991

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(91)90035-x

zbMATH Keywords

convergenceheat equationHilbert spaceHilbert-Schmidt operatorsGalerkin approximationslinear quadratic optimal control probleminfinite-dimensional operator Riccati differential equations

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Existence theories for optimal control problems involving ordinary differential equations (49J15) Numerical solutions to equations with linear operators (65J10) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Existence theories for optimal control problems involving partial differential equations (49J20) Linear differential equations in abstract spaces (34G10) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

Related Items (10)

The persistence of ideal shock waves ⋮ Affine pure-jump processes on positive Hilbert-Schmidt operators ⋮ Multiscale Differential Riccati Equations for Linear Quadratic Regulator Problems ⋮ Role of numerical range in approximation-solvability of nonlinear functional equations ⋮ Phi-pseudo-monotonicity and approximation-solvability of nonlinear equations ⋮ Phi-Stable Operators and Inner Approximation-Solvability ⋮ Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data ⋮ A Max-plus Dual Space Fundamental Solution for a Class of Operator Differential Riccati Equations ⋮ Joint Online Parameter Estimation and Optimal Sensor Placement for the Partially Observed Stochastic Advection-Diffusion Equation ⋮ Sparse Grid Approximation of the Riccati Operator for Closed Loop Parabolic Control Problems with Dirichlet Boundary Control

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