# METT VIII - 8th Workshop on Matrix Equations and Tensor Techniques

Nov 6 – 8, 2019
MPI Magdeburg
Europe/Berlin timezone

## Differential Riccati Equation - A Galerkin Approach

Nov 7, 2019, 11:35 AM
25m
Prigogine (MPI Magdeburg)

### Prigogine

#### MPI Magdeburg

MPI for Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Magdeburg
Talk Talks

### Speaker

Maximilian Behr (Max Planck Institute for Dynamics of Complex Technical Systems)

### Description

We consider the differential Riccati equation,
$$\dot{X} = A^T X + X A - X BB^T X + C^T C.$$ The differential Riccati equation as well as the algebraic Riccati equation play important roles in applied mathematics like control theory and system theory. In our talk, we focus on the large-scale case. The numerical solution of these equation is challenging, in particular, because of the enormous amount of storage. A general approach, that has led to several algorithms, bases on an invariant subspace $Q \subseteq \mathbb R^{n\times n}$ such that $X(t) \in Q$ for all $t$. After identifying a suitable invariant subspace, we develop a Galerkin approach for the numerical solution of the differential Riccati equation. We review Davison-Maki methods for the numerical solution of the resulting equation.

### Primary author

Maximilian Behr (Max Planck Institute for Dynamics of Complex Technical Systems)

### Co-authors

Jan Heiland (Max Planck Institute for Dynamics of Complex Technical Systems)

### Presentation materials

There are no materials yet.