Unconditionnally stable scheme for Riccati equation

TL;DR

This paper introduces an unconditionally stable numerical scheme for solving matrix Riccati equations in control problems, ensuring positive definiteness at each step and demonstrating convergence and effectiveness through numerical tests.

Contribution

The paper proposes a novel unconditionally stable numerical scheme for matrix Riccati equations that guarantees positive definiteness and convergence, validated by numerical experiments.

Findings

Scheme is unconditionally stable and preserves positive definiteness.

Convergence is proven in the scalar case.

Numerical experiments confirm effectiveness on classical test cases.

Abstract

We present a numerical scheme for the resolution of matrix Riccati equation used in control problems. The scheme is unconditionnally stable and the solution is definite positive at each time step of the resolution. We prove the convergence in the scalar case and present several numerical experiments for classical test cases.