On Practical Fixed-Time Convergence for Differential Riccati Equations

Sergiy Zhuk (1) , Andrey Polyakov (2)

1 IBM Research - Ireland
2 VALSE - Finite-time control and estimation for distributed systems

Sufficient conditions for fixed-time convergence of matrix differential Riccati equations towards an ellipsoid in the space of symmetric non-negative matrices are proposed. These conditions are based on the classical concept of uniform complete observability. The fixed-time convergence is demonstrated for the Riccati matrix and its inverse. This convergence is then used to design a globally convergent observer for bilinear chaotic differential equations (e.g. equations with zero Lyapunov exponents). Convergence of the observer is confirmed by numerical experiments with ODEs obtained by finite-difference discretization of a hyperbolic PDE in 1D (Burgers-Hopf equation).

Mots clés: nonlinear filtering; uniform observability; Lyapunov exponents; bilinear systems; Riccati equations; fixed-time convergence

Domaines: Automatique

Sergiy Zhuk, Andrey Polyakov. On Practical Fixed-Time Convergence for Differential Riccati Equations. 2019. ⟨hal-02390409⟩