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On Practical Fixed-Time Convergence for Differential Riccati Equations

Sergiy Zhuk 1 Andrey Polyakov 2
2 VALSE - Finite-time control and estimation for distributed systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : 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).
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Submitted on : Tuesday, December 3, 2019 - 9:42:22 AM
Last modification on : Thursday, March 24, 2022 - 3:43:01 AM
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Sergiy Zhuk, Andrey Polyakov. On Practical Fixed-Time Convergence for Differential Riccati Equations. 2019. ⟨hal-02390409⟩

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