Mean-square exponential stabilization of coupled hyperbolic systems with random parameters

Jean Auriol (1) , Mike Pereira (2) , Balazs Kulcsar (3)

1 L2S - Laboratoire des signaux et systèmes
2 GEOSCIENCES - Centre de Géosciences
3 Chalmers University of Technology [Göteborg]

In this paper, we consider a system of two coupled scalar-valued hyperbolic partial differential equations (PDEs) with random parameters. We formulate a stability condition under which the classical backstepping controller (designed for a nominal system whose parameters are constant) stabilizes the system. More precisely, we guarantee closed-loop mean-square exponential stability under random system parameter perturbations, provided the nominal parameters are sufficiently close to the stochastic ones on average. The proof is based on a Lyapunov analysis, the Lyapunov functional candidate describing the contraction of L 2-norm of the system states. An illustrative traffic flow regulation example shows the viability and importance of the proposed result.

Mots clés: PDE backstepping stochastic parameters exponential stability Lyapunov function; PDE; backstepping; stochastic parameters; exponential stability; Lyapunov function

Domaines: Equations aux dérivées partielles [math.AP]

Jean Auriol, Mike Pereira, Balazs Kulcsar. Mean-square exponential stabilization of coupled hyperbolic systems with random parameters. 22nd World Congress of the International Federation of Automatic Control (IFAC 2023), Jul 2023, Yokohama, France. ⟨10.1016/j.ifacol.2023.10.991⟩. ⟨hal-04051077v2⟩