Abstract
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 L2-norm of the system states. An illustrative traffic flow regulation example shows the viability and importance of the proposed result.
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