Jean Auriol

Sondre Wiersdalen, Mike Pereira, Annika Lang et al.

This technical note examines exponential stability of the null solution to a large class of compartmental systems governed by ordinary differential equations. Sufficient conditions under which these systems admit a linear Lyapunov function are provided. The coefficients of the Lyapunov functions and the exponential decay rate they yield are obtained from an eigenvalue problem. For a special case of the system class considered, we derive an equivalence between attractivity of the null solution and the existence of a linear Lyapunov function.

Yihuai Zhang, Jean Auriol, Huan Yu

This paper addresses the problem of robust stabilization for linear hyperbolic Partial Differential Equations (PDEs) with Markov-jumping parameter uncertainty. We consider a 2 x 2 heterogeneous hyperbolic PDE and propose a control law using operator learning and the backstepping method. Specifically, the backstepping kernels used to construct the control law are approximated with neural operators (NO) in order to improve computational efficiency. The key challenge lies in deriving the stability conditions with respect to the Markov-jumping parameter uncertainty and NO approximation errors. The mean-square exponential stability of the stochastic system is achieved through Lyapunov analysis, indicating that the system can be stabilized if the random parameters are sufficiently close to the nominal parameters on average, and NO approximation errors are small enough. The theoretical results are applied to freeway traffic control under stochastic upstream demands and then validated through numerical simulations.

Yihuai Zhang, Jean Auriol, Nicolas Espitia et al.

This paper introduces a new framework for event-triggered gain scheduling applied to linear hyperbolic Partial Differential Equations (PDEs) with time- and space-varying coefficients. The approach leverages neural operators to address the challenges of real-time control in such systems. At each triggering time, the control input is designed using the classical static backstepping control law, while the gains of the boundary controller are updated according to the triggering mechanism and the spatial variation of the coefficients. Neural operators are employed to learn the mapping between the system parameters in the PDEs and the corresponding backstepping kernels. By integrating neural operators into the event-triggered framework, we eliminate the need to repeatedly solve complex kernel equations at every triggering instant, thereby reducing computational overhead while ensuring closed-loop stability. The proposed method is validated through theoretical analysis and numerical simulations, demonstrating its effectiveness and strong potential for real-time control of time-varying hyperbolic PDE systems.