Chapitre D'ouvrage Année : 2025

Some insights on the practical control of hyperbolic systems

Jean Auriol

Résumé

In this chapter, we present some recent developments in the practical control of hyperbolic systems. Although our primary focus lies on scalar balance laws, most of the results showcased herein can be extended to non-scalar systems or interconnected configurations. The control strategies proposed in this chapter are said to be practical as they are constructive, easily implementable, and offer degrees of freedom that can be tailored to satisfy specific performance requirements. We first design finite-time stabilizing controllers using the backstepping approach. Then, we show that finite-time stabilization can yield vanishing robustness margins. Therefore, we introduce tuning parameters in the design to allow for potential trade-offs between performance specifications (e.g., robustness and convergence rate). Finally, we consider possible approximations of the control law in view of practical implementation and give generic conditions to guarantee closedloop stability.

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hal-04315386 , version 1 (30-11-2023)

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Jean Auriol. Some insights on the practical control of hyperbolic systems. Control Theory and Inverse Problems, Springer Nature Switzerland, pp.21-57, 2025, Trends in Mathematics, ⟨10.1007/978-3-031-68046-5_2⟩. ⟨hal-04315386⟩
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