Abstract
This chapter proposes some non-trivial extensions of the classical high-gain observer designs for finite-dimensional nonlinear systems to some classes of infinite-dimensional ones, written as triangular systems of coupled first-order hyperbolic Partial Differential Equations (PDEs), where an observation of one only coordinate of the state is considered as the system’s output. These forms may include some epidemic models and tubular chemical reactors. To deal with this problem, depending on the number of distinct velocities of the hyperbolic system, direct and indirect observer designs are proposed. We first show intuitively how direct observer design can be applied to quasilinear partial integrodifferential hyperbolic systems of balance laws with a single velocity, as a natural extension of the finite-dimensional case. We then introduce an indirect approach for systems with distinct velocities (up to three velocities), where an infinite-dimensional state transformation first maps the system into suitable systems of PDEs and the convergence of the observer is subsequently exhibited in appropriate norms. This indirect approach leads to the use of spatial derivatives of the output in the observer dynamics.
The original version of this chapter was revised: The author’s name “Gildas Besançon” incorrect on the website, correction have been incorporated. The correction to this chapter is available at https://doi.org/10.1007/978-3-030-74628-5_10
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Change history
22 December 2021
The original version of the book was published with incorrect author’s name on website in chapter 5 have been corrected from Gildas Besan to Gildas Besançon.
The chapter and book have been updated with the changes.
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Kitsos, C., Besançon, G., Prieur, C. (2022). Contributions to the Problem of High-Gain Observer Design for Hyperbolic Systems. In: Jiang, ZP., Prieur, C., Astolfi, A. (eds) Trends in Nonlinear and Adaptive Control. Lecture Notes in Control and Information Sciences, vol 488. Springer, Cham. https://doi.org/10.1007/978-3-030-74628-5_5
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DOI: https://doi.org/10.1007/978-3-030-74628-5_5
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