Forwarding techniques for the global stabilization of dissipative infinite-dimensional systems coupled with an ODE

Swann Marx; Lucas Brivadis; Daniele Astolfi

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arXiv · 2009.10379

Forwarding techniques for the global stabilization of dissipative infinite-dimensional systems coupled with an ODE

Swann Marx·Lucas Brivadis·Daniele Astolfi

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Abstract

This paper deals with the stabilization of a coupled system composed by an infinite-dimensional system and an ODE. Moreover, the control, which appears in the dynamics of the ODE, is subject to a general class of nonlinearities. Such a situation may arise, for instance, when the actuator admits a dynamics. The open-loop ODE is exponentially stable and the open-loop infinite-dimensional system is dissipative, i.e., the energy is nonincreasing, but its equilibrium point is not necessarily attractive. The feedback design is based on an extension of a finite-dimensional method, namely the forwarding method. We propose some sufficient conditions that imply the well-posedness and the global asymptotic stability of the closed-loop system. As illustration, we apply these results to a transport equation coupled with an ODE.

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Swann Marx, Lucas Brivadis, Daniele Astolfi. 2020-09-22. Forwarding techniques for the global stabilization of dissipative infinite-dimensional systems coupled with an ODE. https://arxiv.org/abs/2009.10379

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