Forwarding design for stabilization of a coupled transport equation-ODE with a cone-bounded input nonlinearity

Marx, Swann; Brivadis, Lucas; Astolfi, Daniele

doi:10.1109/cdc42340.2020.9304178

“…Then, following the proof of [22,Theorem 2], one can prove that w(t, x) = 0, which shows that (v) holds for (11). Moreover, from standard Sobolev injections results, the canonical embedding from D(S) into H is compact, i.e., S has compact resolvent.…”

Section: Remarkmentioning

confidence: 77%

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

Marx

¹

,

Brivadis

²

,

Astolfi

³

2021

Math. Control Signals Syst.

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14

0

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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 openloop 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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“…See also [21]. △ Remark 2 (Nonlinear design and small control) Note that the feedback law ( 17) can be also modified in…”

mentioning

confidence: 99%

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

Marx,

Brivadis,

Astolfi

2020

Preprint

Self Cite

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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 openloop 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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Repetitive control design based on forwarding for nonlinear minimum-phase systems

Astolfi

¹

,

Marx

²

,

Wouw

³

2021

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We propose a new design for a repetitive control scheme for nonlinear minimum-phase systems with arbitrary relative degree and globally Lipschitz nonlinearities. We represent the delay of the repetitive control scheme as a transport equation and we propose a new forwarding-based (partial) state-feedback design that uses not only the boundary information of the delay, but the entire state of the transport equation representing the delay. Through a rigorous mathematical analysis, we show that, from a theoretical point of view, asymptotic convergence of the desired regulated output can be achieved with the proposed control design.

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Forwarding design for stabilization of a coupled transport equation-ODE with a cone-bounded input nonlinearity

Cited by 4 publications

References 31 publications

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

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

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

Repetitive control design based on forwarding for nonlinear minimum-phase systems

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