Funnel control for boundary control systems

Puche, Marc; Reis, Timo; Schwenninger, Felix L.

doi:10.3934/eect.2020079

Cited by 11 publications

(8 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For such systems, the feasibility of funnel control has to be investigated directly for the (nonlinear) closed-loop system, see e.g. [48] for a boundary controlled heat equation, [47] for a general class of boundary control systems, [6] for the monodomain equations (which represents defibrillation processes of the human heart) and [4] for the Fokker-Planck equation corresponding to the Ornstein-Uhlenbeck process.…”

Section: Resultsmentioning

confidence: 99%

Funnel control of nonlinear systems

Berger

Ilchmann

Ryan

2021

Math. Control Signals Syst.

View full text Add to dashboard Cite

Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by r-th-order functional differential equations, encompassing inter alia systems with unknown “control direction” and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic accuracy objectives. Two fundamental properties underpin the system class: bounded-input bounded-output stable internal dynamics, and a high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems).

show abstract

Section: Resultsmentioning

confidence: 99%

Funnel control of nonlinear systems

Berger

Ilchmann

Ryan

2021

Math. Control Signals Syst.

View full text Add to dashboard Cite

show abstract

“…For such systems, the feasibility of funnel control has to be investigated directly for the (nonlinear) closed-loop system, see e.g. [49] for a boundary controlled heat equation, [48] for a general class of boundary control systems, [6] for the monodomain equations (which represents defibrillation processes of the human heart) and [4] for the Fokker-Planck equation corresponding to the Ornstein-Uhlenbeck process.…”

Section: Discussionmentioning

confidence: 99%

Funnel control of nonlinear systems

Berger¹,

Ilchmann²,

Ryan³

2020

Preprint

View full text Add to dashboard Cite

Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by r-th order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic performance objectives. Two fundamental properties underpin the system class: boundedinput bounded-output stable internal dynamics, and a weak high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems).

show abstract

“…On the other hand, not even every linear, infinite-dimensional system has a well-defined (integer-valued) relative degree: In that case, results as in [18,1] cannot be applied. Instead, the feasibility of funnel control has to be investigated directly for the (nonlinear) closed-loop system, see [26] for a boundary controlled heat equation and [25] for a general class of boundary control systems.…”

Section: Introductionmentioning

confidence: 99%

Funnel control in the presence of infinite-dimensional internal dynamics

Berger

Puche

Schwenninger

2020

Systems & Control Letters

Self Cite

View full text Add to dashboard Cite

We consider output trajectory tracking for a class of uncertain nonlinear systems whose internal dynamics may be modelled by infinite-dimensional systems which are bounded-input, bounded-output stable. We describe under which conditions these systems belong to an abstract class for which funnel control is known to be feasible. As an illustrative example, we show that for a system whose internal dynamics are modelled by a transport equation, which is not exponentially stable, we obtain prescribed performance of the tracking error.

show abstract

Funnel control for boundary control systems

Cited by 11 publications

References 21 publications

Funnel control of nonlinear systems

Funnel control of nonlinear systems

Funnel control of nonlinear systems

Funnel control in the presence of infinite-dimensional internal dynamics

Contact Info

Product

Resources

About