Predictive feedback boundary control of semilinear and quasilinear 2x2 hyperbolic PDE-ODE systems
We present a control design for semilinear and quasilinear 2x2 hyperbolic partial differential equations with the control input at one boundary and a nonlinear ordinary differential equation coupled to the other. The controller can be designed to asymptotically stabilize the system at an equilibrium...
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| Main Authors | , , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
19.05.2021
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| Subjects | |
| Online Access | Get full text |
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| Abstract | We present a control design for semilinear and quasilinear 2x2 hyperbolic
partial differential equations with the control input at one boundary and a
nonlinear ordinary differential equation coupled to the other. The controller
can be designed to asymptotically stabilize the system at an equilibrium or
relative to a reference signal. Two related but different controllers for
semilinear and general quasilinear systems are presented and the additional
challenges in quasilinear systems are discussed. Moreover, we present an
observer that estimates the distributed PDE state and the unmeasured ODE state
from measurements at the actuated boundary only, which can be used to also
solve the output feedback control problem. |
|---|---|
| AbstractList | We present a control design for semilinear and quasilinear 2x2 hyperbolic
partial differential equations with the control input at one boundary and a
nonlinear ordinary differential equation coupled to the other. The controller
can be designed to asymptotically stabilize the system at an equilibrium or
relative to a reference signal. Two related but different controllers for
semilinear and general quasilinear systems are presented and the additional
challenges in quasilinear systems are discussed. Moreover, we present an
observer that estimates the distributed PDE state and the unmeasured ODE state
from measurements at the actuated boundary only, which can be used to also
solve the output feedback control problem. |
| Author | Aamo, Ole Morten Strecker, Timm Cantoni, Michael |
| Author_xml | – sequence: 1 givenname: Timm surname: Strecker fullname: Strecker, Timm – sequence: 2 givenname: Ole Morten surname: Aamo fullname: Aamo, Ole Morten – sequence: 3 givenname: Michael surname: Cantoni fullname: Cantoni, Michael |
| BackLink | https://doi.org/10.48550/arXiv.2105.09039$$DView paper in arXiv |
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| Snippet | We present a control design for semilinear and quasilinear 2x2 hyperbolic
partial differential equations with the control input at one boundary and a
nonlinear... |
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| SubjectTerms | Mathematics - Optimization and Control |
| Title | Predictive feedback boundary control of semilinear and quasilinear 2x2 hyperbolic PDE-ODE systems |
| URI | https://arxiv.org/abs/2105.09039 |
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