# Reduced order controllers for Burgers' equation with a nonlinear observer

Jeanne Atwell; Jeffrey Borggaard; Belinda King

International Journal of Applied Mathematics and Computer Science (2001)

- Volume: 11, Issue: 6, page 1311-1330
- ISSN: 1641-876X

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topAtwell, Jeanne, Borggaard, Jeffrey, and King, Belinda. "Reduced order controllers for Burgers' equation with a nonlinear observer." International Journal of Applied Mathematics and Computer Science 11.6 (2001): 1311-1330. <http://eudml.org/doc/207557>.

@article{Atwell2001,

abstract = {A method for reducing controllers for systems described by partial differential equations (PDEs) is applied to Burgers' equation with periodic boundary conditions. This approach differs from the typical approach of reducing the model and then designing the controller, and has developed over the past several years into its current form. In earlier work it was shown that functional gains for the feedback control law served well as a dataset for reduced order basis generation via the proper orthogonal decomposition (POD)@. However, the test problem was the two-dimensional heat equation, a problem in which the physics dominates the system in such a way that controller efficacy is difficult to generalize. Here, we additionally incorporate a nonlinear observer by including the nonlinear terms of the state equation in the differential equation for the compensator.},

author = {Atwell, Jeanne, Borggaard, Jeffrey, King, Belinda},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {stabilized finite elements; Burgers' equation; reduced order controllers; minmax control design; proper orthogonal decomposition},

language = {eng},

number = {6},

pages = {1311-1330},

title = {Reduced order controllers for Burgers' equation with a nonlinear observer},

url = {http://eudml.org/doc/207557},

volume = {11},

year = {2001},

}

TY - JOUR

AU - Atwell, Jeanne

AU - Borggaard, Jeffrey

AU - King, Belinda

TI - Reduced order controllers for Burgers' equation with a nonlinear observer

JO - International Journal of Applied Mathematics and Computer Science

PY - 2001

VL - 11

IS - 6

SP - 1311

EP - 1330

AB - A method for reducing controllers for systems described by partial differential equations (PDEs) is applied to Burgers' equation with periodic boundary conditions. This approach differs from the typical approach of reducing the model and then designing the controller, and has developed over the past several years into its current form. In earlier work it was shown that functional gains for the feedback control law served well as a dataset for reduced order basis generation via the proper orthogonal decomposition (POD)@. However, the test problem was the two-dimensional heat equation, a problem in which the physics dominates the system in such a way that controller efficacy is difficult to generalize. Here, we additionally incorporate a nonlinear observer by including the nonlinear terms of the state equation in the differential equation for the compensator.

LA - eng

KW - stabilized finite elements; Burgers' equation; reduced order controllers; minmax control design; proper orthogonal decomposition

UR - http://eudml.org/doc/207557

ER -

## References

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