### Abstract

This paper proposes a methodology for output feedback control of parabolic PDE systems with input constraints. Initially, Galerkin's method is used for the derivation of a finite-dimensional ODE system that captures the dominant dynamics of the PDE system. This ODE system is then used as the basis for the synthesis, via Lyapunov techniques, of stabilizing bounded output feedback control laws that use only measurements of the outputs and provide, at the same time, an explicit characterization of the set of admissible control actuator locations that can be used to guarantee closed-loop stability for a given initial condition. Precise conditions that guarantee stability of the constrained closed-loop parabolic PDE system are provided. The proposed output feedback design is shown to recover, asymptotically, the set of stabilizing actuator locations obtained under state feedback, as the separation between the fast and slow eigenvalues of the spatial differential operator increases.

Original language | English (US) |
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Pages (from-to) | 541-546 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 1 |

State | Published - Dec 1 2001 |

Event | 40th IEEE Conference on Decision and Control (CDC) - Orlando, FL, United States Duration: Dec 4 2001 → Dec 7 2001 |

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### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*,

*1*, 541-546.

}

*Proceedings of the IEEE Conference on Decision and Control*, vol. 1, pp. 541-546.

**Output feedback control of parabolic PDE systems with input constraints.** / El-Farra, Nael H.; Armaou, Antonios; Christofides, Panagiotis D.

Research output: Contribution to journal › Conference article

TY - JOUR

T1 - Output feedback control of parabolic PDE systems with input constraints

AU - El-Farra, Nael H.

AU - Armaou, Antonios

AU - Christofides, Panagiotis D.

PY - 2001/12/1

Y1 - 2001/12/1

N2 - This paper proposes a methodology for output feedback control of parabolic PDE systems with input constraints. Initially, Galerkin's method is used for the derivation of a finite-dimensional ODE system that captures the dominant dynamics of the PDE system. This ODE system is then used as the basis for the synthesis, via Lyapunov techniques, of stabilizing bounded output feedback control laws that use only measurements of the outputs and provide, at the same time, an explicit characterization of the set of admissible control actuator locations that can be used to guarantee closed-loop stability for a given initial condition. Precise conditions that guarantee stability of the constrained closed-loop parabolic PDE system are provided. The proposed output feedback design is shown to recover, asymptotically, the set of stabilizing actuator locations obtained under state feedback, as the separation between the fast and slow eigenvalues of the spatial differential operator increases.

AB - This paper proposes a methodology for output feedback control of parabolic PDE systems with input constraints. Initially, Galerkin's method is used for the derivation of a finite-dimensional ODE system that captures the dominant dynamics of the PDE system. This ODE system is then used as the basis for the synthesis, via Lyapunov techniques, of stabilizing bounded output feedback control laws that use only measurements of the outputs and provide, at the same time, an explicit characterization of the set of admissible control actuator locations that can be used to guarantee closed-loop stability for a given initial condition. Precise conditions that guarantee stability of the constrained closed-loop parabolic PDE system are provided. The proposed output feedback design is shown to recover, asymptotically, the set of stabilizing actuator locations obtained under state feedback, as the separation between the fast and slow eigenvalues of the spatial differential operator increases.

UR - http://www.scopus.com/inward/record.url?scp=0035710763&partnerID=8YFLogxK

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M3 - Conference article

AN - SCOPUS:0035710763

VL - 1

SP - 541

EP - 546

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -