### Abstract

This paper presents a new algorithm for the closed-loop H_{∞} composite control of weakly coupled bilinear systems with time-varying parameter uncertainties and exogenous disturbance using the successive Galerkin approximation (SGA). By using weak coupling theory, the robust H _{∞} control can be obtained from two reduced-order robust H _{∞} control problems in parallel. The H_{∞} control theory guarantees robust closed-loop performance but the resulting problem is difficult to solve for uncertain bilinear systems. In order to overcome the difficulties inherent in the H_{∞} control problem, two H _{∞} control laws are constructed in terms of the approximated solution to two independent Hamilton-Jacobi-Isaac equations using the SGA method. One of the purposes of this paper is to design a closed-loop parallel robust H_{∞} control law for the weakly coupled bilinear systems with parameter uncertainties using the SGA method. The other is to reduce the computational complexity when the SGA method is applied to the high order systems.

Original language | English |
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Pages (from-to) | 689-696 |

Number of pages | 8 |

Journal | International Journal of Control, Automation and Systems |

Volume | 4 |

Issue number | 6 |

Publication status | Published - 2006 Dec 1 |

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### Keywords

- Bilinear system
- H control
- Parallel processing
- Parameter uncertainty
- Successive Galerkin approximation
- Weak coupling

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

**Parallel robust H _{∞} control for weakly coupled bilinear systems with parameter uncertainties using successive Galerkin approximation.** / Kim, Young Joong; Lim, Myo Taeg.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Parallel robust H∞ control for weakly coupled bilinear systems with parameter uncertainties using successive Galerkin approximation

AU - Kim, Young Joong

AU - Lim, Myo Taeg

PY - 2006/12/1

Y1 - 2006/12/1

N2 - This paper presents a new algorithm for the closed-loop H∞ composite control of weakly coupled bilinear systems with time-varying parameter uncertainties and exogenous disturbance using the successive Galerkin approximation (SGA). By using weak coupling theory, the robust H ∞ control can be obtained from two reduced-order robust H ∞ control problems in parallel. The H∞ control theory guarantees robust closed-loop performance but the resulting problem is difficult to solve for uncertain bilinear systems. In order to overcome the difficulties inherent in the H∞ control problem, two H ∞ control laws are constructed in terms of the approximated solution to two independent Hamilton-Jacobi-Isaac equations using the SGA method. One of the purposes of this paper is to design a closed-loop parallel robust H∞ control law for the weakly coupled bilinear systems with parameter uncertainties using the SGA method. The other is to reduce the computational complexity when the SGA method is applied to the high order systems.

AB - This paper presents a new algorithm for the closed-loop H∞ composite control of weakly coupled bilinear systems with time-varying parameter uncertainties and exogenous disturbance using the successive Galerkin approximation (SGA). By using weak coupling theory, the robust H ∞ control can be obtained from two reduced-order robust H ∞ control problems in parallel. The H∞ control theory guarantees robust closed-loop performance but the resulting problem is difficult to solve for uncertain bilinear systems. In order to overcome the difficulties inherent in the H∞ control problem, two H ∞ control laws are constructed in terms of the approximated solution to two independent Hamilton-Jacobi-Isaac equations using the SGA method. One of the purposes of this paper is to design a closed-loop parallel robust H∞ control law for the weakly coupled bilinear systems with parameter uncertainties using the SGA method. The other is to reduce the computational complexity when the SGA method is applied to the high order systems.

KW - Bilinear system

KW - H control

KW - Parallel processing

KW - Parameter uncertainty

KW - Successive Galerkin approximation

KW - Weak coupling

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UR - http://www.scopus.com/inward/citedby.url?scp=33845258327&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33845258327

VL - 4

SP - 689

EP - 696

JO - International Journal of Control, Automation and Systems

JF - International Journal of Control, Automation and Systems

SN - 1598-6446

IS - 6

ER -