### Abstract

A generalized linear-quadratic optimal control problem for systems with delay is formulated. The optimal solution is given as a state feedback form which requires a solution of coupled infinite-dimensional Riccati equations. It is shown that the closed-loop system formed by the optimal state feedback control has some desirable sensitivity and robustness properties. The generalization exists in the state quadratic form of the cost functional, which makes it possible to discuss a pole location problem within the framework of the linear-quadratic optimal control problem. It is also shown that the generalized cost functional contains a special class of cost functionals for which the optimal control can be realized by solving only a finite-dimensional Riccati equation. Based on these results about the generalized linear-quadratic optimal control, a design method of feedback controls is proposed and an illustrative example is then presented.

Original language | English |
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Pages (from-to) | 773-780 |

Number of pages | 8 |

Journal | Automatica |

Volume | 24 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1988 |

### Fingerprint

### Keywords

- Control system design
- feedback control
- linear optimal regulator
- pole placement
- robustness
- time lag systems

### ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

*Automatica*,

*24*(6), 773-780. https://doi.org/10.1016/0005-1098(88)90053-2

**The linear-quadratic optimal control approach to feedback control design for systems with delay.** / Uchida, Kenko; Shimemura, E.; Kubo, T.; Abe, N.

Research output: Contribution to journal › Article

*Automatica*, vol. 24, no. 6, pp. 773-780. https://doi.org/10.1016/0005-1098(88)90053-2

}

TY - JOUR

T1 - The linear-quadratic optimal control approach to feedback control design for systems with delay

AU - Uchida, Kenko

AU - Shimemura, E.

AU - Kubo, T.

AU - Abe, N.

PY - 1988

Y1 - 1988

N2 - A generalized linear-quadratic optimal control problem for systems with delay is formulated. The optimal solution is given as a state feedback form which requires a solution of coupled infinite-dimensional Riccati equations. It is shown that the closed-loop system formed by the optimal state feedback control has some desirable sensitivity and robustness properties. The generalization exists in the state quadratic form of the cost functional, which makes it possible to discuss a pole location problem within the framework of the linear-quadratic optimal control problem. It is also shown that the generalized cost functional contains a special class of cost functionals for which the optimal control can be realized by solving only a finite-dimensional Riccati equation. Based on these results about the generalized linear-quadratic optimal control, a design method of feedback controls is proposed and an illustrative example is then presented.

AB - A generalized linear-quadratic optimal control problem for systems with delay is formulated. The optimal solution is given as a state feedback form which requires a solution of coupled infinite-dimensional Riccati equations. It is shown that the closed-loop system formed by the optimal state feedback control has some desirable sensitivity and robustness properties. The generalization exists in the state quadratic form of the cost functional, which makes it possible to discuss a pole location problem within the framework of the linear-quadratic optimal control problem. It is also shown that the generalized cost functional contains a special class of cost functionals for which the optimal control can be realized by solving only a finite-dimensional Riccati equation. Based on these results about the generalized linear-quadratic optimal control, a design method of feedback controls is proposed and an illustrative example is then presented.

KW - Control system design

KW - feedback control

KW - linear optimal regulator

KW - pole placement

KW - robustness

KW - time lag systems

UR - http://www.scopus.com/inward/record.url?scp=38249027583&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249027583&partnerID=8YFLogxK

U2 - 10.1016/0005-1098(88)90053-2

DO - 10.1016/0005-1098(88)90053-2

M3 - Article

VL - 24

SP - 773

EP - 780

JO - Automatica

JF - Automatica

SN - 0005-1098

IS - 6

ER -