### Abstract

This paper introduces the definition of the nonstandard linear discrete-time singularly perturbed system and then shows how to solve the corresponding linear-quadratic optimal control problem since the methodology that exists in the literature for the solution of the standard singularly perturbed discrete linear-quadratic optimal control problem can not be extended to the corresponding nonstandard counterpart. The solution of the optimal control problem is obtained in terms of the pure-slow and pure-fast, reduced-order, continuous-time, algebraic Riccati equations. An example is included to illustrate the efficiency of the proposed method.

Original language | English |
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Pages (from-to) | 163-174 |

Number of pages | 12 |

Journal | Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm |

Volume | 9 |

Issue number | 2 |

Publication status | Published - 2002 Jun 1 |

### Fingerprint

### Keywords

- Optimal control
- Order reduction
- Parallel computation
- Riccati equation
- Singular perturbation

### ASJC Scopus subject areas

- Applied Mathematics
- Discrete Mathematics and Combinatorics

### Cite this

**Optimal Control of Linear Nonstandard Singularly Perturbed Discrete Systems.** / Lim, Myo Taeg; Kang, Chung Gu; Kim, Beom S.

Research output: Contribution to journal › Article

*Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm*, vol. 9, no. 2, pp. 163-174.

}

TY - JOUR

T1 - Optimal Control of Linear Nonstandard Singularly Perturbed Discrete Systems

AU - Lim, Myo Taeg

AU - Kang, Chung Gu

AU - Kim, Beom S.

PY - 2002/6/1

Y1 - 2002/6/1

N2 - This paper introduces the definition of the nonstandard linear discrete-time singularly perturbed system and then shows how to solve the corresponding linear-quadratic optimal control problem since the methodology that exists in the literature for the solution of the standard singularly perturbed discrete linear-quadratic optimal control problem can not be extended to the corresponding nonstandard counterpart. The solution of the optimal control problem is obtained in terms of the pure-slow and pure-fast, reduced-order, continuous-time, algebraic Riccati equations. An example is included to illustrate the efficiency of the proposed method.

AB - This paper introduces the definition of the nonstandard linear discrete-time singularly perturbed system and then shows how to solve the corresponding linear-quadratic optimal control problem since the methodology that exists in the literature for the solution of the standard singularly perturbed discrete linear-quadratic optimal control problem can not be extended to the corresponding nonstandard counterpart. The solution of the optimal control problem is obtained in terms of the pure-slow and pure-fast, reduced-order, continuous-time, algebraic Riccati equations. An example is included to illustrate the efficiency of the proposed method.

KW - Optimal control

KW - Order reduction

KW - Parallel computation

KW - Riccati equation

KW - Singular perturbation

UR - http://www.scopus.com/inward/record.url?scp=0242543922&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242543922&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0242543922

VL - 9

SP - 163

EP - 174

JO - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

JF - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

SN - 1492-8760

IS - 2

ER -