### Abstract

This paper presents an output feedback control law, hereafter called the Linear Quadratic Random Delay Compensator (LQRDC), for application to processes that are subjected to randomly varying distributed delays. LQRDC is synthesized in the stochastic setting based on dynamic programming. The closed-loop LQRDC system includes the plant dynamics, state estimator and delayed control commands, and is constructed in the sensor-time frame which may be time-skewed relative to the controller-time frame. A pair of discrete-time modified matrix Riccati equations and a pair of matrix Lyapunov equations are constructed by using Lagrangian multipliers and the matrix minimum principle. The performance cost is formulated as the conditional expectation of a quadratic functional adjoined with an equality constraint involving the dynamic of the conditional covariance of the closed-loop system state.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Editors | Anon |

State | Published - Dec 1 1996 |

Event | Proceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4) - Kobe, Jpn Duration: Dec 11 1996 → Dec 13 1996 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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Volume | 1 |

ISSN (Print) | 0191-2216 |

### Other

Other | Proceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4) |
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City | Kobe, Jpn |

Period | 12/11/96 → 12/13/96 |

### Fingerprint

### 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*(Proceedings of the IEEE Conference on Decision and Control; Vol. 1).

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*Proceedings of the IEEE Conference on Decision and Control.*Proceedings of the IEEE Conference on Decision and Control, vol. 1, Proceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4), Kobe, Jpn, 12/11/96.

**Stochastic optimal control under randomly varying distributed delays.** / Tsai, Nan Chyuan; Ray, Asok.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Stochastic optimal control under randomly varying distributed delays

AU - Tsai, Nan Chyuan

AU - Ray, Asok

PY - 1996/12/1

Y1 - 1996/12/1

N2 - This paper presents an output feedback control law, hereafter called the Linear Quadratic Random Delay Compensator (LQRDC), for application to processes that are subjected to randomly varying distributed delays. LQRDC is synthesized in the stochastic setting based on dynamic programming. The closed-loop LQRDC system includes the plant dynamics, state estimator and delayed control commands, and is constructed in the sensor-time frame which may be time-skewed relative to the controller-time frame. A pair of discrete-time modified matrix Riccati equations and a pair of matrix Lyapunov equations are constructed by using Lagrangian multipliers and the matrix minimum principle. The performance cost is formulated as the conditional expectation of a quadratic functional adjoined with an equality constraint involving the dynamic of the conditional covariance of the closed-loop system state.

AB - This paper presents an output feedback control law, hereafter called the Linear Quadratic Random Delay Compensator (LQRDC), for application to processes that are subjected to randomly varying distributed delays. LQRDC is synthesized in the stochastic setting based on dynamic programming. The closed-loop LQRDC system includes the plant dynamics, state estimator and delayed control commands, and is constructed in the sensor-time frame which may be time-skewed relative to the controller-time frame. A pair of discrete-time modified matrix Riccati equations and a pair of matrix Lyapunov equations are constructed by using Lagrangian multipliers and the matrix minimum principle. The performance cost is formulated as the conditional expectation of a quadratic functional adjoined with an equality constraint involving the dynamic of the conditional covariance of the closed-loop system state.

UR - http://www.scopus.com/inward/record.url?scp=0030377956&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030377956&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:0030377956

T3 - Proceedings of the IEEE Conference on Decision and Control

BT - Proceedings of the IEEE Conference on Decision and Control

A2 - Anon, null

ER -