Stochastic optimal control under randomly varying distributed delays

Nan Chyuan Tsai, Asok Ray

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)

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 languageEnglish (US)
Title of host publicationProceedings of the IEEE Conference on Decision and Control
Editors Anon
StatePublished - Dec 1 1996
EventProceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4) - Kobe, Jpn
Duration: Dec 11 1996Dec 13 1996

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume1
ISSN (Print)0191-2216

Other

OtherProceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4)
CityKobe, Jpn
Period12/11/9612/13/96

Fingerprint

Riccati equations
Dynamic programming
Closed loop systems
Feedback control
Controllers
Sensors
Costs

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Tsai, N. C., & Ray, A. (1996). Stochastic optimal control under randomly varying distributed delays. In Anon (Ed.), Proceedings of the IEEE Conference on Decision and Control (Proceedings of the IEEE Conference on Decision and Control; Vol. 1).
Tsai, Nan Chyuan ; Ray, Asok. / Stochastic optimal control under randomly varying distributed delays. Proceedings of the IEEE Conference on Decision and Control. editor / Anon. 1996. (Proceedings of the IEEE Conference on Decision and Control).
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Tsai, NC & Ray, A 1996, Stochastic optimal control under randomly varying distributed delays. in Anon (ed.), 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.

Proceedings of the IEEE Conference on Decision and Control. ed. / Anon. 1996. (Proceedings of the IEEE Conference on Decision and Control; Vol. 1).

Research output: Chapter in Book/Report/Conference proceedingChapter

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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.

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Tsai NC, Ray A. Stochastic optimal control under randomly varying distributed delays. In Anon, editor, Proceedings of the IEEE Conference on Decision and Control. 1996. (Proceedings of the IEEE Conference on Decision and Control).