Design of risk-sensitive optimal control for stochastic recurrent neural networks by using Hamilton-Jacobi-Bellman equation

Ziqian Liu; Nirwan Ansari; Miltiadis Kotinis; Stephen C. Shih

doi:10.1109/CDC.2010.5717009

Design of risk-sensitive optimal control for stochastic recurrent neural networks by using Hamilton-Jacobi-Bellman equation

Ziqian Liu, Nirwan Ansari, Miltiadis Kotinis, Stephen C. Shih

Electrical and Computer Engineering

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

Abstract

This paper presents a theoretical design for the stabilization of stochastic recurrent neural networks with respect to a risk-sensitive optimality criterion. This approach is developed by using the Hamilton-Jacobi-Bellman equation, Lyapunov technique, and inverse optimality, to obtain a risk-sensitive state feedback controller, which guarantees an achievable meaningful cost for a given risk-sensitivity parameter. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.

Original language	English (US)
Title of host publication	2010 49th IEEE Conference on Decision and Control, CDC 2010
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4151-4156
Number of pages	6
ISBN (Print)	9781424477456
DOIs	https://doi.org/10.1109/CDC.2010.5717009
State	Published - 2010
Event	49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, United States Duration: Dec 15 2010 → Dec 17 2010

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	49th IEEE Conference on Decision and Control, CDC 2010
Country/Territory	United States
City	Atlanta
Period	12/15/10 → 12/17/10

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

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10.1109/CDC.2010.5717009

Cite this

Liu, Z., Ansari, N., Kotinis, M., & Shih, S. C. (2010). Design of risk-sensitive optimal control for stochastic recurrent neural networks by using Hamilton-Jacobi-Bellman equation. In 2010 49th IEEE Conference on Decision and Control, CDC 2010 (pp. 4151-4156). Article 5717009 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2010.5717009

Liu, Ziqian ; Ansari, Nirwan ; Kotinis, Miltiadis et al. / Design of risk-sensitive optimal control for stochastic recurrent neural networks by using Hamilton-Jacobi-Bellman equation. 2010 49th IEEE Conference on Decision and Control, CDC 2010. Institute of Electrical and Electronics Engineers Inc., 2010. pp. 4151-4156 (Proceedings of the IEEE Conference on Decision and Control).

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title = "Design of risk-sensitive optimal control for stochastic recurrent neural networks by using Hamilton-Jacobi-Bellman equation",

abstract = "This paper presents a theoretical design for the stabilization of stochastic recurrent neural networks with respect to a risk-sensitive optimality criterion. This approach is developed by using the Hamilton-Jacobi-Bellman equation, Lyapunov technique, and inverse optimality, to obtain a risk-sensitive state feedback controller, which guarantees an achievable meaningful cost for a given risk-sensitivity parameter. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.",

author = "Ziqian Liu and Nirwan Ansari and Miltiadis Kotinis and Shih, {Stephen C.}",

year = "2010",

doi = "10.1109/CDC.2010.5717009",

language = "English (US)",

isbn = "9781424477456",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "4151--4156",

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address = "United States",

note = "49th IEEE Conference on Decision and Control, CDC 2010 ; Conference date: 15-12-2010 Through 17-12-2010",

}

Liu, Z, Ansari, N, Kotinis, M & Shih, SC 2010, Design of risk-sensitive optimal control for stochastic recurrent neural networks by using Hamilton-Jacobi-Bellman equation. in 2010 49th IEEE Conference on Decision and Control, CDC 2010., 5717009, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 4151-4156, 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5717009

Design of risk-sensitive optimal control for stochastic recurrent neural networks by using Hamilton-Jacobi-Bellman equation. / Liu, Ziqian; Ansari, Nirwan; Kotinis, Miltiadis et al.
2010 49th IEEE Conference on Decision and Control, CDC 2010. Institute of Electrical and Electronics Engineers Inc., 2010. p. 4151-4156 5717009 (Proceedings of the IEEE Conference on Decision and Control).

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

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AU - Kotinis, Miltiadis

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N2 - This paper presents a theoretical design for the stabilization of stochastic recurrent neural networks with respect to a risk-sensitive optimality criterion. This approach is developed by using the Hamilton-Jacobi-Bellman equation, Lyapunov technique, and inverse optimality, to obtain a risk-sensitive state feedback controller, which guarantees an achievable meaningful cost for a given risk-sensitivity parameter. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.

AB - This paper presents a theoretical design for the stabilization of stochastic recurrent neural networks with respect to a risk-sensitive optimality criterion. This approach is developed by using the Hamilton-Jacobi-Bellman equation, Lyapunov technique, and inverse optimality, to obtain a risk-sensitive state feedback controller, which guarantees an achievable meaningful cost for a given risk-sensitivity parameter. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.

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SN - 9781424477456

T3 - Proceedings of the IEEE Conference on Decision and Control

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BT - 2010 49th IEEE Conference on Decision and Control, CDC 2010

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 49th IEEE Conference on Decision and Control, CDC 2010

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ER -

Liu Z, Ansari N, Kotinis M, Shih SC. Design of risk-sensitive optimal control for stochastic recurrent neural networks by using Hamilton-Jacobi-Bellman equation. In 2010 49th IEEE Conference on Decision and Control, CDC 2010. Institute of Electrical and Electronics Engineers Inc. 2010. p. 4151-4156. 5717009. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2010.5717009

Design of risk-sensitive optimal control for stochastic recurrent neural networks by using Hamilton-Jacobi-Bellman equation

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