Probability distribution modelling to improve stability in nonlinear MIMO control

Randa Herzallah; David Lowe

doi:10.1109/CCA.2003.1223139

Probability distribution modelling to improve stability in nonlinear MIMO control

Randa Herzallah, David Lowe

Research output: Chapter in Book/Published conference output › Conference publication

Abstract

We consider the direct adaptive inverse control of nonlinear multivariable systems with different delays between every input-output pair. In direct adaptive inverse control, the inverse mapping is learned from examples of input-output pairs. This makes the obtained controller sub optimal, since the network may have to learn the response of the plant over a larger operational range than necessary. Moreover, in certain applications, the control problem can be redundant, implying that the inverse problem is ill posed. In this paper we propose a new algorithm which allows estimating and exploiting uncertainty in nonlinear multivariable control systems. This approach allows us to model strongly non-Gaussian distribution of control signals as well as processes with hysteresis. The proposed algorithm circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider.

Original language	English
Title of host publication	Proceedings of 2003 IEEE Conference on Control Applications (CCA)
Publisher	IEEE
Pages	954-959
Number of pages	6
Volume	2
ISBN (Print)	0-7803-772-9
DOIs	https://doi.org/10.1109/CCA.2003.1223139
Publication status	Published - 25 Jun 2003
Event	2003 IEEE Conference on Control Applications - Istanbul, Turkey Duration: 23 Jun 2003 → 25 Jun 2003

Conference

Conference	2003 IEEE Conference on Control Applications
Abbreviated title	CCA 2003
Country/Territory	Turkey
City	Istanbul
Period	23/06/03 → 25/06/03

Bibliographical note

©2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

Keywords

statistical distributions
multivariable control systems
stability
MIMO systems
nonlinear control systems
hysteresis
dynamic programming
neural nets
probability distribution modelling
nonlinear MIMO control
direct adaptive inverse con

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10.1109/CCA.2003.1223139

Probability distribution modelling to improve stability in nonlinear MIMO control
©2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
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Cite this

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title = "Probability distribution modelling to improve stability in nonlinear MIMO control",

abstract = "We consider the direct adaptive inverse control of nonlinear multivariable systems with different delays between every input-output pair. In direct adaptive inverse control, the inverse mapping is learned from examples of input-output pairs. This makes the obtained controller sub optimal, since the network may have to learn the response of the plant over a larger operational range than necessary. Moreover, in certain applications, the control problem can be redundant, implying that the inverse problem is ill posed. In this paper we propose a new algorithm which allows estimating and exploiting uncertainty in nonlinear multivariable control systems. This approach allows us to model strongly non-Gaussian distribution of control signals as well as processes with hysteresis. The proposed algorithm circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider.",

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author = "Randa Herzallah and David Lowe",

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AU - Lowe, David

N1 - ©2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

PY - 2003/6/25

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N2 - We consider the direct adaptive inverse control of nonlinear multivariable systems with different delays between every input-output pair. In direct adaptive inverse control, the inverse mapping is learned from examples of input-output pairs. This makes the obtained controller sub optimal, since the network may have to learn the response of the plant over a larger operational range than necessary. Moreover, in certain applications, the control problem can be redundant, implying that the inverse problem is ill posed. In this paper we propose a new algorithm which allows estimating and exploiting uncertainty in nonlinear multivariable control systems. This approach allows us to model strongly non-Gaussian distribution of control signals as well as processes with hysteresis. The proposed algorithm circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider.

AB - We consider the direct adaptive inverse control of nonlinear multivariable systems with different delays between every input-output pair. In direct adaptive inverse control, the inverse mapping is learned from examples of input-output pairs. This makes the obtained controller sub optimal, since the network may have to learn the response of the plant over a larger operational range than necessary. Moreover, in certain applications, the control problem can be redundant, implying that the inverse problem is ill posed. In this paper we propose a new algorithm which allows estimating and exploiting uncertainty in nonlinear multivariable control systems. This approach allows us to model strongly non-Gaussian distribution of control signals as well as processes with hysteresis. The proposed algorithm circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider.

KW - statistical distributions

KW - multivariable control systems

KW - stability

KW - MIMO systems

KW - nonlinear control systems

KW - hysteresis

KW - dynamic programming

KW - neural nets

KW - probability distribution modelling

KW - nonlinear MIMO control

KW - direct adaptive inverse con

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M3 - Conference publication

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SP - 954

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BT - Proceedings of 2003 IEEE Conference on Control Applications (CCA)

PB - IEEE

T2 - 2003 IEEE Conference on Control Applications

Y2 - 23 June 2003 through 25 June 2003

ER -

Probability distribution modelling to improve stability in nonlinear MIMO control

Abstract

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Bibliographical note

Keywords

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