Adaptive dynamic inversion via time-scale separation

Naira Hovakimyan; Eugene Lavretsky; Chengyu Cao

doi:10.1109/TNN.2008.2001221

Adaptive dynamic inversion via time-scale separation

Naira Hovakimyan, Eugene Lavretsky, Chengyu Cao

Research output: Contribution to journal › Article › peer-review

Abstract

This paper presents a full state feedback adaptive dynamic inversion method for uncertain systems that depend nonlinearly upon the control input. Using a specialized set of basis functions that respect the monotonic property of the system nonlinearities with respect to control input, a state predictor is defined for derivation of the adaptive laws. The adaptive dynamic inversion controller is defined as a solution of a fast dynamical equation, which achieves time-scale separation between the state predictor and the controller dynamics. Lyapunov-based adaptive laws ensure that the predictor tracks the state of the nonlinear system with bounded errors. As a result, the system state tracks the desired reference model with bounded errors. Benefits of the proposed design method are demonstrated using Van der Pol dynamics with nonlinear control input.

Original language	English (US)
Pages (from-to)	1702-1711
Number of pages	10
Journal	IEEE Transactions on Neural Networks
Volume	19
Issue number	10
DOIs	https://doi.org/10.1109/TNN.2008.2001221
State	Published - 2008

Keywords

Adaptive control
Nonaffine systems
Time-scale separation
Ultimate boundedness

ASJC Scopus subject areas

Software
Computer Science Applications
Computer Networks and Communications
Artificial Intelligence

Online availability

10.1109/TNN.2008.2001221

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title = "Adaptive dynamic inversion via time-scale separation",

abstract = "This paper presents a full state feedback adaptive dynamic inversion method for uncertain systems that depend nonlinearly upon the control input. Using a specialized set of basis functions that respect the monotonic property of the system nonlinearities with respect to control input, a state predictor is defined for derivation of the adaptive laws. The adaptive dynamic inversion controller is defined as a solution of a fast dynamical equation, which achieves time-scale separation between the state predictor and the controller dynamics. Lyapunov-based adaptive laws ensure that the predictor tracks the state of the nonlinear system with bounded errors. As a result, the system state tracks the desired reference model with bounded errors. Benefits of the proposed design method are demonstrated using Van der Pol dynamics with nonlinear control input.",

keywords = "Adaptive control, Nonaffine systems, Time-scale separation, Ultimate boundedness",

author = "Naira Hovakimyan and Eugene Lavretsky and Chengyu Cao",

note = "Funding Information: Manuscript received July 8, 2007; revised January 29, 2008; accepted June 4, 2008. First published August 26, 2008; current version published October 8, 2008. This work was supported by the United States Air Force under Contracts FA9550-05-1-0157 and FA9550-04-C-0047. N. Hovakimyan is with the Department of Mechanical Science and Engineering of University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA (e-mail: nhovakim@illinois.edu). E. Lavretsky is with Phantom Works, The Boeing Company, Huntington Beach, CA 92649 USA (e-mail: eugene.lavretsky@boeing.com). C. Cao is with the University of Connecticut, Storrs, CT 06269 USA (e-mail: ccao@uconn.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNN.2008.2001221",

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AU - Hovakimyan, Naira

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AU - Cao, Chengyu

N1 - Funding Information: Manuscript received July 8, 2007; revised January 29, 2008; accepted June 4, 2008. First published August 26, 2008; current version published October 8, 2008. This work was supported by the United States Air Force under Contracts FA9550-05-1-0157 and FA9550-04-C-0047. N. Hovakimyan is with the Department of Mechanical Science and Engineering of University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA (e-mail: nhovakim@illinois.edu). E. Lavretsky is with Phantom Works, The Boeing Company, Huntington Beach, CA 92649 USA (e-mail: eugene.lavretsky@boeing.com). C. Cao is with the University of Connecticut, Storrs, CT 06269 USA (e-mail: ccao@uconn.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNN.2008.2001221

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N2 - This paper presents a full state feedback adaptive dynamic inversion method for uncertain systems that depend nonlinearly upon the control input. Using a specialized set of basis functions that respect the monotonic property of the system nonlinearities with respect to control input, a state predictor is defined for derivation of the adaptive laws. The adaptive dynamic inversion controller is defined as a solution of a fast dynamical equation, which achieves time-scale separation between the state predictor and the controller dynamics. Lyapunov-based adaptive laws ensure that the predictor tracks the state of the nonlinear system with bounded errors. As a result, the system state tracks the desired reference model with bounded errors. Benefits of the proposed design method are demonstrated using Van der Pol dynamics with nonlinear control input.

AB - This paper presents a full state feedback adaptive dynamic inversion method for uncertain systems that depend nonlinearly upon the control input. Using a specialized set of basis functions that respect the monotonic property of the system nonlinearities with respect to control input, a state predictor is defined for derivation of the adaptive laws. The adaptive dynamic inversion controller is defined as a solution of a fast dynamical equation, which achieves time-scale separation between the state predictor and the controller dynamics. Lyapunov-based adaptive laws ensure that the predictor tracks the state of the nonlinear system with bounded errors. As a result, the system state tracks the desired reference model with bounded errors. Benefits of the proposed design method are demonstrated using Van der Pol dynamics with nonlinear control input.

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Adaptive dynamic inversion via time-scale separation

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