Technical Notes and Correspondence

International Journal of Control, Automation and Systems 2009; 7(2): 311-317

Published online April 6, 2009

https://doi.org/10.1007/s12555-009-0218-4

© The International Journal of Control, Automation, and Systems

Stabilizing Adaptive Controller for Uncertain Dynamical Systems: An LMI Approach

Sandip Ghosh, Sarit K. Das, and Goshaidas Ray*

Indian Institute of Technology, India

Abstract

Adaptive stabilization of a class of linear systems with matched and unmatched uncertainties is considered in this paper. The proposed controller indeed stabilizes the uncertain system for any positive values of its non-adaptive gain that may be tuned to enhance dynamic response of system. The performance of uncertain system along with the Algebraic Riccati Equation that arises from the adaptive stabilizing controller is now formulated as a multi-objective Linear Matrix Inequality optimization problem. The decay rate and a factor governing the ultimate bound of the system states are considered to characterize the closed loop system performance. Finally, the effectiveness of the proposed controller is illustrated via stabilizing a mass-spring system.

Keywords Adaptive control, linear matrix inequality (LMI), uncertain systems.

Article

Technical Notes and Correspondence

International Journal of Control, Automation and Systems 2009; 7(2): 311-317

Published online April 1, 2009 https://doi.org/10.1007/s12555-009-0218-4

Copyright © The International Journal of Control, Automation, and Systems.

Stabilizing Adaptive Controller for Uncertain Dynamical Systems: An LMI Approach

Sandip Ghosh, Sarit K. Das, and Goshaidas Ray*

Indian Institute of Technology, India

Abstract

Adaptive stabilization of a class of linear systems with matched and unmatched uncertainties is considered in this paper. The proposed controller indeed stabilizes the uncertain system for any positive values of its non-adaptive gain that may be tuned to enhance dynamic response of system. The performance of uncertain system along with the Algebraic Riccati Equation that arises from the adaptive stabilizing controller is now formulated as a multi-objective Linear Matrix Inequality optimization problem. The decay rate and a factor governing the ultimate bound of the system states are considered to characterize the closed loop system performance. Finally, the effectiveness of the proposed controller is illustrated via stabilizing a mass-spring system.

Keywords: Adaptive control, linear matrix inequality (LMI), uncertain systems.

IJCAS
July 2024

Vol. 22, No. 7, pp. 2055~2340

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