Research Papers

A New Approach to the Control Design of Fuzzy Dynamical Systems

[+] Author and Article Information
Ye-Hwa Chen

The George W. Woodruff School of Mechanical Engineering,  Georgia Institute of Technology, Atlanta, GA 30332 yehwa.chen@me.gatech.edu

We note, however, that Kalman's recent comment on probability does not automatically assume him an advocate for fuzzy theory. His view on the latter has been unchanged [6,7].

J. Dyn. Sys., Meas., Control 133(6), 061019 (Nov 22, 2011) (9 pages) doi:10.1115/1.4004579 History: Received December 29, 2009; Revised March 10, 2011; Published November 22, 2011; Online November 22, 2011

A new approach to the control design for fuzzy dynamical systems is proposed. For a fuzzy dynamical system, the uncertainty lies within a fuzzy set. The desirable system performance is twofold: one deterministic and one fuzzy. While the deterministic performance assures the bottom line, the fuzzy performance enhances the cost consideration. Under this setting, a class of robust controls is proposed. The control is deterministic and is not if-then rules-based. An optimal design problem associated with the control is then formulated as a constrained optimization problem. We show that the problem can be solved and the solution exists and is unique. The closed-form solution and cost are explicitly shown. The resulting control is able to guarantee the prescribed deterministic performance and minimize the average fuzzy performance.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 2

Fuzzy dynamical system performance (control versus no control)

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Figure 3

Control histories

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Figure 4

Comparison of system performance under different γmin

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Figure 5

Comparison of control magnitude under different γmin



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