Abstract
In Chap. 7, we developed adaptive output feedback fuzzy control schemes of single-input single-output (SISO) discrete-time nonlinear systems with multiple input–output delays based on their T–S fuzzy approximation models. The goal of this chapter is to extend the results in Chap. 7 to multiple-input multiple-output (MIMO) nonlinear systems. We will develop a solution framework for adaptive fuzzy control of MIMO discrete-time nonlinear systems, by modeling them using discrete-time T–S fuzzy systems, parameterizing T–S fuzzy systems with uncertain parameters, designing and analyzing an adaptive control scheme for such systems, and establishing and evaluating desired adaptive control system properties.
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Notes
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From (8.62), if \(h^i_{jk}(t) > \beta ^{ib}_{0jk}\), then \(f^i_{jk}(t) = \beta ^{ib}_{0jk} - h^i_{jk}(t) < 0\) so that \(q^i_{jk}(t) = f^i_{jk}(t)(\beta ^{ib}_{0jk} - \beta ^i_{0jk}) \le 0\) as \(\beta ^{ib}_{0jk} - \beta ^i_{0jk} \ge 0\) by definition of \(\beta ^{ib}_{0jk}\) (it is similar when \(h^i_{jk}(t) < \beta ^{ia}_{0jk}\)).
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References
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Qi R, Tao G, Jiang B (2014) Adaptive control of MIMO time-varying systems with indicator function based parametrization. Automatica 50(5):1369–1380
Tao G, Ioannou PA (1989) Robust stability and performance improvement of multivariable adaptive control systems. Int J Control 50(5):1825–1855
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Qi, R., Tao, G., Jiang, B. (2019). Adaptive T–S Fuzzy Control Using Output Feedback: MIMO Case. In: Fuzzy System Identification and Adaptive Control. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-19882-4_8
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DOI: https://doi.org/10.1007/978-3-030-19882-4_8
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