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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
- 3.
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 \(h^i_{jk}(t) < \beta ^{ia}_{0jk}\)).
- 4.
References
Goodwin GC, Sin KS (1984) Adaptive filtering prediction and control. Prentice-Hall, Englewood Cliffs, NJ
Qi R, Tao G, Jiang B, Gong H (2011) Adaptive control of MIMO T-S fuzzy systems with general delay matrice. In: Proceeding of the 18th IFAC world congress. Milano, Italy, pp 3446–3450
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
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-030-19882-4_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-19881-7
Online ISBN: 978-3-030-19882-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)