Variable-structure backstepping controller for multivariable nonlinear systems with actuator nonlinearities based on adaptive fuzzy system. (English) Zbl 1436.93073
Summary: In this paper, a novel robust adaptive fuzzy control is presented for a quite general class of multivariable nonlinear systems with actuators’ nonlinearities (saturation with dead zone) and uncertain dynamics. The backstepping concept in combination with the variable-structure control framework and Lyapunov approach is used to design this adaptive fuzzy control. The fuzzy systems are incorporated in the controller for approximating online the unknown system dynamics. In the controller design and stability analysis, the control gain matrices, which are not necessarily symmetric and definite, are decomposed via the so-called SDU matrix decomposition lemma into a product of three main useful matrices, namely a symmetric definite-positive matrix, a diagonal constant matrix with \(+ 1\) or \(- 1\) in its main diagonal and a unity upper triangular matrix. It is shown that the proposed adaptive fuzzy control is able to ensure the uniform ultimate boundedness of all solutions of the closed-loop system, as well as the convergence of the underlying tracking errors. Finally, in a numerical simulation framework, the effectiveness of the presented controller is illustrated on two practical examples.
MSC:
| 93C42 | Fuzzy control/observation systems |
| 93C40 | Adaptive control/observation systems |
| 93C05 | Linear systems in control theory |
| 93B12 | Variable structure systems |
| 93B35 | Sensitivity (robustness) |
Keywords:
fuzzy control; adaptive backstepping control; variable-structure control; MIMO nonlinear systems; actuator nonlinearities; robot manipulator; helicopter systemReferences:
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