Abstract
This paper proposes a novel scheme of the multi-objective robust control design for a class of uncertain nonlinear systems in strict-feedback-form based on Takagi–Sugeno fuzzy model (TSFM). The nonlinear system contains both the matched and the unmatched uncertainties and also subjected to the external disturbances. The TSFM provides the generalization of the linear systems concepts to the nonlinear systems field in a convex framework. First, a new sliding surface is defined using a convex combination of the surfaces which are defined for each fuzzy rule consequence local linear subsystems. Then, their gains are designed optimally via a generalized eigenvalue problem (GEVP). Also, the upper-bounds of the matched and unmatched uncertainties are estimated using the adaptive update laws. The multi-objective control aims not only to satisfy the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> -optimization performance, but also, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -stability region is formulated to improve the transient response performance. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> -optimization characterization and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -stability design conditions are derived in terms of new linear matrix inequalities (LMIs) conditions. Finally, the effectiveness of the proposed approach is demonstrated by considering a comparative practical example.
Highlights
Takagi-Sugeno (T-S) fuzzy model with sector nonlinearity approaches is commonly used to describe an exact model of a nonlinear system with uncertainties [1]
In this paper, for the strict-feedback form of the nonlinear systems represented by the Takagi–Sugeno fuzzy model (TSFM), a new robust control scheme was developed based on back-stepping sliding mode controls (BSMCs)
In the first step, a BSMC is developed to be optimized for the TSFM of the nonlinear system
Summary
Takagi-Sugeno (T-S) fuzzy model with sector nonlinearity approaches is commonly used to describe an exact model of a nonlinear system with uncertainties [1]. The basic idea behind the T-S fuzzy approach is to decompose a non-linear system into several local linear models. Each linear model aggregates in a convex structure in terms of the normalized weighting. The linear control theory can be applied to each local linear model. The nonlinear control can be obtained by fuzzy blending. These advantages make the T-S fuzzy model a useful tool to model the complex nonlinear system
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