Fuzzy Control for Nonlinear Systems via Neural-Network-Based Approach

Stability analysis and robustness design of nonlinear systems: An NN-based approach

“…For further details on NN-based modeling schemes see Appendix A (Definitions 1 and 2 and Remark 1). Nonlinear system (1) can be approximated in LDI representational form (11). The LDI representation has the same rules as the T-S fuzzy model which combines the flexibility of fuzzy logic theory and the rigorous mathematical analysis tools found in linear system theory into a unified framework (for more details, please see [11] and the references therein).…”

“…Nonlinear system (1) can be approximated in LDI representational form (11). The LDI representation has the same rules as the T-S fuzzy model which combines the flexibility of fuzzy logic theory and the rigorous mathematical analysis tools found in linear system theory into a unified framework (for more details, please see [11] and the references therein). Tanaka and Sugeno [12] proposed the so-called "parallel distributed compensation" (PDC) control concept for the fuzzy control of T-S fuzzy systems.…”

“…According to the above NN-based model (11) and the PDC scheme (13), the model of a nonlinear system (1) can be represented by the following closed-loop controlled system:…”

“…This is what makes LMI techniques so efficient for solving complex control problems [9]. It is widely known that stability is an essential property of control systems, and has often been investigated in literature related to fuzzy dynamic systems (see [10][11][12][13]24,25] and the references cited therein). A look at these studies shows that the stability of the controlled system can be guaranteed by Lyapunov and LMI derived fuzzy control laws.…”

“…Convergence of the learning processes was also guaranteed by the adaptive learning rate and stability analysis was performed using the Lyapunov function. In this study, an NN-based approach is adopted to eliminate the effects of modeling errors in the representation of nonlinear systems [11]. A linear differential inclusion (LDI) state-space representation is used to deal with the problem of stability analysis in the NN models.…”