zbMATH — the first resource for mathematics

Stable fuzzy adaptive control for a class of nonlinear systems. (English) Zbl 0942.93018
The study presents an adaptive fuzzy control for a class of nonlinear systems. The control law consists of a fuzzy controller \(u_f({\mathbf x},{\mathbf a})\) and a compensation control block \((u_c)\) whose outputs are combined additively, namely \(u= u_f({\mathbf x},{\mathbf a})+ u_c\) where \({\mathbf a}\) is a vector of parameters of the fuzzy controller. Considering an \(n\)th order nonlinear dynamic system, the authors derive stable control schemes based on the Lyapunov stability approach. Simulation experiments are included.

93C42 Fuzzy control/observation systems
93D21 Adaptive or robust stabilization
93C10 Nonlinear systems in control theory
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
Full Text: DOI
[1] Chen, B.S.; Lee, C.H.; Chang, Y.C., H∞ tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach, IEEE trans. fuzzy systems, 4, 1, 32-43, (1996)
[2] Chen, C.L.; Chen, P.C.; Chen, C.K., Analysis and design of fuzzy control systems, Fuzzy sets and systems, 57, 125-140, (1993) · Zbl 0792.93079
[3] Isidori, A., Nonlinear control systems: an introduction, (1989), Springer Berlin · Zbl 0569.93034
[4] Kiszka, J.B.; Gupta, M.M.; Nikiforuk, P.N., Energetic stability of fuzzy dynamic systems, IEEE trans. SMC, 15, 6, 783-792, (1985) · Zbl 0588.93061
[5] Kumar, S.R.; Majumder, D.D., Application of circle criteria for stability analysis of linear SISO and MIMO system associated with fuzzy logic controllers, IEEE trans. SMC, 14, 2, 345-349, (1984)
[6] Maeda, M.; Fukumiya, E., Stability analysis of fuzzy control system by 3D space display, IEEE trans. JSME, 58, 87-94, (1992)
[7] Ollero, A.; Aracil, J.; Gacia-Cerezo, A., Robust design of rule-based fuzzy controllers, Fuzzy sets and systems, 70, 249-273, (1995)
[8] Ray, K.S.; Ghosh, A.; Majumder, D.D., L2-stability and related design concept for SISO linear system associated with fuzzy logic controllers, IEEE trans. SMC, 14, 6, 932-939, (1984) · Zbl 0559.93033
[9] Su, C.Y.; Stepanenko, Y., Adaptive control of a class of nonlinear systems with fuzzy logic, IEEE trans. fuzzy systems, 2, 4, 285-294, (1994)
[10] Tanaka, K.; Ikeda, T.; Wang, H.P., Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H∞ control theory, and linear matrix inequalities, IEEE trans. fuzzy systems, 4, 1, 1-13, (1996)
[11] Tanaka, K.; Sugeno, M., Stability analysis and design of fuzzy control systems, Fuzzy sets and systems, 45, 135-156, (1992) · Zbl 0758.93042
[12] Wang, L.X., Stable adaptive fuzzy control of nonlinear system, IEEE trans. fuzzy systems, 1, 2, 146-155, (1993)
[13] Wang, L.X.; Mendel, J.M., Fuzzy basis function, universal approximation, and orthogonal least square learning, IEEE trans. neural network, 3, 5, 807-814, (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.