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Direct adaptive fuzzy control for a class of MIMO nonlinear systems. (English) Zbl 1128.93032
Summary: This article presents a direct adaptive fuzzy control scheme for a class of uncertain continuous-time multi-input multi-output nonlinear (MIMO) dynamic systems. Within this scheme, fuzzy systems are employed to approximate an unknown ideal controller that can achieve control objectives. The adjustable parameters of the used fuzzy systems are updated using a gradient descent algorithm that is designed to minimize the error between the unknown ideal controller and the fuzzy controller. The stability analysis of the closed-loop system is performed using a Lyapunov approach. In particular, it is shown that the tracking errors are bounded and converge to a neighborhood of the origin. Simulations performed on a two-link robot manipulator illustrate the approach and exhibit its performance.

##### MSC:
 93C42 Fuzzy control/observation systems 93C40 Adaptive control/observation systems 93C10 Nonlinear systems in control theory 93B40 Computational methods in systems theory (MSC2010) 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory
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##### References:
 [1] DOI: 10.1016/S0005-1098(00)00083-2 · Zbl 0967.93060 · doi:10.1016/S0005-1098(00)00083-2 [2] DOI: 10.1109/91.919249 · doi:10.1109/91.919249 [3] Chekireb H, Contr. and Intelligent Syst. 31 pp 113– (2003) [4] DOI: 10.1049/ip-cta:20045059 · doi:10.1049/ip-cta:20045059 [5] DOI: 10.1016/S0165-0114(02)00279-8 · Zbl 1037.93053 · doi:10.1016/S0165-0114(02)00279-8 [6] DOI: 10.1109/5.364486 · doi:10.1109/5.364486 [7] Krstic M, Nonlinear and Adaptive Control Design (1995) [8] Labiod S, Archives of Cont. Sci. 13 pp 95– (2003) [9] DOI: 10.1016/j.fss.2004.10.009 · Zbl 1142.93365 · doi:10.1016/j.fss.2004.10.009 [10] DOI: 10.1109/TFUZZ.2002.806314 · doi:10.1109/TFUZZ.2002.806314 [11] DOI: 10.1109/91.771089 · doi:10.1109/91.771089 [12] Passino KM, Fuzzy Control (1998) [13] DOI: 10.1016/0005-1098(95)00147-6 · Zbl 0847.93031 · doi:10.1016/0005-1098(95)00147-6 [14] DOI: 10.1109/9.40741 · Zbl 0693.93046 · doi:10.1109/9.40741 [15] Slotine JE, Applied Nonlinear Control (1991) [16] DOI: 10.1109/91.531775 · doi:10.1109/91.531775 [17] DOI: 10.1109/91.324808 · doi:10.1109/91.324808 [18] DOI: 10.1016/S0165-0114(97)00205-4 · Zbl 0942.93018 · doi:10.1016/S0165-0114(97)00205-4 [19] Tong SC, Fuzzy sets and Syst. 101 pp 39– (1999) [20] DOI: 10.1016/S0165-0114(98)00058-X · Zbl 0976.93050 · doi:10.1016/S0165-0114(98)00058-X [21] Wang LX, Adaptive Fuzzy Systems and Control: Design and Stability Analysis (1994) [22] DOI: 10.1109/TAC.2003.820138 · Zbl 1364.93229 · doi:10.1109/TAC.2003.820138
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