Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems. (English) Zbl 1113.93070
Summary: A direct adaptive fuzzy control scheme for a class of uncertain continuous-time single-input single-output (SISO) nonaffine nonlinear dynamic systems. Based on the implicit function theory, the existence of an ideal controller, that can achieve control objectives, is firstly shown. Since the implicit function theory guarantees only the existence of the ideal controller and does not provide a way for constructing it, a fuzzy system is employed to approximate this unknown ideal control law. The adjustable parameters in the used fuzzy system are updated using a gradient descent adaptation algorithm. This algorithm is designed in order to minimize a quadratic cost function of the error between the unknown ideal implicit controller and the used fuzzy control law. The stability analysis of the closed-loop system is performed using a Lyapunov approach. In particular, it is shown that the tracking error converges to a neighborhood of zero. The effectiveness of the proposed adaptive control scheme is demonstrated through the simulation of a simple nonaffine nonlinear system.
MSC:
| 93C42 | Fuzzy control/observation systems |
| 93C10 | Nonlinear systems in control theory |
| 93C40 | Adaptive control/observation systems |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93B40 | Computational methods in systems theory (MSC2010) |
Keywords:
fuzzy systems; fuzzy control; adaptive control; gradient descent method; nonaffine nonlinear systemsReferences:
| [1] | Blazic, S.; Skrjanc, I.; Matko, D., Globally stable direct fuzzy model reference adaptive control, Fuzzy Sets and Systems, 139, 3-33 (2003) · Zbl 1025.93502 |
| [2] | R. Boukezzoula, S. Galichet, L. Foulloy, Fuzzy adaptive control for non-affine systems, in: Proc. IEEE Internat. Conf. Fuzzy Systems, 2003, pp. 543-548.; R. Boukezzoula, S. Galichet, L. Foulloy, Fuzzy adaptive control for non-affine systems, in: Proc. IEEE Internat. Conf. Fuzzy Systems, 2003, pp. 543-548. |
| [3] | Chang, Y. C., Robust tracking control for nonlinear MIMO systems via fuzzy approaches, Automatica, 36, 1535-1545 (2000) · Zbl 0967.93060 |
| [4] | Chang, Y. C., Adaptive fuzzy-based tracking control for nonlinear SISO systems via VSS and \(H^\infty\) approaches, IEEE Trans. Fuzzy Systems, 9, 278-292 (2001) |
| [5] | Ge, S. S.; Zhang, J., Neural-network control of nonaffine nonlinear system with zero dynamics by state and output feedback, IEEE Trans. Neural Networks, 14, 4, 900-918 (2003) |
| [6] | Golea, N.; Golea, A.; Benmahammed, K., Stable indirect fuzzy adaptive control, Fuzzy sets and Systems, 137, 353-366 (2003) · Zbl 1037.93053 |
| [7] | Ioannou, P.; Sun, J., Robust Adaptive Control (1996), Prentice-Hall, Inc.: Prentice-Hall, Inc. Englewood Cliffs, NJ, Electronic copy at \(\langle\) http://www-rcf.usc.edu/\( \sim\) ioannou/Robust_Adaptive_Control.htm \(\rangle \) · Zbl 0747.93048 |
| [8] | Labiod, S.; Boucherit, M. S., Direct stable fuzzy adaptive control of a class of SISO nonlinear systems, Arch. Control Sci., 13, 1, 95-110 (2003) · Zbl 1151.93376 |
| [9] | Labiod, S.; Boucherit, M. S.; Guerra, T. M., Adaptive fuzzy control of a class of MIMO nonlinear systems, Fuzzy Sets and Systems, 151, 1, 59-77 (2005) · Zbl 1142.93365 |
| [10] | Li, H.-X.; Tong, S. C., A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems, IEEE Trans. Fuzzy Systems, 11, 1, 24-34 (2003) |
| [11] | Ordonez, R.; Passino, K. M., Stable multi-input multi-output adaptive fuzzy/neural control, IEEE Trans. Fuzzy Systems, 7, 3, 345-353 (1999) |
| [12] | Park, J.-H.; Kim, S.-H., Direct adaptive output-feedback fuzzy controller for nonaffine nonlinear system, IEE Proc. Control Theory Appl., 151, 1, 65-72 (2004) |
| [13] | Park, J.-H.; Park, G.-T.; Kim, S.-H.; Moon, C.-J., Direct adaptive self-structuring fuzzy controller for nonaffine nonlinear system, Fuzzy Sets and Systems, 153, 3, 429-445 (2005) · Zbl 1068.93035 |
| [14] | Polycarpou, M. M.; Ioannou, P. A., A robust adaptive nonlinear control design, Automatica, 32, 3, 423-427 (1996) · Zbl 0847.93031 |
| [15] | Spooner, J. T.; Passino, K. M., Stable adaptive control using fuzzy systems and neural networks, IEEE Trans. Fuzzy Systems, 4, 339-359 (1996) |
| [16] | Su, C. Y.; Stepanenko, Y., Adaptive control of a class of nonlinear systems with fuzzy logic, IEEE Trans. Fuzzy Systems, 2, 285-294 (1994) |
| [17] | Tang, Y.; Zhang, N.; Li, Y., Stable fuzzy adaptive control for a class of nonlinear systems, Fuzzy sets and Systems, 104, 279-288 (1999) · Zbl 0942.93018 |
| [18] | Tong, S. C.; Li, Q.; Chai, T., Fuzzy adaptive control of a class of nonlinear systems, Fuzzy sets and Systems, 101, 31-39 (1999) · Zbl 0952.93077 |
| [19] | Tong, S. C.; Tang, J.; Wang, T., Fuzzy adaptive control of multivariable nonlinear systems, Fuzzy Sets and Systems, 111, 153-167 (2000) · Zbl 0976.93049 |
| [20] | J. Wang, S.S. Ge, T.H. Lee, Adaptive fuzzy sliding mode control of a class of nonlinear systems, in: Proc. Third Asian Control Conf., 2000, pp. 599-604.; J. Wang, S.S. Ge, T.H. Lee, Adaptive fuzzy sliding mode control of a class of nonlinear systems, in: Proc. Third Asian Control Conf., 2000, pp. 599-604. |
| [21] | Wang, L. X., Adaptive Fuzzy Systems and Control: Design and Stability Analysis (1994), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ |
| [22] | P.-S. Yoon, J.-H. Park, G.-T. Park, Adaptive fuzzy control of nonaffine nonlinear systems using Takagi-Sugeno fuzzy models, in: Proc. IEEE Internat. Conf. Fuzzy Systems, 2001, pp. 642-645.; P.-S. Yoon, J.-H. Park, G.-T. Park, Adaptive fuzzy control of nonaffine nonlinear systems using Takagi-Sugeno fuzzy models, in: Proc. IEEE Internat. Conf. Fuzzy Systems, 2001, pp. 642-645. |
| [23] | T. Zhang, S.S. Ge, C.C. Hang, Direct adaptive control of non-affine nonlinear system using multilayer neural networks, in: Proc. ACC, 1998, pp. 515-519.; T. Zhang, S.S. Ge, C.C. Hang, Direct adaptive control of non-affine nonlinear system using multilayer neural networks, in: Proc. ACC, 1998, pp. 515-519. |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
