Abstract
This paper considers the globally stabilizing adaptive controller design for a class of more general uncertain high-order nonlinear systems with unknown control coefficients. Although the existing literature has solved the problem, for n-dimensional systems, the existing methods need at least n + 1 dynamic updating laws for the unknown parameters to construct the stabilizing adaptive controller; that is, the dimension of the dynamic compensator is not less than n + 1, and therefore, there exists serious overparametrization. In this paper, by defining some new unknown parameters which need dynamic updating, also by using adding a power integrator and related adaptive technique, the overparametrization is successfully solved and a new approach is given to design stabilizing adaptive controller based on only one parameter updating law. A simulation example is finally provided to demonstrate the validness of the proposed approach.
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References
Kanellakopoulos I, Kokotović P V, Morse S. Systematic design of adaptive controllers for feedback linearizable systems. IEEE Trans Autom Control, 1991, 36: 1241–1253
Krstić M, Kanellakopoulos I, Kokotović P V. Nonlinear and Adaptive Control Design. New York: John Wiley & Sons, INC, 1995
Jiang Z P, Praly L. Design of robust adaptive controllers for nonlinear systems with dynamics uncertainties. Automatica, 1998, 34: 825–840
Ye X D, Jiang J P. Adaptive nonlinear design without a priori knowledge of control directions. IEEE Trans Autom Control, 1998, 43: 1617–1621
Zhou J, Wen C Y, Zhang Y. Adaptive output control of nonlinear systems with uncertain dead-zone nonlinearity. IEEE Trans Autom Control, 2006, 51: 504–511
Pan Z, Liu Y, Shi S. Output feedback stabilization for stochastic nonlinear systems in observer canonical form with stable zero-dynamics. Sci China Ser F-Inf Sci, 2001, 44: 292–308
Liu Y, Pan Z, Shi S. Output feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitive cost. IEEE Trans Autom Control, 2003, 48: 509–514
Liu Y, Zhang J. Reduced-order observer-based control design for nonlinear stochastic systems. Syst Control Lett, 2004, 52: 123–135
Liu Y, Zhang J. Practical output-feedback risk-sensitive control for stochastic nonlinear systems with stable zerodynamics. SIAM J Control Opt, 2006, 45: 885–926
Lin W, Qian C. Adding one power integrator: A tool for global stabilization of high order lower-triangular systems. Syst Control Lett, 2000, 39: 339–351
Lin W, Qian C. A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans Autom Control, 2001, 46: 1061–1079
Lin W, Qian C. Adaptive control of nonlinear parameterized system: A nonsmooth feedback framework. IEEE Trans Autom Control, 2002, 47: 757–774
Lin W, Qian C. Adaptive control of nonlinearly parameterized systems: The smooth feedback case. IEEE Trans Autom Control, 2002, 47: 1249–1266
Lin W, Pongvuthithum R. Nonsmooth adaptive stabilization of cascade systems with nonlinear parameterization via partial-state feedback. IEEE Trans Autom Control, 2003, 48: 1809–1816
Lin W, Pongvuthithum R. Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization. IEEE Trans Autom Control, 2003, 48: 1737–1749
Qian C, Lin W. Recursive observer design, homogeneous approximation, and nonsmooth output feedback stabilization of nonlinear systems. IEEE Trans Autom Control, 2006, 51: 1457–1471
Sun Z, Liu Y. Adaptive practical output tracking control for high-order nonlinear uncertain systems. Acta Autom Sin, 2008, 34: 984–989
Sun Z, Liu Y. Adaptive state-feedback stabilization for a class of high-order nonlinear uncertain systems. Automatica, 2007, 43: 1772–1783
Sun Z, Liu Y. Adaptive stabilization for a large class of high-order nonlinear uncertain systems. Intl J Control, 2009, 82: 1275–1287
Li W, Xie X. Inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable. Automatica, 2009, 45: 498–503
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Zhang, J., Liu, Y. A new approach to adaptive control design without overparametrization for a class of uncertain nonlinear systems. Sci. China Inf. Sci. 54, 1419–1429 (2011). https://doi.org/10.1007/s11432-011-4299-3
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DOI: https://doi.org/10.1007/s11432-011-4299-3