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Adaptive dynamic surface control: A simplified algorithm for adaptive backstepping control of nonlinear systems. (English) Zbl 0969.93037
The authors discuss nonlinear uncertain systems of the form $$\align x_j &= x_{j+1}+ a_j f_j(x_1,\dots, x_j),\quad j= 1,\dots, n-1,\\ x_n &= u+ a_nf_n(x_1,\dots, x_n),\quad y= x_1,\endalign$$ where $a_i$, $i= 1,\dots, n$, are the unknown constant parameters and $f_i: \bbfR^i\to \bbfR$ are $C^1$-functions with $f_i(0,\dots, 0)= 0$. By extending the dynamic surface control technique due to {\it D. Swaroop} et al. [Proceedings of the 1997 American Control Conference, Albuquerque, NM (1997)], the authors propose a new algorithm for adaptive backstepping control of the above system. Since one adds first-order low pass filters, this algorithm can be implemented without differentiating any model nonlinearities. Using a singular perturbation theorem in {\it H. K. Khalil} [Nonlinear systems, New York, Macmillan (1992)], the combined adaptive backstepping first-order filter system is proven to be semi-globally stable for sufficiently fast filters. A detailed numerical example is also given.

93D21Adaptive or robust stabilization
93C40Adaptive control systems
93C70Time-scale analysis and singular perturbations
93B51Design techniques in systems theory
93C10Nonlinear control systems
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