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**Robust learning control for a class of nonlinear systems with periodic and aperiodic uncertainties.**
*(English)*
Zbl 1051.93039

The authors consider the output tracking problem for a nonlinear system having a triangular form
\[
\begin{cases} \dot x_1= x_2+ w_1(x_1, t)+ \phi^T_1(x_1)\gamma(t)\\ \dot x_2= x_3+ w_2(x_1,x_2, t)+ \phi^T_2(x_1, x_2)\gamma(t)\\ \vdots\\ \dot x_n= u+ w_n(x_1,\dots, x_n, t)+ \phi^T_n(x_1,\dots, x_n)\gamma(t)\\ y= x_1\end{cases}
\]
where the functions \(w_i\) represent bounded (with known bounds) unstructured uncertainties, the functions \(\phi_i\) are known, and the function \(\gamma\) is unknown but periodic. The signal to be tracked is generated by a linear stable system. The method proposed by the authors is a combination of robust learning control and the backstepping procedure. A control law (consisting of three terms) is constructed in order to learn and approximate the unknown periodic function (by the use of a repetitive learning mechanism) and to suppress the unstructured bounded uncertainties (by using a robust control technique). The proposed control law is applied to the control of a chaotic Van der Pol attractor.

Reviewer: Andrea Bacciotti (Torino)

### MSC:

93B51 | Design techniques (robust design, computer-aided design, etc.) |

93C10 | Nonlinear systems in control theory |

93D15 | Stabilization of systems by feedback |

### Keywords:

Iterative learning; Robust control; Nonlinear systems; Time-varying system; Control synthesis; Output tracking; Backstepping; Periodic function
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\textit{Y.-P. Tian} and \textit{X. Yu}, Automatica 39, No. 11, 1957--1966 (2003; Zbl 1051.93039)

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### References:

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