Universal \(\lambda\)-tracking for nonlinearly-perturbed systems without restrictions on the relative degree
This paper considers an adaptive tracking problem for a class of nonlinear perturbed linear single-input single-output minimum-phase systems \((A,b,c; f)\), where \((A,b,c)\) is a state-space realization of the underlying linear system and \(f\) denotes the nonlinear perturbation. The relative degree of \((A,b,c)\) may be arbitrary, but is assumed to be known. The nonlinear perturbation \(f\) satisfies \[ \|f(t,x)\|\leq \alpha(1+|cx|^q)\quad\text{for all }x\text{ and almost all }t, \] where \(\alpha> 0\) and \(q\) is a known positive integer. Given \(\lambda>0\), a high-gain control strategy is given which guarantees that for all reference signals and all output noise signals in \(W^{1,\infty}\), the tracking error approaches the interval \([-\lambda, \lambda]\).
scientific article; zbMATH DE number 1325712