Adaptive dynamic surface control of high-order strict feedback nonlinear systems with parameter estimations

In this study, for a class of uncertain high-order SFNSs, an adaptive DSC method is proposed. To avoid the “differential explosion” problem, multiple (if necessary) first-order low-pass filters are introduced at every step of the control design. The parameter estimation errors are reconstructed and integrated into the adaptive laws using a set of low-pass filters. The truncation operation is introduced to avoid the unbounded integral operations when computing the regression matrices. The projection operator is introduced to avoid the singularity problem of the control law. It is proved that the tracking error and the parameter estimation errors ultimately converge to an arbitrarily small neighborhood around zero.