Adaptive Control With Guaranteed Transient Behavior and Zero Steady-State Error for Systems With Time-Varying Parameters

It is nontrivial to achieve global zero-error regulation for uncertain nonlinear systems. The underlying problem becomes even more challenging if mismatched uncertainties and unknown time-varying control gain are involved, yet certain performance specifications are also pursued. In this work, we present an adaptive control method, which, without the persistent excitation (PE) condition, is able to ensure global zero-error regulation with guaranteed output performance for parametric strict-feedback systems involving fast time-varying parameters in the feedback path and input path. The development of our control scheme benefits from generalized $t$-dependent and $x$-dependent functions, a novel coordinate transformation and “congelation of variables” method. Both theoretical analysis and numerical simulation verify the effectiveness and benefits of the proposed method.