Adaptive Control for Nonlinear System With Time-Varying Parameters and Unknown Time-varying Control Coefficient

In this paper, a stability control issue for a class of single-input single-output(SISO) time-varying nonlinear systems with mismatched uncertainties and completely unknown time-varying input coefficient is investigated. Combining with the so-called congelation of variables method and a special type of Nussbaum function, a backstepping-based adaptive control scheme was proposed in our paper, which is able to achieve asymptotical stability in the presence of rapidly changing system parameters and absence of a priori knowledge of direction and amplitude of input coefficient. Through theory analysis and numerical simulation, it is demonstrated that the proposed algorithm guarantee the ultimately uniformly boundedness(UUB) of the signals in closed-loop system and realize asymptotical stability.