Design and stability analysis of a variable structure adaptive backstepping controller

This paper presents the design and stability analysis of a Variable Structure Adaptive Backstepping Controller (VS‐ABC) for linear plants with relative degree one, using only input/output measurements. Instead of traditional integral adaptive laws for estimating the plant parameters, switching laws are proposed to increase robustness to parametric uncertainties and disturbances, as well as to improve transient response. Moreover, the controller design is more intuitive when compared with the original adaptive backstepping controller, since the relay amplitudes are related to the plant nominal parameters and their respective uncertainties. Simplified algorithm versions are also presented, named Compact and Relay VS‐ABC, which reduce the practical implementation complexity, and encourage applications in industrial environments.