Adaptive homo‐backstepping tracking control for strict‐feedback systems in presence of unknown dead‐zones

An adaptive homo‐backstepping control for nonlinear strict‐feedback systems subjected to unknown actuator dead‐zone and disturbance is investigated. A sliding‐mode‐based integral filter is constructed and used to approximate the desired feedback control in the backstepping‐like recursive design technique. Subsequently, the problem of “explosion of complexity” is solved by obviating the analytic derivatives deduction for virtual control in the conventional backstepping technology. The actuator dead‐zone dynamic is modeled as the combination of a line and a disturbance‐like term, which makes the controller design simpler. The interconnected control module and filter module in the resulting closed‐loop system satisfy the input‐to‐state practically stability‐modularity condition, provided that the small‐gain theorem is exploited to ensure the stability of closed‐loop system. The proposed approach cannot only mitigate the effect of dead‐zone but also solve the problem of explosion of complexity in the previous literature. Numerical simulations performed on a manipulator with a brushed DC motor are introduced to illustrate the effectiveness of underlying control scheme.