Adaptive asymptotic tracking control for nonlinear systems with state constraints and input saturation

Highlights：

• Unlike [37–39] where only the practical tracking is ensured, we further consider asymptotic tracking control. To this end, a new function transformation different from the other states is proposed for the tracking error variable. Therefore, the proposed method can make that the tracking error asymptotically converges to zero and will stay within the given boundaries.

• To solve the problem of input saturation ignored in many papers [32–39], a smooth function is constructed to approximate the saturation nonlinearity. In the last step of the controller design, an auxiliary system is designed to deal with the effect of input saturation, where the positive integrable function is introduced to achieve asymptotic tracking.

摘要

•Different from some existing results about state constraints [32–36], a nonlinear function transformation related to the state is introduced, and then the purpose of state constraints is achieved by proving the boundedness of the transformed function without the feasibility conditions about the virtual controller. Besides, the boundary functions of state constraints don’t need to be strictly positive or negative, which is more practical.•Unlike [37–39] where only the practical tracking is ensured, we further consider asymptotic tracking control. To this end, a new function transformation different from the other states is proposed for the tracking error variable. Therefore, the proposed method can make that the tracking error asymptotically converges to zero and will stay within the given boundaries.•To solve the problem of input saturation ignored in many papers [32–39], a smooth function is constructed to approximate the saturation nonlinearity. In the last step of the controller design, an auxiliary system is designed to deal with the effect of input saturation, where the positive integrable function is introduced to achieve asymptotic tracking.