Barrier Lyapunov Function-Based Asymptotic Tracking Control for Irregular Ellipsoidal Output Constraints

Most existing barrier Lyapunov function (BLF)-based control schemes are only able to handle box-type constraints. However, many physical constraints are ellipsoidal constraints in real-world applications. Therefore, an asymptotic tracking control scheme embedded with an improved command filter is proposed for MIMO nonlinear systems under irregular ellipsoidal output constraints. A novel transformation function, explicitly depending on original constraints, is constructed. With such a design, not only ellipsoidal constraints but also partial ellipsoidal constraints, box-type constraints, and their combination-type constraints can be handled. Moreover, an innovative adaptive nonlinear filter is designed to resolve the complexity explosion problem caused by the repeated differentiations of virtual controllers. Different from the existing filters, the boundary layer errors of the proposed adaptive filter are fully compensated. Furthermore, tracking error is proved to be asymptotically converged to zero with the existence of model uncertainties and external disturbances. In addition, all signals within the closed-loop system are rigorously proved to be bounded. A numerical example is presented to verify the effectiveness of the designed control strategy.