Barrier Function-Based Asymptotic Tracking Control of Uncertain Nonlinear Systems With Multiple States Constraints

This technical note focus on the tracking control problem of uncertain nonlinear systems with multiple states constraints. Based on the Barrier Lyapunov function and backstepping technology, a new continuous smooth control solution can be ultimately synthesized to realize asymptotic tracking control in presence of multiple states constraints and modeling uncertainties. Firstly, the modeling uncertainties are divided into periodic and un-periodic components and Fourier expansion technology is employed to translate the periodic disturbance into the form which can be easily compensated. Then the Barrier Lyapunov function are flexibly utilized to design the virtual control law of every step and the final controller, which can guarantee the specified states within certain bounds regardless of the amplitude of system output. Meanwhile, a novel nonlinear control technology is introduced to each design step to realize the final asymptotic tracking control despite the matched and mismatched uncertainties. By analyzing the choice of the control parameters, the backstepping cross-term is skillfully dealt with and the stability of the whole system is proved rigorously. Finally, the simulation results on a three-order nonlinear hydraulic system demonstrate the satisfactory performance of the proposed control method.