Approximation-Free Prescribed Performance Control With Virtual Condition Guarantee

This letter investigates the problem of output tracking control subject to transient and steady-state performance constraints for unknown pure-feedback systems. On the basis of monotonicity theory, we propose a universal mapping-based barrier Lyapunov function (MBLF) which addresses the performance constraints without any sign limitation. Then an approximation-free controller is derived via the joint use of backstepping technique and MBLF. Through the Lyapunov stability analysis, it is proved that this controller can stabilize all the closed-loop signals including MBLF, and moreover the prescribed output tracking is achieved under a naturally satisfied initial virtual condition, and without any sacrifice of output overshoot performance. In the end, a simulation example is provided to demonstrate the effectiveness of the proposed scheme, and also the superiority over the existing ones.