Dynamic surface control for a class of state-constrained non-linear systems with uncertain time delays

The problem of tracking control for a class of uncertain time-delay non-linear system with state constraint is addressed. To prevent constraint violation, the tangent barrier Lyapunov function (TBLF) is firstly used for time-delay non-linear system. By ensuring boundedness of the TBLF in the closed loop, besides those limits are not transgressed, the authors also tackle scenarios wherein parametric uncertainties and time delays are presented. Asymptotically tracking stable in the sense of uniformly ultimate boundedness is achieved without violation of the constraint. Finally, the performance of the proposed control has been illustrated through a chaotic system.