Cross backstepping sliding mode control using integral barrier Lyapunov function for cross‐strict feedback systems

Abstract Cross‐backstepping control for a type of uncertain non‐strict‐feedback non‐linear systems with time‐varying partial state constraints is the main subject of this work. Non‐strict‐feedback non‐linear systems are partitioned into two strict‐feedback non‐linear subsystems: constrained subsystem and unconstrained subsystem. An integral barrier Lyapunov function (IBLF) is used in each step of the backstepping design for the constrained subsystem to guarantee the boundedness of the fictional or actual state tracking errors. The effect of uncertainty is reduced using a hybrid cross‐backstepping sliding mode control (SMC) technique. The algorithm employs a systematic approach to developing control laws for non‐linear systems with matched and unmatched uncertainties. The simulation results of the proposed controller are juxtaposed with those of the cross backstepping with the time‐varying barrier Lyapunov function (TVBLF). The results demonstrate the overall better performance of the proposed method.