This paper intends to design an integral backstepping Lyapunov redesign controller (IBLRC) for various uncertain strict‐feedback‐form nonlinear systems. The pros and cons of backstepping Lyapunov redesign resulted in the design idea. An integral term is incorporated in conventional backstepping with Lyapunov redesign to indirectly decrease chattering and steady‐state error of a reference signal tracking when unknown static parameters and matched and unmatched dynamic uncertainties exist. The closed‐loop system is mathematically confirmed as stable in a Lyapunov frame, and we ultimately reach uniformly semi‐global boundedness of all signals. Simulation results of the proposed IBLRC are juxtaposed with those of the classic backstepping with the Lyapunov redesign. The proposed IBLRC realizes excellent tracking and enhanced robust performance than the BLRC for time‐varying and step tracking references.

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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. Nonstrict-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.

The cover image is based on the Research Article Integral Backstepping Lyapunov Redesign Control of Uncertain Nonlinear Systems by Esmaeil Jalalabadi et al., https://doi.org/10.1049/cth2.12229.