Input-to-state stability-modular command filtered back-stepping control of strict-feedback systems

Controlling non-linear strict-feedback systems is a focused research in control theory. In this study, the authors consider a novel command filtered back-stepping control that obviates the need to compute analytic derivatives in the traditional back-stepping design. An input-to-state stability (ISS)-modular approach is presented by combining the command filtered back-stepping method with the sliding-mode-based integral filters, ISS analysis and the small-gain theorem. The ISS-modular approach provides a simple and effective way for controlling non-linear systems by the command filtered back-stepping approach, simultaneously solving the problem of `explosion of complexity`. Numerical simulations are included to demonstrate the effectiveness of the proposed approach.