Backstepping dynamic surface control for a class of non-linear systems with time-varying output constraints

The barrier Lyapunov function (BLF) and its variants such as the asymmetric barrier Lyapunov function (ABLF) combined with backstepping technique have recently been employed to handle constraints for a class of non-linear systems. However, the repeated differentiation in backstepping will result in the requirement of high-order differentiability and the complexity of controllers in the multiple-state high-order systems. This study introduces dynamic surface control (DSC) to deal with these problems. The authors propose a backstepping DSC scheme based on the ABLF to address time-varying output constraints for a class of non-linear systems. The proposed control scheme can avoid the proliferation and singularity of repeated differentiation. As a consequence, it can relax the requirements of high-order differentiability for stabilising functions and high power of output tracking error transformation involved in ABLF synthesis. The new controller can be proved to guarantee that all the closed-loop signals remain bounded, and to ensure output constraints never violated. Comparison studies with previous work validate that DSC incorporated with ABLF can achieve favourable performance bounded within constraints, and it can also ensure fast and stable tracking convergence in the presence of disturbance. Experimental results illustrate the effectiveness of the presented method.