On performance recovery of robust dynamic surface control

Abstract

Robust dynamic surface control (RDSC) is effective in alleviating the implementation difficulty of backstepping-based multiple-surface sliding control (MSSC) for a class of strict-feedback nonlinear systems with mismatched uncertainties. However, the synthesis and analysis of the classical RDSC are conservative, which not only may lead to an impractical control law but also cannot fully reveal the technical nature of RDSC. This article provides a comprehensive study of a preferred RDSC law with an approximation of the signum function based on the singular perturbation theory. By formulating the control problem into a singular perturbation form, it is proven that the preferred RDSC recovers the performance of MSSC as the decrease of a filter parameter. The attractive features of the preferred RDSC revealed during the proposed synthesis and analysis include: (a) the control gain can be significantly reduced resulting in a sharp decrease of control energy and (b) the closed-loop stability can be guaranteed by only decreasing the filter parameter. Simulation results have been shown to be consistent with the theoretical findings. K E Y W O R D S backstepping, nonlinear system, robustness, singular perturbation, sliding mode control, uncertainty 1 3094

Robust adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems with unknown control directions

“…However, it should be pointed out that the use of the first-order filters inevitably complicates the computation and causes the filtering errors, which will be added to the difficulty in getting small steady-state. Otherwise, the classical DSC is conservative in the following aspects (Pan et al, 2020): (a) on the control synthesis, due to the need of a small filter parameter, thus may cause high control gains and substantial energy costs resulting in an impractical control law; and (b) on the control analysis, the closed-loop stability relies on both large control gain parameters and a small filter parameter. This can lead to loss of global stability and asymptotic tracking.…”