Command-filter Based Predefined-time Control for State-constrained Nonlinear Systems Subject to Preassigned Performance Metrics

This paper tackles the predefined-time control problem for nonlinear systems (NSs) subject to preassigned performance metrics (PPMs) and state constraints. To meet the PPMs and state constraints, a predefined performance control (PPC) based barrier Lyapunov functions (BLF) is designated to acquire the performance metrics and the satisfaction of state constraints. The proposed control approach combines the predefined-time control with the recursive design of command-filter backstepping to achieve the preset convergence time based on designing indicators while also ensuring the satisfaction of the desired PPMs and constraint conditions. In addition, the command-filter design eliminates the requirement of proving the continuity of high-order derivatives of the virtual control signals, resulting in a significant reduction in the complexity of stability analyses related to predefined-time convergence of the closed-loop signals. The stability analyses and simulation results of two examples provide support for the effectiveness and applicability of the proposed command-filter predefined-time control approach.