Prescribed-time homogeneous filter-based saturation-tolerant prescribed control for nonlinear systems with input and state quantization

This paper addresses saturation-tolerant prescribed control (SPC) for nonlinear systems with fully quantized input/states under performance constraints. The key challenge lies in reconciling discontinuous, non-differentiable quantized signals with backstepping design requirements, while maintaining prescribed performance. Three innovative solutions are developed: Firstly, prescribed-time homogeneous filters are developed to generate smooth state estimates, thereby enabling recursive backstepping implementation. Then, a compensation mechanism is designed to ensure controller continuity. Lastly, an auxiliary dynamic system is introduced to balance input saturation and performance constraints. Based on the above solutions, a saturation-tolerant quantized control strategy is proposed to ensure that the tracking error remains bounded within prescribed performance bounds under simultaneous input/state quantization and input saturation. The core advancement resolves the fundamental incompatibility between quantization-induced discontinuities and backstepping’s differentiability requirements through filtered state reconstruction, enabling performance-guaranteed control under dual quantization and saturation constraints. Finally, the simulation results are depicted to verify the validity of the derived method.