Prescribed-time consensus for stochastic multi-agent systems with input saturation

This paper presents a novel distributed prescribed-time consensus framework for stochastic multi-agent systems with heterogeneous input saturation constraints. Addressing critical gaps in existing literature, we develop an integrated control scheme that combines prescribed-time methods with dynamic saturation techniques for the framework of stochastic system theory. Firstly, a novel distributed prescribed-time protocol is proposed, which circumvents the limitations of the properties of the stochastic algebraic Riccati equation, enabling simplified controller design with guaranteed convergence time. Then, an advanced constraint-handling mechanism is developed that accommodates heterogeneous saturation limits while enhancing control performance via dynamic adaptation strategies. The unified framework is constructed that achieves stochastic consensus for general linear multi-agent systems under input constraints within a user-specified time. Theoretical analysis proves both prescribed-time mean-square and almost sure consensus, while numerical simulations demonstrate the effectiveness of the theoretical results and superior performance over conventional low-gain methods.