Criteria for mean-nonovershooting tracking control of stochastic nonlinear systems and application in mass–spring–damper systems

This paper addresses mean-nonovershooting tracking control for stochastic nonlinear systems. Existing methods have limitations such as initial-state restrictions, ambiguous control parameters and high computational burden. We propose a backstepping strategy using a novel square-root-type control gain parameter. Based on stochastic Lyapunov stability theory, virtual controllers and a final control law are designed to ensure mean boundedness of all closed-loop signals and prove that the tracking error mean remains negative, achieving mean-nonovershooting control. Compared with existing studies, the proposed method relaxes initial-state restrictions, requiring only that the initial output is less than the initial reference signal, thus reducing conservatism. The control parameters are clearly defined and easy to implement. Simulations of a mass–spring–damper system validate the algorithm's effectiveness, demonstrating advantages in zero overshoot and fast convergence.