Research on Uncertain Stochastic Nonlinear System Based on Piecewise Loosely Constrained Nonlinear Characteristics and Backstepping Design Through Memristor Mode

In this paper, we mainly study the output feedback control problem of stochastic nonlinear system based on loose growth conditions and applies the research results to the electric vehicle control system of underwater oil and gas pipelines, which can improve the speed and stability of the equipment system. Firstly, the concept of randomness is introduced to study the tracking control problem of the system, which meet the more general polynomial function growth conditions. A combination of static and dynamic output feedback practices is proposed. The tracking controller makes all the states of the system, which meet boundedness and ensures that the tracking error of the system converges to a small neighborhood of zero. Secondly, the system is extended to the parameter uncertain system, the controller with complete dynamic gain is constructed by proving the boundedness of the system state and gain. Furtherly, the nonlinear term of the system satisfies the more relaxed power growth condition, combined with the inverse method to construct a set of Lyapunov functions and obtain the controller to ensure that the system is asymptotically probabilistic stability in the global scope. Finally, through the ocean library in the Simulation X software, the controller design results are imported into the underwater electro-hydraulic actuator model to verify the effectiveness.