The paper is concerned with station keeping control problem via backstepping for an autonomous underwater vehicle (AUV) systems with nonlinear continuous function. This paper is the first time to using backstepping control method for stochastic nonlinear systems. Under nonlinear growth conditions, when the AUV motion affected the driving force, resistance of ocean and the force generated by current the difficulty arising from the underwater robot system output feedback makes the station keeping problems challenging and forward-looking. There exist two problems to research the fast response time and good station keeping, respectively. There a new control method is proposed for the first time to construct a backstepping stabilizing controller. In this paper, a concept of randomness to study the station keeping control problem of output feedback of stochastic nonlinear systems, remove the original harsher growth conditions, make it meet the more general function growth conditions. In order to deal with the station error of system converges to arbitrarily small domains. Under all the states of the system meet boundedness, a coordinate transformation is proposed. A useful technical theorem is proposed in the stability analysis to show that combined with the backstepping method to cleverly construct a set of Lyapunov functions, and obtain the output controller to ensure that the system is asymptotically probabilistic in the global scope. Finally, through the ocean library in the Simulation X simulation software and the Hardware-in-the-loop simulation, the controller design results are imported into the AUV actuator model to verify the effectiveness of the controller design.

In this paper, an underwater robot system with nonlinear characteristics is studied by a backstepping method. Based on the state preservation problem of an Autonomous Underwater Vehicle (AUV), this paper applies the backstepping probabilistic gain controller to the nonlinear system of the AUV for the first time. Under the comprehensive influence of underwater resistance, turbulence, and driving force, the motion of the AUV has strong coupling, strong nonlinearity, and an unpredictable state. At this time, the system’s output feedback can solve the problem of an unmeasurable state. In order to achieve a good control effect and extend the cruising range of the AUV, first, this paper will select the state error to make it a new control objective. The system’s control is transformed into the selection of system parameters, which greatly simplifies the degree of calculation. Second, this paper introduces the concept of a stochastic backstepping control strategy, in which the robot’s actuators work discontinuously. The actuator works only when there is a random disturbance, and the control effect is not diminished. Finally, the backstepping probabilistic gain controller is designed according to the nonlinear system applied to the simulation model for verification, and the final result confirms the effect of the controller design.

In this paper, the backstepping control problem is addressed by backstepping technique for a class of high-order stochastic nonaffine nonlinear systems. Different from existing papers, the nonlinear vector terms of system depend on the unmeasurable states besides the measurable output, and replace the high order index from constant value to varying value in order to allow the result to apply to the more general situations. The maximum value interval of observer gain parameter is chosen to ensure the closed-loop system globally asymptotically stable in probability. The efficiency of the output-feedback controller is illustrated by a hydraulic mechanical system simulation.

This paper addresses tracking control problems for autonomous underwater vehicle (AUV) systems with coupled nonlinear functions. For the first time, the radial basis function (RBF) is applied to the model reference adaptive control system, and the vehicle horizontal plane model is proposed. When the AUV movement is affected by the driving force, ocean resistance, and the force generated by the water current, the expected output of the AUV’s system is difficult to meet the expectations, making the AUV trajectory tracking problems challenging. There are two main options for finding suitable controllers for AUVs. The first is making the AUV model achieve better stability using a more complex controller. The second is the simpler controller structure, which can ensure faster system feedback. The RBF and model reference adaptive control (MEAC) system are combined to increase the number of hidden layers, increasing the AUV tracking stability. Because the embedded computing module of an AUV is a bit limited, 31 hidden layers are chosen to simplify the controller structures. A couple of Lyapunov functions are designed for the expected surge and sway velocities, and the vehicle tracking error gradually converges to (0,0). The controller design results are imported into the AUV actuator model by software, and after 0.64 s, the AUV tracking error is less than 1%. At last, the vehicle tracking experiments were carried out, showing that after 0.5 s, the AUV tracking error was less than 1%.

This paper focuses on a special class of stochastic nonlinear time-delay system with more weak conditions in which the drift and diffusion vectors depend on all the states, including the unmeasurable states for the first time. By introducing a high-gain observer, finding the maximum value interval of high-gain for the desired performance and choosing an appropriate Lyapunov-Krasoviskii function, an output-feedback controller is designed to ensure the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability and the output can be almost regulated to the origin surely. A practice example of mechanical movement system is provided to demonstrate the efficiency of the output-feedback controller.