Adaptive RBF Neural Network Tracking Control of Stochastic Nonlinear Systems with Actuators and State Constraints

• Published in: Mathematics (Basel) Vol. 12; no. 9; p. 1378
• Main Authors: Zhang, Jianhua, Li, Yinguang
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.05.2024
• Subjects: actuator constraint; Actuators; adaptive; Analysis; Control systems; Control systems design; Controllers; Design; full-state constraints; Hyperbolic functions; Inequality; Liapunov functions; Neural networks; NN fixed time control; Nonlinear control; Nonlinear systems; Randomness; stochastic nonlinear systems; Stochastic systems; Tracking control
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math12091378

This paper investigates the adaptive neural network (NN) tracking control problem for stochastic nonlinear systems with multiple actuator constraints and full-state constraints. The issue of system full-state constraints is tackled by a generalized barrier Lyapunov function (GBLF), and the output constraints of the system are considered to be in the form of time-varying functions, which are more in line with the needs of real physical systems. The NN approximation technique is utilized to overcome the influence of the uncertainty term on controller design due to randomness. Based on the backstepping technique, a neural adaptive fixed-time tracking control strategy is designed. Under the designed control strategy, the tracking accuracy of the controlled system can reach the expectation in a fixed time. The multi-actuator constraints are converted into a generalized mathematical model to simplify the controller design process. Using the characteristics of the hyperbolic tangent function, a new function called practical virtual control signal is designed using the virtual control signal as the input. Due to the saturation constraint property of the hyperbolic tangent function, it is theoretically ensured that no state of the system exceeds the constraints through to the new form of the virtual controller. Using the adaptive controller constructed in this paper, the controlled system is semi-global fixed-time stabilized in probability (SGFSP). Finally, the effectiveness of the proposed control strategy is further verified by simulation examples.