State constrained control strategy for stochastic nonlinear systems based on small gain and tangent function properties

In stochastic system control, the existence of randomness makes it challenging to limit the system state within the required range. The objective of this paper is to design a small gain adaptive controller with state constraints in the presence of uncertain factors such as unknown covariance noise and interference. A property of tangent barrier function is investigated, so that barrier Lyapunov function can be novel imbedded into the small gain controller and there is no violation of the time-varying constraints in the stochastic setting. Meanwhile, it has provided a detailed explanation in the remarks regarding the relationship between the new properties and the differential homeomorphism transformation method. Under the framework of the backstepping method, the combination of changing supply function and the small gain approach is used to obtain the stochastic input-to-state practically stability Lyapunov function of the subsystem, overcoming the influence of unknown covariance noise, unknown dynamics, and unknown parameters. Experimental results have shown the effectiveness of the entire system design.