Adaptive neural control for stochastic nonholonomic systems with full-state constraints and unknown covariance noise

Abstract

In this paper, adaptive neural control is investigated for a class of stochastic nonholonomic systems disturbed by unknown covariance noise under the condition of full-state constraints. Compared with the related literatures, this paper largely generalizes the results in recent works on stochastic nonholonomic systems. The distinctive features of this paper are three folds: the full-state constrains are introduced; the restriction assumed on incremental covariance is removed; the growth assumptions imposed on drift and diffusion terms are somewhat weakened. In the control design procedure, the barrier Lyapunov function (BLF) is applied to conquer the effect of full-state constraints to system performance, unknown covariance noise is compensated with the aid of adaptive control design, the radial basis function neural networks are utilized to approximate unknown nonlinear functions and the backstepping technique is used to construct the desired controller. Then, by adopting the switching strategy to eliminate the phenomenon of uncontrollability, the proposed adaptive neural controller renders the closed-loop system to be semi-globally uniformly ultimately bounded. Moreover, the system states remain in the defined compact sets and the output tracks the reference signal well. Finally, the simulation example shows the effectiveness of the proposed scheme.

Keywords:

• Stochastic nonholonomic systems
• full-state constraints
• adaptive neural control
• BLF
• state feedback

2020 Mathematics Subject Classifications:

• Stochastic systems and control
• Stochastic systems in control theory

Data availability

The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.

Disclosure statement

The authors declare no potential conflict of interests.

Additional information

Funding

This paper was supported by the Program for Natural Scientific Research Foundation of Ningxia (2020AAC03062, 2021AAC03081), the National Natural Science Foundation (61963032), the Undergraduate Innovation and Entrepreneurship Training Program of Ningxia University (G2021107490008), and the funding scheme of Key scientific research of Henan's higher education institutions (22A120009).