Adaptive neural network control for nonholonomic systems with time-varying asymmetric constraints and iISS inverse dynamics

The method of adaptive neural network stabilization is investigated for uncertain nonholonomic systems with bounded or unbounded time-varying constraints and integral input-to-state (iISS) inverse dynamics in this paper. The iISS-Lyapunov function is introduced to handle the unmolded inverse dynamics of nonholonomic systems by using the method of changing supply rates. By constructing a tan-type structure barrier Lyapunov function to address the time-varying constraints of \(x_{0}\) $x_0$ -subsystem. A generalized state \(x_{n+1}\) $x_{n+1}$ is introduced for employing the discontinuous state scaling transformation, and the original x-subsystem is transformed into a new constrained system. Then, transforming the new system into an unconstrained system is implemented by constructing the nonlinear state-dependent functions, utilizing neural networks with adaptive control to compensate for the nonlinear uncertainties. The designed adaptive neural networks control strategy guarantees that every state of the original system is asymptotically regulated to zero without violating time-varying asymmetric state constraints and remains bounded. Finally, the simulation results obtained from discussing different initial value cases demonstrate the proposed method is efficacious.