Stabilization of nonlinear nonholonomic systems with multiplicative stochastic state sensing noise

This paper studies the stabilization of nonlinear nonholonomic systems with multiplicative stochastic sensor uncertainty. Compared with existing results on nonlinear nonholonomic systems, this paper considers the influence of stochastic noise on sensors. Specifically, by applying the backstepping method and the input-to-state scaling technique, a new control design scheme is developed in which the control gain is appropriately designed to deal with sensor noise and the nonlinear functions simultaneously. By employing tools from stochastic analysis, it is verified that the closed-loop system almost surely has a unique global solution, that its origin is mean square stable, and that the state can almost surely be adjusted to zero. Finally, two examples are presented to verify the proposed control scheme.