Global Asymptotic Stabilization of Nonlinear Deterministic Systems Using Wiener Processes

The objective of this study is to present a noise-assisted stabilization method and a constructive method for designing a stabilizing controller. We investigate the stabilization of a deterministic nonlinear affine system by using a controller with a Wiener process. Our approach focuses on the global asymptotic stabilization of nonholonomic systems. The proposed method for designing a stabilizing controller is based on the notion of a stochastic control Lyapunov function. We show that if there exists a stochastic control Lyapunov function with small control property, the designed controller globally asymptotically stabilizes a given system with probability one.