Exponential Stabilization of Stochastic Feedforward Nonlinear Systems: A Dynamic Gain Approach

This article solves the problem of almost sure exponential stabilization via output feedback control for stochastic feedforward nonlinear systems with the unknown growth rate. A novel dynamic gain is introduced not only to cope with system uncertainties but also to ensure exponential convergence. Based on this dynamic gain, an adaptive output feedback controller is explicitly constructed. By introducing an improved stochastic analysis method, we rigorously prove that the closed-loop system has an almost surely unique solution, all the closed-loop signals are bounded almost surely, and the solution of the closed-loop system tends to the equilibrium position exponentially fast.