Adaptive Passivity And Feedback Stabilization Of A Class Of Nonlinear Stochastic Systems

This paper addresses several important issues including stochastic passivity,feedback equivalence and global stabilization for a class of nonlinear stochastic adaptive sys-tems.We investigate the relationship between a stochastic adaptive passive system and the corresponding zero-output system.Different from the deterministic case.it is shown for the first time that feedback equivalence to a stochastic adaptive passive system re-quires a weakly minimum-phase condition.Following the stochastic adaptive passivity theory,global stabilization results are established for a class of nonlinear stochastic adap-tive systems with relative degree1≤r<n. An adaptive controller that solves the problem of rendering a system passive is presented for a special class of systems with parametric uncertainty.Stability results can be given without requiring commonly used assumptions such as linearity in the parameters.