Approximate feedback linearisation and stabilisation of nonlinear stochastic systems

Abstract

This paper addresses the design of a practically sound control architecture to solvethe problem of feedback linearisation and stabilisation of single-input single-output nonlinearstochastic systems. We first present a causal method to obtain, from measurements of the state,a-posterioriestimates of the variations of the Brownian motion which affected the system. Thenwe employ these estimates to design a control law that approximately compensates for thediffusive dynamics of the system. We address the local stabilisation problem and we prove thatthe control law which performs the proposed stochastic compensations stabilises a broader classof systems with respect to feedback laws without compensation. We finally validate the theorythrough a numerical example.