Normal form and exact feedback linearisation of nonlinear stochastic systems: the ideal case
Author(s)
Mellone, Alberto
Scarciotti, giordano
Type
Conference Paper
Abstract
This paper introduces the concepts of stochastic relative degree, normal form and exact feedback linearisation for single-input single-output nonlinear stochastic systems. The systems are defined by stochastic differential equations in which both the drift and the diffusion terms are nonlinear functions of the states and the control input. First, we define new differential operators and the concept of stochastic relative degree. Then we introduce a suitable coordinate change and we show that the dynamics of the transformed state has a simplified structure, which we name normal form. Finally, we show that a condition on the stochastic relative degree of the system is sufficient for it to be rendered linear via a coordinate change and a nonlinear feedback. We provide an analytical example to illustrate the theory.
Date Issued
2020-03-12
Date Acceptance
2019-07-19
Citation
2019 IEEE 58th Conference on Decision and Control (CDC), 2020
Publisher
IEEE
Journal / Book Title
2019 IEEE 58th Conference on Decision and Control (CDC)
Copyright Statement
© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Source
2019 IEEE Conference on Decision and Control (CDC)
Publication Status
Published
Start Date
2019-12-11
Finish Date
2019-12-13
Coverage Spatial
Nice, France