NDLI: Estimating the Region of Attraction for Uncertain Polynomial Systems Using Polynomial Chaos Functions and Sum of Squares Method

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Ataei, Armin Wang, Qian
Copyright Year	2012
Abstract	We present a general formulation for estimation of the region of attraction (ROA) for nonlinear systems with parametric uncertainties using a combination of the polynomial chaos expansion (PCE) theorem and the sum of squares (SOS) method. The uncertain parameters in the nonlinear system are treated as random variables with a probability distribution. First, the decomposition of the uncertain nonlinear system under consideration is performed using polynomial chaos functions. This yields to a deterministic subsystem whose state variables correspond to the deterministic coefficient components of the random basis polynomials in PCE. This decomposed deterministic subsystem contains no uncertainty. Then, the ROA of the deterministic subsystem is derived using sum of squares method. Finally, the ROA of the original uncertain nonlinear system is derived by transforming the ROA spanned in the decomposed deterministic subsystem back to the original spatial-temporal space using PCE. This proposed framework on estimation of the robust ROA (RROA) is based on a combination of PCE and SOS and is specially useful, with appealing computation efficiency, for uncertain nonlinear systems when the uncertainties are non-affine or when they are associated with a specific probability distribution.
Sponsorship	Dynamic Systems and Control Division
Starting Page	671
Ending Page	675
Page Count	5
File Format	PDF
ISBN	9780791845301
DOI	10.1115/DSCC2012-MOVIC2012-8786
Volume Number	Volume 2: Legged Locomotion; Mechatronic Systems; Mechatronics; Mechatronics for Aquatic Environments; MEMS Control; Model Predictive Control; Modeling and Model-Based Control of Advanced IC Engines; Modeling and Simulation; Multi-Agent and Cooperative Systems; Musculoskeletal Dynamic Systems; Nano Systems; Nonlinear Systems; Nonlinear Systems and Control; Optimal Control; Pattern Recognition and Intelligent Systems; Power and Renewable Energy Systems; Powertrain Systems
Conference Proceedings	ASME 2012 5th Annual Dynamic Systems and Control Conference joint with the JSME 2012 11th Motion and Vibration Conference
Language	English
Publisher Date	2012-10-17
Publisher Place	Fort Lauderdale, Florida, USA
Access Restriction	Subscribed
Subject Keyword	Chaos Uncertainty Theorems (mathematics) Computation Statistical distributions Polynomials Nonlinear systems
Content Type	Text
Resource Type	Article

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