Title
Nonlinear Stochastic Control Part I: A Moment-Based Approach
Abstract
This paper describes a new stochastic control methodology for nonlinear affine systems subject to parametric and functional uncertainties, with random excitations. The primary objective of this method is to control the statistical nature of the state of a nonlinear system to designed (attainable) statistical properties (e.g. moments). This methodology involves a constrained optimization problem for obtaining the undetermined control parameters, where the norm of the error between the desired and actual stationary moments of state/output responses is minimized subject to constraints on moments corresponding to a stationary distribution. To overcome the difficulties in solving the associated Fokker-Planck equation, generally experienced in nonlinear stochastic control and filtering problems, an approximation using the direct quadrature method of moments is proposed. In this innovative approach, the state probability density function is expressed in terms of a finite collection of Dirac delta functions, with the associated weights and locations determined by moment equations. The advantages of the proposed method are: (1) robustness with respect to parametric and functional uncertainties; (2) ability to control any specified stationary moments of the states/output probability density function; and (3) the state process can be Non-Gaussian. A numerical simulation is used to demonstrate the capability of the proposed nonlinear stochastic control method. Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
Publication Date
1-1-2009
Publication Title
AIAA Guidance, Navigation, and Control Conference and Exhibit
Number of Pages
-
Document Type
Article; Proceedings Paper
Personal Identifier
scopus
DOI Link
https://doi.org/10.2514/6.2009-5627
Copyright Status
Unknown
Socpus ID
78049256933 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/78049256933
STARS Citation
Xu, Yunjun and Vedula, Prakash, "Nonlinear Stochastic Control Part I: A Moment-Based Approach" (2009). Scopus Export 2000s. 12653.
https://stars.library.ucf.edu/scopus2000/12653