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

Socpus ID

78049256933 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/78049256933

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