NDLI: Cost Moment Control and Verification Theorem for Nonlinear Stochastic Systems

Content Provider	IEEE Xplore Digital Library
Author	Chang-Hee Won
Copyright Year	2006
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Temple Univ., Philadelphia, PA (Chang-Hee Won)
Abstract	In this paper we consider a system which is nonlinear in the state and linear in control action. Then we optimize the distribution of the cost function using the statistical control method. In statistical control, the optimal controller is found by optimizing any cost moments or cumulants. The optimal controller is found via the Hamilton-Jacobi-Bellman equation. As a part of statistical control, we investigate n-th moment optimal control in this paper. The Hamilton-Jacobi-Bellman equation for the n-th cost moment case is presented as a necessary condition for optimality. Then the verification theorem for n-th moment control is proved. We solve the optimizing controller for the first cost moment utilizing the derived HJB equation and the verification theorem, we verify that the new theory reduces to classical LQG result for a linear system with quadratic cost. Furthermore, we solve time-invariant nonlinear system by transforming the HJB equation to a first order partial differential equation using the pseudo-inversion method. Even though that the necessary and sufficient conditions are more easily derived, we conclude that n-th moment control generates more complicated controller then n-th cost cumulant case
Starting Page	2583
Ending Page	2588
File Size	183515
Page Count	6
File Format	PDF
ISBN	1424401712
DOI	10.1109/CDC.2006.377201
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-12-13
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Nonlinear control systems Control systems Stochastic systems Cost function Optimal control Nonlinear equations Partial differential equations Optimization methods Linear systems Nonlinear systems
Content Type	Text
Resource Type	Article

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