Receding horizon covariance control.

Bibliographic Details
Main Author: Wendel, Eric
Other Authors: Bhattacharya, Raktim (Thesis advisor)
Format: Thesis eBook
Language:English
Published: [College Station, Tex.] : [Texas A&M University], [2012]
Subjects:
Online Access:Link to OAK Trust copy

MARC

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100 1 |a Wendel, Eric. 
245 1 0 |a Receding horizon covariance control. 
264 1 |a [College Station, Tex.] :  |b [Texas A&M University],  |c [2012] 
300 |a 1 online resource. 
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500 |a "Major Subject: Aerospace Engineering" 
588 |a Description from author supplied metadata (automated record created 2012-10-22 13:24:58). 
502 |b Master of Science  |c Texas A&M University  |d 2012  |o http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11691 
504 |a Includes bibliographical references. 
516 |a Text (Thesis) 
520 3 |a Covariance assignment theory, introduced in the late 1980s, provided the only means to directly control the steady-state error properties of a linear system subject to Gaussian white noise and parameter uncertainty. This theory, however, does not extend to control of the transient uncertainties and to date there exist no practical engineering solutions to the problem of directly and optimally controlling the uncertainty in a linear system from one Gaussian distribution to another. In this thesis I design a dual-mode Receding Horizon Controller (RHC) that takes a controllable, deterministic linear system from an arbitrary initial covariance to near a desired stationary covariance in finite time. The RHC solves a sequence of free-time Optimal Control Problems (OCP) that directly controls the fundamental solution matrices of the linear system; each problem is a right-invariant OCP on the matrix Lie group GLn of invertible matrices. A terminal constraint ensures that each OCP takes the system to the desired covariance. I show that, by reducing the Hamiltonian system of each OCP from T?GLn to gln? x GLn, the transversality condition corresponding to the terminal constraint simplifies the two-point Boundary Value Problem (BVP) to a single unknown in the initial or final value of the costate in gln?. These results are applied in the design of a dual-mode RHC. The first mode repeatedly solves the OCPs until the optimal time for the system to reach the de- sired covariance is less than the RHC update time. This triggers the second mode, which applies covariance assignment theory to stabilize the system near the desired covariance. The dual-mode controller is illustrated on a planar system. The BVPs are solved using an indirect shooting method that numerically integrates the fundamental solutions on R4 using an adaptive Runge-Kutta method. I contend that extension of the results of this thesis to higher-dimensional systems using either in- direct or direct methods will require numerical integrators that account for the Lie group structure. I conclude with some remarks on the possible extension of a classic result called Lie?s method of reduction to receding horizon control. 
500 |a Electronic resource. 
650 4 |a Major Aerospace Engineering. 
653 |a covariance control theory 
653 |a Lie group actions 
653 |a receding horizon control 
653 |a Hamiltonian systems 
653 |a optimal control theory 
700 1 |a Bhattacharya, Raktim,  |e thesis advisor. 
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