eprintid: 21610
rev_number: 17
eprint_status: archive
userid: 2641
dir: disk0/00/02/16/10
datestamp: 2016-08-24 12:53:26
lastmod: 2016-09-26 12:38:51
status_changed: 2016-08-24 12:53:26
type: doctoralThesis
metadata_visibility: show
creators_name: La, Huu Chuong
title: Dual Control for Nonlinear Model Predictive Control
subjects: ddc-510
divisions: i-110001
adv_faculty: af-11
cterms_swd: Dual Control
cterms_swd: Nonlinear Model Predictive Control
cterms_swd: Partial Stability
cterms_swd: Optimal Experimental Design
abstract: In this thesis we treat the problem of Dual Control for Nonlinear Model Predictive Control (NMPC) from a perspective of Optimal Experimental Design (OED).

Controlling uncertain processes poses great challenges as well as offers opportunities for mathematicians in recent years. While the Dynamic Programming principle might
hold, its applicability is limited to a few very simple cases. This calls for the study of approximation methods and real-time algorithms.

In this work we study optimal control problems with uncertain parameters and states and develop new methods based on Dual Control. We first carry out a sensitivity analysis to assess the effect of uncertainty on the control performance. By analyzing the interplay between the performance control task and the information gain task, we propose novel approaches to the Dual Control problem in the context of NMPC with the help of OED.

Furthermore, we present the statistical background and probabilistic bounds for the realized controller performance with respect to the original objective. Therefore, we essentially fill a gap in the literature.

As NMPC drives the process in the course of time and the estimation procedure runs, it is of interest to understand the convergence properties and the asymptotic properties
of the parameter and state estimates. We devote one chapter to the investigation of asymptotic properties of the Least Squares (LS) estimates, showing that in some cases
the estimation problem is ill-posed leading to divergence. With the use of a sequential LS method, however, convergence can be retained. A convergence result is established.

On the other hand, we observe that for some processes, if the states of interest are stable, the convergence of parameter estimates may become irrelevant. This motivates
our study on partial stability for NMPC which extends the classical stability analysis of NMPC by several fundamental results, including general stability results without
terminal costs or terminal constraints.

Another source of motivation for this thesis is the study of nonlinear Optimal Experimental Design. Since optimal designs are computed for specific values of parameters
but the true ones are unknown, it is important to assess the optimality of designs as well as to find a way to reach the true parameters. This motivates our study on sequential
OED in the framework of Dual Control. For this purpose, we reformulate the problem of sequential OED to make it applicable for the Dynamic Programming principle. We
also build a bridge between continuous designs and discrete designs by presenting several results on finite support for continuous OED.

The methods have been implemented and we illustrate the obtained results by examples ranging from classics to practical applications in vehicle control and chemical
engineering.
date: 2016
id_scheme: DOI
id_number: 10.11588/heidok.00021610
ppn_swb: 1658756681
own_urn: urn:nbn:de:bsz:16-heidok-216108
date_accepted: 2016-07-20
advisor: HASH(0x55de57c89b20)
language: eng
bibsort: LAHUUCHUONDUALCONTRO2016
full_text_status: public
place_of_pub: Heidelberg, Germany
citation:   La, Huu Chuong  (2016) Dual Control for Nonlinear Model Predictive Control.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/21610/1/La_Dissertation.pdf