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Dual Control for Nonlinear Model Predictive Control

La, Huu Chuong

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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.

Item Type: Dissertation
Supervisor: Bock, Prof. Dr. Dr. h.c. mult. Hans Georg
Place of Publication: Heidelberg, Germany
Date of thesis defense: 20 July 2016
Date Deposited: 24 Aug 2016 12:53
Date: 2016
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Dean's Office of The Faculty of Mathematics and Computer Science
Subjects: 510 Mathematics
Controlled Keywords: Dual Control, Nonlinear Model Predictive Control, Partial Stability, Optimal Experimental Design
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