3,494 research outputs found
Gaussian process based model predictive control : a thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Engineering, School of Engineering and Advanced Technology, Massey University, New Zealand
The performance of using Model Predictive Control (MPC) techniques is highly dependent
on a model that is able to accurately represent the dynamical system. The datadriven
modelling techniques are usually used as an alternative approach to obtain such
a model when first principle techniques are not applicable. However, it is not easy to
assess the quality of learnt models when using the traditional data-driven models, such
as Artificial Neural Network (ANN) and Fuzzy Model (FM). This issue is addressed in
this thesis by using probabilistic Gaussian Process (GP) models.
One key issue of using the GP models is accurately learning the hyperparameters.
The Conjugate Gradient (CG) algorithms are conventionally used in the problem of
maximizing the Log-Likelihood (LL) function to obtain these hyperparameters. In this
thesis, we proposed a hybrid Particle Swarm Optimization (PSO) algorithm to cope with
the problem of learning hyperparameters. In addition, we also explored using the Mean
Squared Error (MSE) of outputs as the fitness function in the optimization problem.
This will provide us a quality indication of intermediate solutions.
The GP based MPC approaches for unknown systems have been studied in the past
decade. However, most of them are not generally formulated. In addition, the optimization
solutions in existing GP based MPC algorithms are not clearly given or are
computationally demanding. In this thesis, we first study the use of GP based MPC approaches
in the unconstrained problems. Compared to the existing works, the proposed
approach is generally formulated and the corresponding optimization problem is eff-
ciently solved by using the analytical gradients of GP models w.r.t. outputs and control
inputs. The GPMPC1 and GPMPC2 algorithms are subsequently proposed to handle
the general constrained problems. In addition, through using the proposed basic and
extended GP based local dynamical models, the constrained MPC problem is effectively
solved in the GPMPC1 and GPMPC2 algorithms. The proposed algorithms are verified
in the trajectory tracking problem of the quadrotor.
The issue of closed-loop stability in the proposed GPMPC algorithm is addressed
by means of the terminal cost and constraint technique in this thesis. The stability
guaranteed GPMPC algorithm is subsequently proposed for the constrained problem. By
using the extended GP based local dynamical model, the corresponding MPC problem
is effectively solved
Effect of Resonant Continuum on Pairing Correlations in the Relativistic Approach
A proper treatment of the resonant continuum is to take account of not only
the energy of the resonant state, but also its width. The effect of the
resonant states on pairing correlations is presented based on the relativistic
mean field theory plus Bardeen-Cooper-Schrieffer(BCS) approximation with a
constant pairing strength. The study is performed in an effective Lagrangian
with the parameter set NL3 for neutron rich even-even Ni isotopes. The results
show that the contribution of the proper treatment of the resonant continuum to
pairing correlations for those nuclei close to neutron drip line is important.
The pairing gaps, Fermi energies, pairing correlation energies, and binding
energies are considerably affected with a proper consideration of the width of
resonant states. The problem of an unphysical particle gas, which may appear in
the calculation of the traditional mean field plus BCS method for nuclei in the
vicinity of drip line could be well overcome when the pairing correlation is
performed by using the resonant states instead of the discretized states in the
continuum.Comment: 19 pages, 8 Postscript figur
A New Method Of Distinguishing Models For The High- Events At HERA
Many explanations for the excess high-Q^2 events from H1 and
ZEUS at HERA have been proposed each with criticisms. We propose a new method
to distinguish different models by looking at a new distribution which is
insensitive to parton distribution function but sensitive to new physics.Comment: 11 pages in revtex plus 3 figures in postscrip
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