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-Q2Q^2 Events At HERA

Many explanations for the excess high-Q^2 $e^+p \to e^+X$ 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