Gaussian Process Model Predictive Control of An Unmanned Quadrotor

The Model Predictive Control (MPC) trajectory tracking problem of an unmanned quadrotor with input and output constraints is addressed. In this article, the dynamic models of the quadrotor are obtained purely from operational data in the form of probabilistic Gaussian Process (GP) models. This is different from conventional models obtained through Newtonian analysis. A hierarchical control scheme is used to handle the trajectory tracking problem with the translational subsystem in the outer loop and the rotational subsystem in the inner loop. Constrained GP based MPC are formulated separately for both subsystems. The resulting MPC problems are typically nonlinear and non-convex. We derived 15 a GP based local dynamical model that allows these optimization problems to be relaxed to convex ones which can be efficiently solved with a simple active-set algorithm. The performance of the proposed approach is compared with an existing unconstrained Nonlinear Model Predictive Control (NMPC). Simulation results show that the two approaches exhibit similar trajectory tracking performance. However, our approach has the advantage of incorporating constraints on the control inputs. In addition, our approach only requires 20% of the computational time for NMPC.Comment: arXiv admin note: text overlap with arXiv:1612.0121

A hierarchical Mamdani-type fuzzy modelling approach with new training data selection and multi-objective optimisation mechanisms: A special application for the prediction of mechanical properties of alloy steels

In this paper, a systematic data-driven fuzzy modelling methodology is proposed, which allows to construct Mamdani fuzzy models considering both accuracy (precision) and transparency (interpretability) of fuzzy systems. The new methodology employs a fast hierarchical clustering algorithm to generate an initial fuzzy model efficiently; a training data selection mechanism is developed to identify appropriate and efficient data as learning samples; a high-performance Particle Swarm Optimisation (PSO) based multi-objective optimisation mechanism is developed to further improve the fuzzy model in terms of both the structure and the parameters; and a new tolerance analysis method is proposed to derive the confidence bands relating to the final elicited models. This proposed modelling approach is evaluated using two benchmark problems and is shown to outperform other modelling approaches. Furthermore, the proposed approach is successfully applied to complex high-dimensional modelling problems for manufacturing of alloy steels, using ‘real’ industrial data. These problems concern the prediction of the mechanical properties of alloy steels by correlating them with the heat treatment process conditions as well as the weight percentages of the chemical compositions

Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models

This tutorial provides a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state-space models together with a software implementation in the statistical programming language R. We employ a step-by-step approach to develop an implementation of the PMH algorithm (and the particle filter within) together with the reader. This final implementation is also available as the package pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some intuition as to how the algorithm operates and discuss some solutions to problems that might occur in practice. To illustrate the use of PMH, we consider parameter inference in a linear Gaussian state-space model with synthetic data and a nonlinear stochastic volatility model with real-world data.Comment: 41 pages, 7 figures. In press for Journal of Statistical Software. Source code for R, Python and MATLAB available at: https://github.com/compops/pmh-tutoria

Lattice dynamical wavelet neural networks implemented using particle swarm optimisation for spatio-temporal system identification

Starting from the basic concept of coupled map lattices, a new family of adaptive wavelet neural networks, called lattice dynamical wavelet neural networks (LDWNN), is introduced for spatiotemporal system identification, by combining an efficient wavelet representation with a coupled map lattice model. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimisation (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the orthogonal projection pursuit algorithm, significant wavelet-neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated waveletneurons are optimised using a particle swarm optimiser. The resultant network model, obtained in the first stage, may however be redundant. In the second stage, an orthogonal least squares (OLS) algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet-neurons from the network. The proposed two-stage hybrid training procedure can generally produce a parsimonious network model, where a ranked list of wavelet-neurons, according to the capability of each neuron to represent the total variance in the system output signal is produced. Two spatio-temporal system identification examples are presented to demonstrate the performance of the proposed new modelling framework