Abstract

To understand complex dynamical systems, approximations are often made by a linearisation about an operating point of interest. The drawback of this linear approximation is that it only describes the system locally, around the operating point. One possible solution to overcome this drawback is to approximate the complex nonlinear dynamical system with a piecewise affine (PWA) system. Approximating nonlinear dynamical systems is very important in system theory where one is interested in simplifying its analysis and numerical simulation. PWA modelling is a very powerful tool to represent nonlinear systems as a collection of a finite number of linear systems. In the literature of PWA, a uniform grid (UG) approximation is the current method being used to approximate a nonlinear system as a PWA system. The drawback of this method is the potential large amount of regions required to obtain a desired accuracy, which is most evident for systems with more than one variable in the domain of the nonlinearity. In order to reduce the number of regions, the proposed research will develop a new methodology for obtaining PWA models using a set of linearisation points (SLP) and the Voronoi partition. First, in order to generate a partition based on a SLP, the curvature of the nonlinearity is used as a tool for selecting appropriate locations for the linearisation points. Next, an algorithm is proposed to automate the SLP approximation for both curves and surfaces. The SLP and UG approximation methods are then compared over several simple examples. Finally, the newly proposed approximation methodology is applied to three case studies: modelling of a nonlinear mechanical system and modelling and control of an unmanned aerial vehicle (UAV) and a micro air vehicle (MAV)