Department of Mathematics and Statistics: Dr. Andrew D. Lewis
http://hdl.handle.net/1974/8
Selected preprints of Dr. Andrew D. Lewis2019-04-04T10:55:25ZAn example with interesting controllability and stabilisation properties
http://hdl.handle.net/1974/212
An example with interesting controllability and stabilisation properties
Hirschorn, Ron M.; Lewis, Andrew D.
A simple three-state system with two inputs is considered. The system's controllability is determined using properties of vector-valued quadratic forms. The quadratic structure is then used as the basis for the design of a homogeneous, discontinuous, stabilising feedback controller. The paper should be seen as an attempt to relate controllability of a system from a point to stabilisability of the system to the same point.
2005-01-01T00:00:00ZReduction, linearization, and stability of relative equilibria for mechanical systems on Riemannian manifolds
http://hdl.handle.net/1974/211
Reduction, linearization, and stability of relative equilibria for mechanical systems on Riemannian manifolds
Bullo, Francesco; Lewis, Andrew D.
Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory ``commute.'' As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.
2004-01-01T00:00:00ZDiscussion on: ``Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty''
http://hdl.handle.net/1974/210
Discussion on: ``Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty''
Lewis, Andrew D.
This is an invited discussion paper on the paper ``Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty'' by Xing-Gang Yan, Sarah K. Spurgeon, and Christopher Edwards, that will appear in the European Journal of Control.
2005-01-01T00:00:00ZRigid body mechanics in Galilean spacetimes
http://hdl.handle.net/1974/209
Rigid body mechanics in Galilean spacetimes
bhand, Ajit; Lewis, Andrew D.
An observer-independent formulation of rigid body dynamics is provided in the general setting of a Galilean spacetime. The equations governing the motion of a rigid body undergoing a rigid motion in a Galilean spacetime are derived on the basis of the principle of conservation of spatial momentum. The formulation of rigid body dynamics is then studied in the presence of an observer. It is seen that an observer defines a connection such that there exist rigid motions that are horizontal with respect to this connection that give the same physical motion of the rigid body, and for which the general equations of motion are exactly the usual Euler equations for a rigid body undergoing rigid motion.
2004-01-01T00:00:00Z