In this paper we analyze normal vector representations. We derive the error of the most widely used representation, namely 3D floating-point normal vectors. Based on this analysis, we show that, in theory, the discretization error inherent to single precision floating-point normals can be achieved by 250.2 uniformly distributed normals, addressable by 51 bits. We review common sphere parameteri...

A general approach is presented for the robust stabilization of controllable systems. The proposed strategy is viable whenever one can compute a finite-time control law that steers the state from any initial condition to a point closer to the desired equilibrium. Under suitable hypotheses, such control law can be applied in an iterative fashion, obtaining exponential convergence of the state to...

The main result of the paper states that almost any analytic single-input control system, which is truly nonlinear, that is not feedback linearizable, with controllable linearization at an equilibrium point, does not admit any symmetry preserving that point. By almost any system, we mean that we exclude a small class of odd systems, that admit just one nontrivial symmetry conjugated to minus id...

application of quantum-dot is a promising technology for implementing digital systems at nano-scale.  quantum-dot cellular automata (qca) is a system with low power consumption and a potentially high density and regularity. also, qca supports the new devices with nanotechnology architecture. this technique works based on electron interactions inside quantum-dots leading to emergence of quantum ...

Let G be a graph on n vertices with Laplacian matrix L and let b be a binary vector of length n. The pair (L,b) is controllable if the smallest L-invariant subspace containing b is of dimension n. The graph G is called essentially controllable if (L,b) is controllable for every b / ∈ ker(L), completely uncontrollable if (L,b) is uncontrollable for every b, and conditionally controllable if it i...

The problem of local controllability for the semilinear plate equation with Dirichlet boundary conditions is studied. By making use of Schauder’s fixed point theorem and the inverse function theorem, we prove that this system is locally controllable under a super-linear assumption on the nonlinearity, that is, the initial states in a small neighborhood of 0 in a certain function space can be dr...

Graphene oxide (GO) provides a potential route to large quantities of graphene, is cheap to make in bulk and easy to process.[1, 2] It is also a starting point for further functionalisation to create chemically modified graphenes (CMGs) e.g. for use in composites, light-harvesting, or as sensors. Understanding the chemical and physical structure of GO is a necessary step towards its controllabl...

This paper addresses the question “Can the object be pushed from here to there?” We characterize the set of objects that are controllable (can be positioned arbitrarily), with and without obstacles, for the cases of point and line pushing contact. For the case of line contact, we find a set of pushing directions that keep the object fixed to the pusher, and we use these pushing directions to fi...

We discuss the approximate controllability of nonlinear fractional integro-differential system under the assumptions that the corresponding linear system is approximately controllable. Using the fixed-point technique, fractional calculus and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional integro-differential equations are form...

This position paper focuses on the problem of stabilization of underactuated and nonholonomic autonomous vehicles at a given posture. The stabilization problem for those systems represents a challenge for nonlinear control theory because the linearization of such systems is not controllable. In fact, as shown by Brockett [6], for this class of systems there does not exist a continuously differe...