Normal Forms for Perturbed Keplerian Systems

Normal Forms for Coupled Takens-Bogdanov Systems

The set of systems of differential equations that are in normal form with respect to a particular linear part has the structure of a module of equivariants, and is best described by giving a Stanley decomposition of that module. In this paper Groebner basis methods are used to determine a Groebner basis for the ideal of relations and a Stanley decomposition for the ring of invariants that arise...

Normal forms for spiking neural P systems

1 Department of Computer Science University of California Santa Barbara, CA 93106, USA [email protected], [email protected] 2 Department of Computer Science, Louisiana Tech University, Ruston PO Box 10348, Louisiana, LA-71272 USA [email protected] 3 Universidad Politécnica de Madrid UPM, Faculdad de Informática Campus de Montegancedo s/n, Boadilla del Monte, 28660 Madrid, Spain [email protected]...

Two Normal Forms for Rewriting P Systems

Controllers for Nonlinear Systems Using Normal Forms

We describe a method of designing local nonlinear controllers for the purposes of stabilizing unstable fixed points (UFP’s) of nonlinear systems by using the methods of normal form theory [Wiggins, 1990; Guckenheimer & Holmes, 1983] to determine a coordinate transformation which makes the system “simpler”. In the transformed system we design a local linear controller to stabilize the desired UF...

Cascade Normal Forms for Underactuated Mechanical Systems

In this paper, we introduce cascade normal forms for underactuated mechanical systems that are convenient for control design. These normal forms are partially linear which results from a well-known fact that underactuated systems can be partially linearized using a change of control [12]. The difficulty arises when the new control appears both in the linear and nonlinear subsystems. We introduc...