In this paper we will study the non-linear oscillation of a conservative system having inertia and static non-linearities. By combining the linearization of the governing equation with the method of harmonic balance, we investigate analytical approximate solutions for the non-linear oscillations of the system. Unlike the classical harmonic balance method, linearization is performed prior to pro...

We revisit the method of Carleman linearization for systems of ordinary differential equations with polynomial right-hand sides. This transformation provides an approximate linearization in a higher-dimensional space through the exact embedding of polynomial nonlinearities into an infinite-dimensional linear system, which is then truncated to obtain a finite-dimensional representation with an a...

Optimal control is one of the most important branches in modern control theory, and linear quadratic regulator (LQR) has been well used and developed in linear control systems. However, there would be several problems in employing LQR to uncertain nonlinear systems. The optimal LQR problem for nonlinear systems often leads to solving a nonlinear two-point boundary-value (TPBV) problem (Tang et ...

Nonlinear evolution of the Landau-Lifshitz type can be exactly linearized. Special cases include the radiation-damped spin system and the superradiant system in the semiclassical regime, in the presence of time-varying driving fields. For these, the resultant linear system is simply that of a spin 1 / 2 particle, with the radiation damping rate, or superradiant characteristic time, manifested a...

Abstract: This paper presents an exact input-output linearization control scheme for rotor speed and rotor flux control of induction motor drive. In this scheme the motor model, is described in the fixed stator frame, and it is linearized, using exact inputoutput linearization technique, allowing a decoupled control of rotor flux and torque. To avoid the use of mechanical sensor, the rotor spee...

A general relationship is established between semiclassical and centroid-based methods for calculating real-time quantum-mechanical correlation functions. It is first shown that the linearized semiclassical initial-value-representation ~LSC-IVR! approximation can be obtained via direct linearization of the forward-backward action in the exact path integral expression for the correlation functio...

This paper presents the technical aspects, theoretical analysis, and comparisons of two new permanent magnet synchronous generator (PMSG) grid-interfaced models named PMSG boost and PMSG rectifierinverter. The exact feedback linearization (EFL) control scheme is used for the effective design and stability analysis of the aforementioned models. The complexity of the EFL control laws is discussed...

We prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints as it has been proposed by Liberti in 2007. The new conditions resolve inconsistencies that can occur when the original method is used. We also present a mixed-integer linear program to compute a minimally-sized lineari...

The estimation of structure from motion has been a central task of computational vision over the last decade. As it is very well known, the problem is nonlinear due to the perspective nature of the measurements. One may ask at this point: does there exist a clever choice of coordinates which simplifies the estimation task? In particular, since "linearity" is a coordinate-dependent notion, is th...