Greene’s criterion for twist mappings asserts the existence of smooth invariant circles with preassigned rotation number if and only if the periodic trajectories with frequency approaching that of the quasi-periodic orbit are linearly stable. We formulate an extension of this criterion for conformally symplectic systems in any dimension and prove one direction of the implication, namely that if...

This paper discusses a design of nonlinear observer by a formal linearization method using an application of Chebyshev Interpolation in order to facilitate processes for synthesizing a nonlinear observer and to improve the precision of linearization. A dynamic nonlinear system is linearized with respect to a linearization function, and a measurement equation is transformed into an augmented lin...

The quadratic assignment problem (QAP) is one of the great challenges in combinatorial optimization. Linearization for QAP is to transform the quadratic objective function into a linear one. Numerous QAP linearizations have been proposed, most of which yield mixed integer linear programs (MILP). Kauffmann and Broeckx’s linearization (KBL) is the current smallest one in terms of the number of va...

This paper presents an adaptive feedback linearization approach to derive helicopter. Ideal feedback linearization is defined for the cases when the system model is known. Adaptive feedback linearization is employed to get asymptotically exact cancellation for the inherent uncertainty in the knowledge of the given parameters of system. The control algorithm is implemented using the feedback lin...

In this article, a novel and efficient collocation method based on Fibonacci wavelets is proposed for the numerical solution of non-linear Hunter–Saxton equation. Firstly, operational matrices integration associated with are constructed by following strategy Chen Hsiao. The merged used to convert given problem into system algebraic equations that can be solved any classical method, such as Newt...