In this paper, we characterize a class of feasible direction methods in nonlinear programming through the concept of partial linearization of the objective function. Based on a feasible point, the objective is replaced by an arbitrary convex and continuously diierentiable function, and the error is taken into account by a rst order approximation of it. A new feasible point is deened through a l...

In this paper, we apply the Laplace decomposition method to obtain a series solutions of the Burgers-Huxley and Burgers-Fisher equations. The technique is based on the application of Laplace transform to nonlinear partial differential equations. The method does not need linearization, weak nonlinearity assumptions or perturbation theory and the nonlinear terms can be easily handled by using the...

In this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the Hunter-Saxton equation. The main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. It is a semi analytical-numerical method t...

We consider the coupling of two nonidentical dynamical systems using an adaptive feedback linearization controller to achieve partial synchronization between the two systems. In addition we consider the case where an additional feedback signal exists between the two systems, which leads to bidirectional coupling. We demonstrate the stability of the adaptive controller, and use the example of co...

The purpose of this paper is to provide a uniied description of iterative algorithms for the solution of traac equilibrium problems. We demonstrate that a large number of well known solution techniques can be described in a uniied manner through the concept of partial linearization, and establish close relationships with other algorithmic classes for nonlinear programming and variational inequa...

ontrol of underactuated biped robots is one of the challenging problems in the robotics field. The main difficulties of this problem that make it hard to control are its highly nonlinear dynamics, open-loop instability and impact event at the end of each step. Partial feedback linearization is a method to control underactuated systems but it is not robust against uncertainties and disturbances....

ontrol of underactuated biped robots is one of the challenging problems in the robotics field. The main difficulties of this problem that make it hard to control are its highly nonlinear dynamics, open-loop instability and impact event at the end of each step. Partial feedback linearization is a method to control underactuated systems but it is not robust against uncertainties and disturbances....

The relation between the solvability of the disturbance decoupling problem for a nonlinear system and its linearization around a working point is investigated. It turns out that generically the solvability of the disturbance decoupling via regular dynamic state feedback is preserved under linearization. This result gives a partial interpretation of introducing integral action in classical PID-c...