Showing papers on "Feedback linearization published in 1969"

A technique for suboptimal feedback control of nonlinear systems

Abstract: A simple easily implemented method is developed for obtaining a suboptimal control law for the optimization problem associated with minimizing a quadratic cost functional for nonlinear systems. The suboptimal control law is derived using a Taylor's series representation for the feedback gain matrix after modeling the nonlinear system by a linear system at each instant of time. The resultant control law is of feedback form and is nonlinear in state. The suboptimal control is obtained without using iterative techniques or any true optimal solutions. A second-order numerical example illustrates the effectiveness of the method and gives a comparison to the results of previous methods.

Optimal linearization in holography.

Abstract: Optimal linearization in holography is studied from the nonlinear system theory point of view. A generalized optimal linearization method for a physical photographic emulsion is presented. A generalized first-order amplitude transmittance (i.e., the generalized transfer function) with respect to the input irradiance is determined. The application of this optimal linearization technique toward a simple point object hologram is demonstrated, and the extension of this linearized procedure for a more complicated object is also discussed. Finally, it is concluded that, instead of restricting the holographic recording in the linear region of the T-E curve of the photographic emulsion, it is possible to obtain the optimum first-order diffraction image. If the nonlinearity of the holographic recording is weak, it is possible to define a linearization such that it will not be possible to perceive the nonlinear distortion.

Nonlinear systems of equations

Abstract: Unlike the other areas which have been discussed tonight , th is problem is not one for which "safe" programs or algorithms exis t which are assured of solving broad classes of problems. Rather, the f i e ld is characterized by the existence of numerous approaches, each of which may work for certain speci f ic types of systems and f a i l for others. Looking towards the future, the s i tuat ion may change with the development of su i t able polyalgorithms which combine a var ie ty of approaches. Typical applications where such systems as (1) arise are:

Design of linear feedback controllers for nonlinear plants

Abstract: Two related methods are developed for designing linear feedback controllers for nonlinear plants with initial states that are unknown but restricted to a given domain. It is shown that the well-known neighboring optimum method of controller design can be considered as a special case of the methods proposed here.

Jump criteria of nonlinear control systems and the validity of statistical linearization approximation

Abstract: We study the conditions for the unique response in a class of nonlinear control systems subject to random inputs using statistical linearization approximation. As in the case of sinusoidal inputs, we show that jump phenomena may occur if the inverse vector locus of the linear part passes through certain regions on the complex plane, where the regions are defined by the characteristics of nonlinear part. Such jump phenomena regions for several typical nonlinearities are given; we also show that, among a restricted class of nonlinearities, the saturation and dead zone produce the largest jump phenomena regions. A new result concerning the validity of statistical linearization approximation of nonlinear control systems is also presented. We show that the condition for the uniqueness of response to a given input in a nonlinear feedback system obtained through statistical linearization approximation is compatible with a related rigorous result, thus providing additional confidence in the applicability of statistical linearization.