Observer Based Compensators for Nonlinear Systems

摘要

The report develops a new method for obtaining higher degree linear approximations of a certain class of nonlinear control systems. The standard approach in the analysis and synthesis of nonlinear systems is a first order approximation by a linear model. The report seeks an approximation for a nonlinear system by a linear model up to higher degrees than one. This is achieved by finding an appropriate nonlinear coordinate transformation-nonlinear feedback pair to perform the higher degree linearization. With the proposed method, one can improve the accuracy of the approximation up to arbitrarily higher degrees, provided certain solvability conditions are satisfied. The Hunt-Su linearizability theorem makes these conditions precise. Our approach to the solution of this linearization problem is similar to Poincare's Normal Form Theorem in formulation, but different in its solution method. The Homological Equations are based on the goal of obtaining a model accurate to a higher degree in the series expansion. A solution to this system of linear equations is equivalent to the solution to the problem of linearization up to higher degrees by coordinate change and feedback. (jhd)