Higher-degree linear approximations of nonlinear systems
In this dissertation, the author develops a new method for obtaining higher degree linear approximations of nonlinear control systems. The standard approach in the analysis and synthesis of nonlinear systems is a first order approximation by a linear model. This is usually performed by obtaining a series expansion of the system at some nominal operating point and retaining only the first degree terms in the series. The accuracy of this approximation depends on how far the system moves away from the normal point, and on the relative magnitudes of the higher degree terms in the series expansion. The approximation is achieved by finding an appropriate nonlinear coordinate transformation-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. This approach is similar to Poincare's Normal Form Theorem in formulation, but different in its solution method. After some mathematical background the author derives a set of equations (called the Homological Equations). A solution to this system of linear equations is equivalent to the solution to the problem of approximate linearization. However, it is generally not possible to solve the system of equations exactly. He outlines a method for systematically finding approximate solutions to these equations using singular value decomposition, while minimizing an error with respect to some defined norm.
- Research Organization:
- California Univ., Davis, CA (USA)
- OSTI ID:
- 6089706
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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