Not Necessarily Linear System Theory
Digital Document
Document
Handle |
Handle
http://hdl.handle.net/11134/20002:860675845
|
||||||
---|---|---|---|---|---|---|---|
Persons |
Persons
Creator (cre): Fish, Andrew Joseph, Jr.
Major Advisor (mja): Jordan, David
Associate Advisor (asa): Pitkin, Edward
Associate Advisor (asa): Knapp, Charles
|
||||||
Title |
Title
Title
Not Necessarily Linear System Theory
|
||||||
Origin Information |
Origin Information
|
||||||
Parent Item |
Parent Item
|
||||||
Resource Type |
Resource Type
|
||||||
Digital Origin |
Digital Origin
reformatted digital
|
||||||
Description |
Description
The main results of this dissertation are: (1) a systems form for a class of nonlinear systems; (2) a control theory for the class of nonlinear systems; (3) a system solution in the form of Taylor's formula for the nonlinear system equations; and (4) a control theory for bilinear systems. The results of this dissertation are derived from a standard representation of a system called the system normal form which consists of a primitive equation and an output equation. The system normal form has many properties that are intuitively satisfying. It is derived from the equations that are obtained from the physical laws that govern the system. The system normal form maintains the integrity of the solutions of these equations. The system normal form may be written in terms of the physical variables of the system. It incorporates the algebraic properties normally found in the frequency representation of nonlinear systems. The system normal form is unique up to control. And the system normal form is applicable to many types of systems including systems with pure delays, integrators, and differentators. Three control laws are derived from the system normal form in this dissertation. The first and most important control law influences the variables of the primitive equation. The second is a control law for output variable control. And the last control law is for point to point control. The prime variable control result consists of an equation that expresses the system controls as a nonlinear function of the prime variables and the system initial conditions, an equation that defines the permissible solutions to the primitive equation, and a set of conditions that insure that the control will produce the desired system response. The output variable control theory translates the desired output response into a desired prime variable response and then uses the results of the prime varible control law. The point to point results rests upon finding a path that meets the initial and final conditions and that is an acceptable m solution to the system equations. These three control laws present a comprehensive control theory for nonlinear systems. The solution for the primitive equation, given the system controls and initial conditions, is given as a truncated Taylor series with error term. Each of the terms of the Taylor series is an i-th order directional derivative of the function that maps the system controls and initial conditions onto the prime variables, in the direction of the first variation of the system controls and the initial conditions, about a known solution, and evaluated at the known solution. Equations are derived for obtaining each of the directional derivatives and the error term. The conditions under which the Taylor's formula with error term exists are determined. In addition to the general nonlinear system results summarized above, a normal form for bilinear system equations is developed. From this form, a control law together with a constraint equation that defines the set of permissible solutions for the system are derived. The theory that is presented in this dissertation is a comprehensive nonlinear system theory that parallels the state space theory for linear systems.
|
||||||
Genre |
Genre
|
||||||
Organizations |
Organizations
Degree granting institution (dgg): University of Connecticut
|
||||||
Extent |
Extent
ix, 275 leaves, bound : illustrations ; 28 cm
|
||||||
Held By | |||||||
Rights Statement |
Rights Statement
|
||||||
Use and Reproduction |
Use and Reproduction
These materials are provided for educational and research purposes only.
|
||||||
Local Identifier |
Local Identifier
ASC Thesis 5141
8008091
|