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Positive Controllability Of Systems With Nearly-Non-Negative Matrices, Theodore Sonne Perry

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper analyzes the controllability of constant coefficient linear differential equations and presents two proofs of a major theorem on controllability. Properties of nearly-non-negative matrices are discussed and in particular a theorem on the behavior of the exponential matrix of nearly-non-negative matrices is proven. These results are then used to prove that the reachable set for systems with nearly-non-negative matrices is limited to the positive hyperoctant.

Interpretation And Application Of Elements Of Differential Geometry And Lie Theory, James R. Brannan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Basic concepts of differential geometry and Lie theory are introduced. Lie transformation groups are applied to linear systems of differential equations and the problem of describing rigid body orientation. Linear Hamiltonian systems are then treated as a Lie system of differential equations. This theory is applied to a particular Hamiltonian system arising from a problem in control theory, the linear state regulator problem.

Shooting Method For Two-Point Boundary Value Problems, John D. Baumann

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper is to develop the shooting method as a technique for approximating the solution to the two-point boundary value problem on the interval [a,b] with the even order differential equation {i.e. n is even)

u⁽ⁿ⁾(t) + f(t, u(t), u⁽ⁱ⁾(t, ),..., u^(n-1)(t)) = 0

and boundary conditions

u(a) = A

u(b) = B

and with at most n-2 other boundary conditions specified at either a or b. The basic proceedure will be illustrated by the following example.

Consider the two-point boundary value problem (0.1) (0.2) (0.3) with the additional boundary conditions …