Nonlinear Systems Analysis
Lecture 7
Sections 3.2, 3.2, 3.4
Dependence on Data, Sensitivity Analysis,
Comparison Principle
Feng-Li LianNTU-EE
Sep04 – Jan05
© Feng-Li Lian 2004
Ch3B-2
Nonlinear Systems Analysis
Outline
Introduction (L5)
Banach Space (L5)
Contraction Mapping Theorem (L5)
Existence and Uniqueness (L6)
Continuous Dependence on Initial Conditions and Parameters (L6)
Differentiability of Solutions and Sensitivity Equations (L7)
Comparison Principle (L7)
© Feng-Li Lian 2004
Ch3B-3
Nonlinear Systems Analysis
Continuous Dependence on Data - 1 (3.2)
© Feng-Li Lian 2004
Ch3B-4
Nonlinear Systems Analysis
Continuous Dependence on Data - 2
© Feng-Li Lian 2004
Ch3B-5
Nonlinear Systems Analysis
Continuous Dependence on Data - 3
© Feng-Li Lian 2004
Ch3B-6
Nonlinear Systems Analysis
Gronwall-Bellman Inequality - 1 (App. A, page 651)
© Feng-Li Lian 2004
Ch3B-7
Nonlinear Systems Analysis
Gronwall-Bellman Inequality - 2
© Feng-Li Lian 2004
Ch3B-8
Nonlinear Systems Analysis
Closeness of Solutions - 1 (3.2)
© Feng-Li Lian 2004
Ch3B-9
Nonlinear Systems Analysis
Closeness of Solutions - 2
© Feng-Li Lian 2004
Ch3B-10
Nonlinear Systems Analysis
Closeness of Solutions - 3
© Feng-Li Lian 2004
Ch3B-11
Nonlinear Systems Analysis
Closeness of Solutions - 4
© Feng-Li Lian 2004
Ch3B-12
Nonlinear Systems Analysis
Dependence on Initial States & Parameters - 1 (3.2)
© Feng-Li Lian 2004
Ch3B-13
Nonlinear Systems Analysis
Dependence on Initial States & Parameters - 2
© Feng-Li Lian 2004
Ch3B-14
Nonlinear Systems Analysis
Dependence on Initial States & Parameters - 3
© Feng-Li Lian 2004
Ch3B-15
Nonlinear Systems Analysis
Dependence on Initial States & Parameters - 4
© Feng-Li Lian 2004
Ch3B-16
Nonlinear Systems Analysis
Dependence on Initial States & Parameters - 5
© Feng-Li Lian 2004
Ch3B-17
Nonlinear Systems Analysis
Dependence on Initial States & Parameters - 6
© Feng-Li Lian 2004
Ch3B-18
Nonlinear Systems Analysis
Dependence on Initial States & Parameters - 7
© Feng-Li Lian 2004
Ch3B-19
Nonlinear Systems Analysis
Differentiability of Solutions - 1 (3.3)
© Feng-Li Lian 2004
Ch3B-20
Nonlinear Systems Analysis
Differentiability of Solutions - 2
© Feng-Li Lian 2004
Ch3B-21
Nonlinear Systems Analysis
Differentiability of Solutions - 3
© Feng-Li Lian 2004
Ch3B-22
Nonlinear Systems Analysis
Sensitivity Equation - 1 (3.3)
© Feng-Li Lian 2004
Ch3B-23
Nonlinear Systems Analysis
Sensitivity Equation - 2
© Feng-Li Lian 2004
Ch3B-24
Nonlinear Systems Analysis
Sensitivity Equation - 3
© Feng-Li Lian 2004
Ch3B-25
Nonlinear Systems Analysis
Comparison Principle - 1 (3.4)
© Feng-Li Lian 2004
Ch3B-26
Nonlinear Systems Analysis
Comparison Principle - 2
© Feng-Li Lian 2004
Ch3B-27
Nonlinear Systems Analysis
Comparison Principle - 3
© Feng-Li Lian 2004
Ch3B-28
Nonlinear Systems Analysis
Example 3.8 - 1 (3.4)
© Feng-Li Lian 2004
Ch3B-29
Nonlinear Systems Analysis
Example 3.8 - 2
