Set-Valued Discrete Approximation of State-Constrained Differential Inclusions

I. A. Chahma: Set-Valued Discrete Approximation of State-Constrained Differential Inclusions
Bayreuther Mathematische Schriften 67, 3 - 161, in: Bayreuth, Germany, 2003

Smart-Link: http://bms.math.uni-bayreuth.de/all_books.html#vol_67
ISBN/ISSN/ISMV Nummer: 0172-1062
MR Nummer: 2084892
Zentralblattnummer: 1073.65055
Keywords: nonlinear differential inclusions; convergence; error analysis; state constraints; stability; Euler's method; Runge-Kutta-methods; numerical examples
Mathematics Subject Classification Code: 65J99 (34A60 65L99 65L05 65L70)


Contents:

  Notations
  Introduction
1. Preliminaries
1.1 Spaces and Limits of Sets
1.2 Set-Valued Mappings and Continuity Concepts
2. Problem Formulation
2.1 Basic Definitions and Results on Differential Inclusions
2.2 Discretization of Differential Inclusions
3. Convergence Analysis of Solutions
3.1 Existence of Continuous and Discrete Solutions
3.2 Stability
3.2.1 Stability in the Continuous Case
a) Non-Smooth Case
b) Smooth Case
3.2.2 Stability in the Discrete Case
a) Non-Smooth Case
b) Smooth Case
3.3 Approximation of Solutions
3.3.1 Approximation of a Discrete Solution
3.3.2 Approximation of a Continuous Solution
4. Computation of Reachable Sets
4.1 Properties of Reachable Sets
4.2 State Discretization
4.2.1 Control Discretization
4.3 Approximate Computation of Reachable Sets
4.4 Computation of Reachable Sets
4.4.1 The Master/Slave System
4.4.1.1 Master program
4.4.1.2 Slave program
5. Numerical Applications
5.1 Linear Two-Dimensional Examples
5.2 Nonlinear Two-Dimensional Examples
5.3 Climate Change Models

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