Intro
Organization
Preface
Contents
Optimal Control and Optimization
Constructive Controllability for Incompressible Vector Fields
1 Introduction
2 Notation and Preliminaries
3 Global Controllability
4 Case of a Compact Manifold
References
Note On Optimal Control Problem Applied to Irrigation with Sectioned Soil
1 Introduction
2 Formulation
3 Problem Analysis
3.1 Hydrological Needs of the Crop
3.2 Existence of Solution
3.3 Maximum Principle in the Normal Form
3.4 Solution Profile
4 Numerical Results
4.1 Function gg Values

4.2 Validation
5 Conclusion
References
On Non-linear Optimization with a Perturbed Objective Function
1 Introduction
2 Preliminaries
2.1 Neutrices and External Numbers
2.2 Some Topological Notions
2.3 Flexible Functions
3 Optimization Problems with a Flexible Objective Function
4 Limits of Flexible Functions
5 Neutrix-Derivatives
6 Nearly Optimal Points and Neutrix Derivatives
7 Neutrix-Partial Derivatives
8 An Implicit Function Theorem for Neutrix-Differentiability
9 Lagrange Multiplier
References

Approximation of the Solution Based on the Decoupling Transformation of Linear Time-Varying Singularly Perturbed System with Delay
1 Introduction
2 Formulation of the Problem
2.1 System Under Investigation
2.2 Degenerate and Boundary Layer Systems
3 Decoupling Transformation and Its Asymptotic Representation
4 The Decoupled System and Its Approximations
5 Solution Approximation
6 Example
7 Conclusion
References
Dynamic Systems
Optimal Cyclic Dynamic of Distributed Population Under Permanent and Impulse Harvesting
1 Introduction
2 Optimal Solution

2.1 Correctness and Boundness of Functional
2.2 Existence of Optimal Strategy
3 Proof of the Existence of an Optimal Harvesting Strategy
References
On the Growth and Oscillation of Fixed Points of Solutions of Linear Differential Equations with Meromorphic Coefficients
1 Introduction and Main Results
2 Preliminary Lemmas
3 Proofs of the Main Results
4 Future Aspects
References
Hesitant Fuzzy Sets Are Observers
1 Introduction
2 Observer as a Control Parameter in Systems
3 Relative Semidynamical Systems
4 Sink Points
5 Application
References

On the Stability of Three-Time-Scale Linear Time-Invariant Singularly Perturbed Systems with State Delay
1 Introduction
2 Statement of the Problem
3 Preliminaries
4 Stability of the TSPLTISD
5 Results and Verifications
6 Conclusion
References
Applications of Dynamic Systems and Optimal Control
The Boolean Determinant Calculus
1 Introduction
2 Theoretical Basis and Its Transfer
2.1 Historical Application
2.2 Transfer to Boolean Algebra
3 Transitions Graph
3.1 Definition: Transitions Graph
4 The Transition Matrix
4.1 Definition: Transition Matrix