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On the dynamics of nonlinear systems with input constraints
Navneet Kapoor1, Prodromos Daoutidis
1GE Corporate Research and Development, P.O. Box 8, Schenectady, New York 12301.
Chaos (Woodbury, N.Y.)
|June 5, 2003
Summary
This study analyzes nonlinear systems with input constraints, providing methods to define controllable regions and invariant sets. These findings are crucial for understanding system behavior under bounded control, demonstrated with chemical reactor examples.
Area of Science:
- Systems and Control Engineering
- Chemical Engineering
- Nonlinear Dynamics
Background:
- Nonlinear systems are prevalent in engineering and science.
- Input constraints are a common challenge in real-world control applications.
- Understanding system stability and controllability under constraints is critical.
Purpose of the Study:
- To develop methods for analyzing nonlinear systems with bounded control inputs.
- To characterize the domain of attraction for controllability.
- To introduce and define regions of invariance within these domains.
Main Methods:
- Dynamical analysis of nonlinear systems.
- Characterization of the domain of attraction.
- Introduction and analysis of regions of invariance.
- Case studies using chemical reactor models.
Main Results:
- A precise characterization of the domain of attraction for an equilibrium point under bounded control.
- The introduction and characterization of regions of invariance within these domains.
- Demonstration of the applicability of these concepts to practical chemical reactor models.
Conclusions:
- The study provides a robust framework for analyzing nonlinear systems with input constraints.
- The developed methods enhance the understanding of controllability and stability.
- The findings have direct implications for the design and control of chemical processes.