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Identification and control of a nonlinear discrete-time system based on its linearization: a unified framework
Lingji Chen1, Kumpati S Narendra
1Scientific SyStems Company, Inc, Woburn, MA 01801, USA.
IEEE Transactions on Neural Networks
|September 24, 2004
Summary
This study introduces a new framework for controlling nonlinear discrete-time systems by separating them into linear and higher-order components. This approach enables precise local control and tracking, with applications in neural network-based system identification and control.
Area of Science:
- Control Theory
- Nonlinear Dynamical Systems
- System Identification
Background:
- Nonlinear discrete-time dynamical systems pose challenges for analysis and control.
- Existing methods often struggle with the complexity of nonlinearities.
Purpose of the Study:
- To develop a unified theoretical framework for identifying and controlling nonlinear discrete-time systems.
- To simplify the analysis of local properties by decomposing the system into linear and higher-order components.
Main Methods:
- Representing nonlinear systems as a sum of linearized and higher-order functions.
- Applying the implicit function theorem for local analysis.
- Utilizing concepts of controllability, observability, and feedback laws.
Main Results:
- Demonstrated local controllability and observability of nonlinear systems.
- Established the existence of feedback laws for local stabilization and tracking.
- Showed that nonlinear systems can exhibit well-defined relative degrees and zero-dynamics, mirroring their linear counterparts under certain conditions.
Conclusions:
- The proposed framework simplifies the control and identification of nonlinear discrete-time systems.
- The results provide theoretical underpinnings for using neural networks as controllers and identifiers for these systems.