Control of nonlinear dynamical systems using neural networks. II. Observability, identification, and control

Area of Science:

• Control Systems Engineering
• Dynamical Systems Theory
• Computational Neuroscience

Background:

• Dynamical systems often require state variable information for effective control and tracking.
• In many real-world scenarios, these state variables are not directly measurable or accessible.

Purpose of the Study:

• To investigate methods for regulating and tracking dynamical systems with unobservable states.
• To establish the theoretical foundation for nonlinear maps used in identification and control under state-inaccessible conditions.

Main Methods:

• Theoretical analysis to establish the existence of nonlinear maps for system identification and control.
• Exploration of the implications of these nonlinear maps for neural network-based implementations.
• Inclusion of simulation results to validate theoretical findings.

Main Results:

• The existence of nonlinear maps essential for identifier and controller design in state-inaccessible systems is proven.
• The paper details how these findings translate to practical neural network realizations.
• Simulation outcomes support the theoretical framework presented.

Conclusions:

• Effective regulation and tracking of dynamical systems are achievable even when state variables are inaccessible.
• Nonlinear maps provide a viable framework for designing identifiers and controllers in such systems.
• Neural network approaches are promising for implementing these control strategies.