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Chaos control and synchronization, with input saturation, via recurrent neural networks
Edgar N Sanchez1, Luis J Ricalde
1CINVESTAV, Unidad Guadalajara, Apartado Postal 31-438, Plaza La Luna, Guadalajara, Jalisco C.P. 45091, Mexico. sanchez@gdl.cinvestav.mx
Summary
This study introduces an adaptive tracking method for non-linear systems with unknown parameters and input saturation. The approach uses recurrent neural networks and Lyapunov methods for robust control and error boundedness.
Area of Science:
- * Control Systems Engineering
- * Artificial Intelligence
- * Nonlinear Dynamics
Background:
- * Addresses the challenge of adaptive tracking in complex non-linear systems.
- * Highlights issues like unknown parameters, unmodelled dynamics, and input saturation.
- * Emphasizes the need for robust control strategies in dynamic environments.
Purpose of the Study:
- * To develop an adaptive tracking control strategy for non-linear systems.
- * To handle uncertainties including unknown parameters, unmodelled dynamics, and input saturation.
- * To ensure tracking error boundedness using a novel control design.
Main Methods:
- * Utilizes a high-order recurrent neural network (RNN) for system identification.
- * Employs Lyapunov methodology to derive a learning law for the RNN.
- * Implements a stabilizing control law combining Lyapunov methods and Sontag's approach.
Main Results:
- * Successfully identifies unknown system dynamics using the proposed RNN.
- * Develops a control law that ensures stability and reference tracking.
- * Establishes boundedness of the tracking error, dependent on a design parameter.
Conclusions:
- * The proposed adaptive tracking method effectively manages non-linear systems with uncertainties.
- * Demonstrates applicability in complex dynamical systems like chaos control and synchronization.
- * Offers a robust solution for adaptive control problems with input saturation.