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Tracking Control of Chaotic Systems via Optimized Active Disturbance Rejection Control

For tracking control of chaotic systems, we develop an active disturbance rejection (ADR) control method. Using the first state of the system as the only available state, a time-varying bandwidth extended state observer reconstructs the remaining states and the total disturbance. A time-varying bandwidth feedback controller forces all the states of the system to follow exactly the reference signal and its derivative. The parameters of the ADR controller are optimized using a genetic algorithm. As the objective function, we chose the weighted sum of the integral of the absolute error and the integral of the absolute control signal. Two chaotic systems—the Duffing system and the Genesio–Tesi system—are considered in computer simulation tests. Results of these simulations are presented to demonstrate the effectiveness of the ADRC method in controlling chaotic systems.