Synchronization of Fractional-Order Chaotic Systems with Model Uncertainty and External Disturbance

This paper is concerned with complete synchronization of fractional-order chaotic systems with both model uncertainty and external disturbance. Firstly, we propose a new dynamic feedback control method for complete synchronization of fractional-order nominal systems (without both uncertainty and disturbance). Then, a new uncertainty and disturbance estimator (UDE)-based dynamic feedback control method for the fractional-order systems with both uncertainty and disturbance is presented, by which the synchronization problem of such fractional-order chaotic systems is realized. Finally, the fractional-order Lorenz system is used to demonstrate the practicability of the proposed results.

Partial Anti-Synchronization of the Fractional-Order Chaotic Systems through Dynamic Feedback Control

This paper investigates the partial anti-synchronization problem of fractional-order chaotic systems through the dynamic feedback control method. Firstly, a necessary and sufficient condition is proposed, by which the existence of the partial anti-synchronization problem is proved. Then, an algorithm is given and used to obtain all solutions of this problem. Moreover, the partial anti-synchronization problem of the fractional-order chaotic systems is realized through the dynamic feedback control method. It is noted that the designed controllers are single-input controllers. Finally, two illustrative examples with numerical simulations are used to verify the correctness and effectiveness of the proposed results.

Improved Key Recovery Attacks on Simplified Version of K2 Stream Cipher

The K2 stream cipher, designed for 32-bit words, is an ISO/IEC 18033 standard and is listed as a recommended algorithm used by the Japanese government in the CRYPTREC project. The main feature of the K2 algorithm is the use of a dynamic feedback control mechanism between the two linear feedback shift registers, which makes the analysis of the K2 algorithm more difficult. In this paper, for its simplified version algorithm, a key recovery attack is performed by using differential attacks. Firstly, for the unknown key, the same IV is fixed in two chosen IV differential attacks, and we use the input differences and the output differences of the S-box to recover the input of S-box; the internal state values can be uniquely determined by taking intersection of the input of S-box. This technology is used to improve the key recovery attack of seven-round algorithm proposed by Deike Priemuth-Schmid. Secondly, we find the constraint relationship between the keystream equations and the unknown differences by introducing the guess difference bit and eliminate the impossible differences by the constraint relationship. Thus, we expand the key recovery attack from seven to nine rounds. The time complexity of the attack is $\boldsymbol{O} \boldsymbol{(2^{113.93})}$, the data complexity is $\boldsymbol{O}\boldsymbol{(2^{8.71})}$ and the success rate is $\textbf{99.07\%}$.

Stabilization of a Class of Complex Chaotic Systems by the Dynamic Feedback Control

The stabilization problem of the complex chaotic system is investigated in this paper. First, a systematic method is proposed, by which a given complex chaotic system can be transformed into its equivalent real chaotic system. Then, both simple and physical controller is designed for the corresponding real chaotic system by the dynamic feedback control method, thereby the controller for the original complex chaotic system is obtained. Especially, for some complex system, the controller is obtained by the linear feedback control method. Finally, two illustrative examples with numerical simulations are used to verify the validity and effectiveness of the theoretical results.

Dynamic Feedback Control And State Observers For A Knee Rehabilitation Device Using Soft Action

Rehabilitation devices with soft components increasingly attract more attention due to their characteristics in human-robot interaction. However, these types of systems have a certain level of complexity when analyzing and controlling. We have designed a 5-link knee rehabilitation device operated on two of the five joints using elastic action to help the movement of the knee. In this work, we simplify the modeling of the rehabilitation device in a smooth acting system of 1 degree of freedom. Subsequently, we present the design and implementation of a dynamic feedback controller to track a desired reference. For the proposed controller, we implemented a state observer to estimate the rigidity of the system and some of the states. As a result, we present the design and implementation of the controller with a status observer, which follows a desired angular path with a desired stiffness. We demonstrate in simulation, through tests aimed at carrying out some rehabilitation routines, to validate the effectiveness and stability of the controlled system, which responds effectively to disturbances.

Two Types of Synchronization Problems in a New 5D Hyperchaotic System

This paper investigates the synchronization problem in a new 5D hyperchaotic system. Firstly, the existence of two types of synchronization problems in the new 5D hyperchaotic system is proved. Then, by the dynamic feedback control method, one complete synchronization problem and three coexistence of complete synchronization and antisynchronization problems in such system are realized. Finally, numerical simulations are used to verify the validity and effectiveness of the theoretical results.

Antisynchronization of the Hyperchaotic Systems with Uncertainty and Disturbance Using the UDE-Based Control Method

In this paper, we investigate the antisynchronization problem of a class of hyperchaotic systems with both model uncertainty and external disturbance. Firstly, combining the dynamic feedback control method and the uncertainty and disturbance estimation (UDE)-based control method, we propose a new UDE-based dynamic feedback control method. Secondly, we take the 4D hyperchaotic system as an example and realize the antisynchronization problem of such system. Finally, the effectiveness and correctness of the proposed method is verified by numerical simulation.