Power-exponential and fixed-time consensus of conformable fractional-order quantum cellular neural networks via event-triggered control

Abstract

Abstract Quantum neural networks (QNNs) are considered to be superior to classical ANNs in machine learning, memory capacity, information processing, and quantum system simulation. However, In a practical and complex system, the dynamic behavior of an open quantum system could not be accurately described by an integer-ordered Schrödinger equation. In this paper, the conformable time-fractional-order Schrödinger equation is proposed, and accordingly, the model of conformable fractional-order quantum cellular neural networks (CFOQCNNs) is established and derived from the as-proposed equation. The properties of the conformable fractional-order derivative are studied and several new inequalities regarding the power-exponential and fixed-time convergence of conformable fractional-order systems are obtained. To save the communication resource, we introduce the event-triggered mechanism to construct the controllers and then the power-exponential and fixed-time synchronizations of the master-slave systems derived from the above CFOQCNNs are studied. We also prove the absence of Zeno behaviors regarding the event-triggered strategies. According to the numerical simulation, the dynamic behavior of the CFOQCNNs is discussed and the dissipativity of the CFOQCNNs is briefly revealed. Then the synchronization behaviors of the master and slave CFOQCNNs under power-exponential and fixed-time event-triggered control are demonstrated, where the effectiveness of the event-triggered control strategy is verified. Control behaviors with different fractional orders are also presented. We also discuss the hybrid of power-exponential control and fixed-time control and illustrate the advantages of the hybrid strategy. In the last, we conclude our studies, analyze the drawbacks of this work, and briefly introduce our future research.