Research on particle swarm optimization algorithm with characteristic of quantum parallel and its application in parameter estimation for fractional-order chaotic systems

Abstract

Parameter estimation for fractional-order chaotic systems is a multi-dimensional optimization problem, which is one of the important issues in fractional-order chaotic control and synchronization. With the characteristic of quantum parallel, a new quantum parallel particle swarm optimization algorithm is proposed for solving the problem of parameter estimation in fractional-order chaotic systems. A new method of quantum coding is presented with quantum parallel characteristic which can make the calculation number of each generation increase exponentially. On the basis of this method, a particle evolution equation composed of quantum current rotation angle, individual optimal rotation angle, and global optimum rotation angle is proposed, which can restraint the behavior of particles in quantum space, and also can improve the search capability of the algorithm. Numerical simulations of the fractional-order Lorenz system and the fractional-order Chen system are conducted and the results demonstrate the effectiveness, robustness and versatility of the proposed algorithm.