基于混合群智能优化算法的混沌系统参数估计

混沌系统的未知系统参数估计是实现混沌控制和同步的首要问题，通过构造一个合理的适应度函数，可将其转化为一个多维搜索空间的优化问题.提出一种融合改进骨干粒子群算法与改进差分进化算法的混合群智能优化方法来解决上述优化问题.对骨干粒子群算法中的粒子位置更新机制以及差分进化算法中的变异操作、交叉操作、交叉概率因子的设计等进行改进，有效兼顾了种群的多样性与算法的收敛性.在此基础上，讨论骨干粒子群优化算法与差分进化的融合优化策略，实现两个算法的协同进化，进一步提高算法的综合优化性能.用6个基准测试函数以及Lorenz混沌系统为例进行仿真实验，结果表明该方法具有全局寻优能力强、收敛速度快、搜索精度高、稳健性好等优点.

Parameter Estimation of Chaotic System Based on Hybrid Swarm Intelligence Optimization Algorithm

Estimation of unknown parameters of chaotic systems is a primary problem in chaos control and synchronization, which could be transformed into an optimization problem with multi-dimensional parameter space by constructing a proper fitness function. A hybrid swarm optimization algorithm combining improved bare bones particle swarm optimization algorithm and improved differential evolution is proposed. Particle position update mechanism, mutation operation, crossover operation, and crossover probability factor design are improved, taking into account both diversity of population and convergence rate of algorithm. On this basis, fusion optimization strategy of bare bones particles swarm optimization algorithm and differential evolution algorithm is discussed. Co-evolution of two algorithms is realized. To test algorithm optimization performance, simulation experiments were carried out with six benchmark functions. It shows that the proposed algorithm has powerful global optimizing ability, more stability, fast convergence speed and higher optimizing precision and so on. Lorenz chaotic system was taken as an example to estimate three unknown system parameters.