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对混沌系统施加微小扰动,使其自某初始点快速到达给定的不动点(目标点)邻域内,从而实现对混沌系统的快速控制。给出了求解混沌系统扰动序列值的无约束优化模型,并应用粒子群算法求解此优化问题。该算法不需要初值和导数信息,并具有控制参数少、容易实现等优点。数字实例表明,对于混沌系统快速控制问题,粒子群算法能求出满足要求的多组扰动序列值,且收敛速度较快、精度较高。
A small perturbation is applied to the chaotic system so that it quickly reaches a given fixed point (target point) neighborhood from some initial point, so that the chaotic system can be quickly controlled. An unconstrained optimization model for solving perturbed sequence values of chaotic systems is given. Particle swarm optimization is used to solve this optimization problem. The algorithm does not need initial value and derivative information, and has fewer control parameters, easy to implement and so on. Numerical examples show that for the problem of fast control of chaotic systems, Particle Swarm Optimization (PSO) can find multiple sets of perturbation sequence values satisfying the requirements, and the convergence speed is fast and the precision is high.