基于混合遗传算法的控制受限热传导系统最优控制问题求解

Optimal control solving of heat transfer system with input constraints by applying hybrid genetic algorithm

混合遗传算法是用粒子群位移转移的思想改变遗传算法的变异规则,利用此算法求解控制受限热传导系统最优控制问题,获得了该问题的分段常量控制。混合遗传算法对热传导系统最优控制问题从时间和空间进行了离散,由有限差分方法得到其离散模型的递推方程,将热传导系统的积分区域划分为多段,每段的控制常量作为混合遗传算法中的基因。此算法不需要求解系统的伴随方程和计算梯度,整个求解过程易于实现,而且克服了梯度法容易陷入局部极值的缺点。应用实例证明混合遗传算法求解精度高于极大值原理算法。

A hybrid genetic algorithm （GA） was studied, in which the position displacement idea of the particle swarm optimization （PSO） was applied to change the mutation operation rule. The algorithm was applied to solve the optimal control problems of heat transfer with input constraints and the optimal piecewise-constant control was obtained. In this method, the discretization of the system from time and space and the basic function were got by finite-difference method. The time domain of heat transfer system was divided into several intervals, and the control in every interval was regarded as the gene of the hybrid CA. The algorithm can be easily realized because it does not depend on the adjoint equations and calculation gradient, and can overcome the flaw of getting into local extreme by gradient method. The results show that the algorithm enhances the solution precision compared with the maximum principle method.