基于Laguerre多项式的分布参数系统最优控制方法

Solution for Optimal Control of Distributed Parameter Systems Based on Laguerre Polynomial

讨论分布参数控制系统最优控制的逼近方法问题。运用Laguerre多项式的正交特性和微分运算矩阵推导出几个有效的结论,把分布参数系统最优控制的积分型性能指标转化为一般的代数式,从而将一类分布参数系统的最优控制问题转化为一般代数极值问题,并给出了具体求解步骤。该方法简化了分布参数系统的最优问题求解,并保持了最优控制和系统状态逼近解的分布参数特性。最后,从理论和对比分析两方面对该算法的逼近效果进行分析,并结合仿真示例验证了方法的有效性。

The optimal control approximation algorithm for distributed parameter systems （DPS） is discussed. Some conclusions are made from the orthogonal property and the integrated operational matrix of Laguerre polynomial, The integral performance index of the optimal control of the systems is changed into a corresponding algebraic form by these conclusions, and the optimal control problem of a class of DPS is transformed into a similar algebraic problem. The searching procedure is presented. The proposed method simplifies the procedure of solving optimal control problems of DPS and the distributed parameter property of optimal control and state is maintained, The approximation effect is analyzed with theory and comparison. Simulation results show the effectiveness of the proposed method.