一类分数阶最优控制问题的高精度数值方法研究（英文）

A High Accuracy Numerical Algorithm for a Class of Fractional Optimal Control Problems

研究了一类具有二次型性能指标的分数阶线性系统最优控制问题的高精度数值方法.首先通过分数阶变分法导出了相应的最优条件和分数阶汉密尔顿系统,然后利用正则分数阶Sturm-Liouville问题的特征函数—分数次雅可比多项式和泛函极值的存在条件,对这类分数阶最优控制问题进行了数值求解,并分析了分数阶变分的收敛性.最后给出了数值算例,验证了方法具有高精度.

A high accurate numerical algorithm for the fractional optimal control problems （FOCPs） with quadratic performance index and fractional dynamic constraint is developed. The necessary optimality conditions and fractional Hamiltonian systems are obtained by the fractional variational principle. Based on the Jacobi poly-fractonomials, which are the eigenfunctions of the regular fractional Sturm-Liouville problem, the FOCPs are solved by combining the necessary condition for the existence of functional extre- mum. The variational convergence is analyzed, and numerical examples are given to confirm the high ac- curacy.