中文摘要：

研究一类离散时间平均场不定线性二次最优控制问题,将问题中的加权矩阵推广到不定的情况,通过最小值原理和拉格朗日乘子法得出一组黎卡提差分方程,以及最优控制的状态反馈表达式,得出黎卡提方程的有解性是最优控制存在的充分条件,并且求出最优的性能指标。

英文摘要：

This paper studies a class of discrete time mean-field indefinite linear quadratic optimal control problem.Weighted matrix in question is extended to the uncertain situation,and a set of Riccati differential equations and the optimal state feedback control are obtained by means of the minimum principle and Lagrange multiplier method.Thus the solution of the Riccati equation is a sufficient condition for the existence of the optimal control,and the optimum performance is determined.