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一、引言 Chen.W.L与Shih.Y.P用walsh函数研究了线性时变系统状态方程的求解,以及线性时变系统基于二次型性能指标的最优反馈控制律的确定。Sannuti,B.E与Shieh.L.S采用方块脉冲函数取代Walsh函数来分析了线性时不变系统。徐宁寿、郑兵用方块脉冲函数分析了线性时变系统与最优线性调节器,导出了分段恒定解的递推算法,但是,他们的算法都末能摆脱矩阵的求逆,不便于实用。他们都末对非线性时变系统导出递推算法。
I. INTRODUCTION Chen.W.L and Shih.Y.P use walsh function to study the solution of the state equation of linear time-varying system and determine the optimal feedback control law based on the quadratic performance index of linear time-varying system. Sannuti, B.E and Shieh.L.S analyze linearly time-invariant systems by using a block-pulse function instead of the Walsh function. Xu Ningshou and Zheng Bing analyzed the linear time-varying system and the optimal linear regulator with the block pulse function, and derived the recursive algorithm of the piecewise constant solutions. However, their algorithms can not get rid of the inversion of the matrix at the end, which is inconvenient and practical. None of them derive a recurrence algorithm for nonlinear time-varying systems.