方块脉冲函数用于非线性系统的分析以及最优控制的综合

本文用方块脉冲函数方法讨论了解非线性微分方程系统的收敛性和稳定性.在分析和综 合非线性系统最优控制规律中,得到了分段恒定解答的递推算法,算法证明简单,除对基于二 次型性能指标的线性时变系统有效外,也可用于求解线性最优控制系统的Riccati方程.

Analysis of Nonlinear Systems and Synthesis of Optimal Control VIA Block-Pulse Functions

In this paper, the convergence and stability of the block-pulse function method in solving nonlinear systems are proved. By applying properties of the block-pulse functions to the analysis and synthesis of nonlinear systems, recursive algorithms of the piecewise constant solutions are obtained. The proof is simple. The method is quite efficient, particularly, for time-varying linear systems with a quadratic performance index. Furthermore, the Riceati equation of the optimal linear control system can also be solved by this method.