奇异线性二次型微分鞍点对策的小波逼近解法

Wavelet Approximation Method for Linear-Quadratic Differential Saddle-Point Game in Singular Systems

研究广义状态系统中线性二次型微分对策鞍点策略的数值求解问题。基于小波多尺度多分辨逼近特性 ,提出了一种数值求解新方法。该法基于Daubechies小波的优良性质 ,特别是将Daubechies小波基的积分运算矩阵、乘积矩阵和快速离散小波变换系数矩阵应用于原问题的主要方程 ,将原问题转化为矩阵代数优化问题 ,避免直接计算耦合Riccati微分方程。算法简洁明了 ,适合于计算机求解。实例计算结果显示 。

This paper studies the numerical problem of the saddle point strategy for linear quadratic differential game in generalized state systems. A new numerical approximation solution method via Daubechies wavelets is proposed. The method is based upon some useful properties of Daubechies wavelets, a special operation matrix of integrate,product and coefficient matrices are applied to the main equation such that the problem is changed into an algebraic optimal problem,which avoids computing a pair of cross coupled Riccati differential equations directly. The procedure is simple and clear,and suit to calculate for computer. An example is illustrated, the result shows that the method is rational and effective.\;