离散时间随机二次型和指数型微分对策控制

Discrete-Time Stochastic Differential Game Control with Linear Quadratic and Exponential Performance Criteria

针对离散随机微分对策系统,研究了二次型和指数型两种性能指标下的鞍点策略问题。通过建立离散随机系统模型,利用动态规划法得到了两种指标函数下的鞍点策略。通过公式推导和数字仿真验证得到,在无系统噪声时,二次型和指数型指标函数下的鞍点策略是相等的;当系统噪声存在且噪声方差较大时,指数型性能指标下双方的控制增益均增大,得到的指标值将随噪声方差增大而减小。

Two discrete-time stochastic differential game control problem are solved whose performance criteria are the expected value of form. Solutions are derived based on Bellman quadratic form and exponential function of quadratic dynamic program. It is shown that when there is no disturbed noise, the solutions with different performance criteria are equivalent to each other, and when the system perturbed by additive white Gaussian noise, the solution with quadratic form performance criteria has no change, correspondingly the solution with exponential form performance criteria is varying dependent on the noise＇s variance, the expected value and the noise＇s variance have inverse proportion relationship.