一致增长波动趋势二次最优闭环模型

The quadratic optimal closed loop model of uniform growth and fluctuation tendency

基于二次最优叠加目标函数ａｔ＝ａ＋ａｔ（０）＋ａｔ（１），给出了一致二次最优闭环模型下的动态Ｒｉｃｃａｔｉ方程的稳态因子解。在已知输入输出数据的情况下，用最大似然参数估计算法建模，并将Ｒｉｃｃａｔｉ稳态因子方程与优化松弛因子算法相结合，对模型进行参数估计，并且从理论上证明了均衡轨道的存在，进而给出了在动态叠加目标函数下的均衡轨道解析表达式，从而完成了一致增长波动趋势下二次最优闭环模型的均衡轨道仿真。

On the basis of the quadratic optimal additional objective function which includes exponential growth and fluctuation tendency besides constant tendency, under the conditions of the uniform quadratic optimal closed loop model, the static solutions of Riccati equation are obtained at first. Estimation of maximum likelihood parameter method is used to construct a model when samples of input and output are known. Then the static Riccati equation and relaxation of optimal factor method are used to estimate the parameters of the model, and the existence of the equilibrium paths is proved theoretically. Furthermore, the analytic formulae of the equilibrium paths are derived under dynamic addition object function. Thus the simulation of equilibrium paths is performed in uniform growth and fluctuation tendency.