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首页> 外文会议>The 8th international conference on optimization: Techniques and Applications >Filtering Solution of Nonlinear Stochastic Optimal Control Problem in Discrete-Time with Model-Reality Differences
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Filtering Solution of Nonlinear Stochastic Optimal Control Problem in Discrete-Time with Model-Reality Differences

机译：具有模型与实际差异的离散时间非线性随机最优控制问题的滤波解

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摘要

In this paper we propose an efficient approach for solving the nonlinear stochastic optimal control problem in discrete-time. The aim is to obtain the filtering solution only by solving the linear model-based optimal control problem iteratively. To do this, a mathematical model, which is a simplified model-based optimal control problem derived from the original optimal control problem, is constructed. It can be seen that this simplified mathematical model is a modified linear quadratic Gaussian optimal control model, where the adjusted parameters are added into the model, aiming to approximate the solution of the original optimal control problem iteratively. Before the iteration begins, the adjusted parameters are zero value and the model is actually a standard linear quadratic Gaussian optimal control model. It is important to note that the reality information is employed in estimating the dynamic of state, where the output from the real plant is measured. During the iterative procedure, the differences among the real plant and the model used are captured by the adjusted parameters and the modified linear quadratic Gaussian optimal control model is optimized with these specified adjusted parameters, in turn, to update their values based on the measured output iteratively. Therefore, the interaction on system optimization and parameter estimation is generated. When the convergence is achieving, the true filtering solution of the original optimal control problem is obtained in spite of model-reality differences. To illustrate the applicable of the proposed algorithm, a problem of nonlinear continuous stirred tank reactor is studied. In conclusion, the efficiency of the proposed algorithm has been shown.
机译：在本文中，我们提出了一种解决离散时间非线性随机最优控制问题的有效方法。目的是仅通过迭代解决基于线性模型的最优控制问题来获得滤波解。为此，构建了数学模型，该数学模型是从原始最优控制问题派生的基于简化模型的最优控制问题。可以看出，这个简化的数学模型是一种改进的线性二次高斯最优控制模型，在模型中添加了调整后的参数，旨在迭代地逼近原始最优控制问题的解。在迭代开始之前，调整后的参数为零值，并且该模型实际上是标准的线性二次高斯最优控制模型。重要的是要注意，现实信息用于估计状态的动态，在此状态下对真实工厂的输出进行测量。在迭代过程中，通过调整后的参数捕获实际工厂和所用模型之间的差异，并使用这些指定的调整后的参数对修改后的线性二次高斯最优控制模型进行优化，从而根据测量的输出更新其值反复地。因此，产生了关于系统优化和参数估计的相互作用。当实现收敛时，尽管存在模型-现实差异，但仍可获得原始最优控制问题的真实滤波解。为了说明该算法的适用性，研究了非线性连续搅拌釜反应器的问题。总之，已证明了所提出算法的效率。

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