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Optimal impulse control for cow parturient paresis treatment design

机译：牛级探析治疗设计的最佳冲动控制

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Parturient paresis(milk fever) is a common disease associated with the onset of parturition in dairy cows. The disease is considered due to a large increased demand for calcium. Several work has mathematically and biologically modelled this process. Based on the existing models on calcium dynamics in diary cows, an optimal impulse treatment is proposed in this paper. The treatment is executed at a fixed time interval and lasts a relatively very small time duration, which is termed as a "fixed time impulse" control. For the optimization, with a selected objective function, a series of equations for optimality are to be satisfied, including control equations, costate equations and state equations. Those impulsive differential equations form a two point boundary value problem and are difficult to solve. A numerical scheme, SNAC(Single Network Adaptive Critic), is then proposed. The algorithm key is to use one neural network to capture the optimal relation between the pre-impulse state and the after-impluse costate. After the neural network is trained and the relation is captured, the optimal impulse dosage of medicine can be provided when a parturient paresis is detected, and the cow's calcium level can be brought back to the normal status. Simulations are presented for illustrative purposes.
机译：父母滋生（牛奶热）是与乳制品奶牛中分娩的暂时相关的常见疾病。由于对钙的需求增加而认为，该疾病被认为是由于较大的需求。几项工作在数学上和生物学模仿此过程。基于日记奶牛中钙动力学的现有模型，本文提出了最佳的脉冲处理。处理以固定的时间间隔执行，并持续相对非常小的持续时间，该持续时间被称为“固定时间脉冲”控制。为了优化，利用所选择的目标函数，应满足一系列最优性的方程，包括控制方程，成本速度方程和状态方程。那些脉冲微分方程形成了两个点边值问题，并且难以解决。然后提出了一个数字方案，SNAC（单一网络自适应评论家）。该算法密钥是使用一个神经网络来捕获预脉冲状态和后型成本之间的最佳关系。在训练神经网络并且捕获关系之后，当检测到津贴性分析时，可以提供药物的最佳脉冲剂量，并且可以将牛的钙水平带回正常状态。呈现用于说明性目的的模拟。

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