## Mechanical and Aerospace Engineering Faculty Research & Creative Works

#### Title

Optimal Impulse Control for Cow Parturient Paresis Treatment Design

#### Abstract

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.

#### Meeting Name

2016 14th International Conference on Control, Automation, Robotics and Vision, ICARCV 2016 (2016: Nov. 13-15, Phuket, Thailand)

#### Department(s)

Mechanical and Aerospace Engineering

This work is supported in part by Science and Technology Commission of Shanghai Project Funds(No. 16511108600)and National Science Foundation of China (Grant Nos.51375293,31570998,51577112).

#### Keywords and Phrases

Boundary value problems; Calcium; Computer vision; Differential equations; Robotics; Control equations; Costate equations; Fixed time interval; Impulsive differential equation; Objective functions; Single network adaptive critics; Treatment design; Two point boundary value problems; Equations of state

#### International Standard Book Number (ISBN)

978-1-5090-3549-6

#### Document Type

Article - Conference proceedings

Citation

text

English