Parameter Estimation And Optimal Control Of Markov Process Model

Pest control has always been an important and popular research topic in forestry and agriculture.Classical optimization control theory is usually based on a set of closed differential equations.Although the traditional theory of optimization based on ordinary differential equations is quite mature,which only provide us with a general description without considering the influence of random factors.Based on the traditional opti-mization algorithm,the computation load is large and the algorithm efficiency is low.Parameter estimation is the premise of optimization.In this paper,the parameter esti-mation method of Markov process model is studied,and the optimization algorithm of stochastic process model is given.In the second section,we study the parameter esti-mation of biochemical reaction systems,and providing several methods for parameter estimation.In this paper,the least squares method is used to estimate the parameters of the deterministic model with ordinary differential,and it is applied to the stochastic process model.The construction of ordinary differential equations is also derived by statistical method,as shown in the appendix.Using the population of aphids as a case study.We wanted to estimate the birth and death rates of aphids,and the migration rate of aphids was determined to be constant.Although the least squares method has a very wide range of applications,Parameter unidentifiability is the most common obsta-cle in least squares parameter estimation.The parameter estimation method combining MCMC with likelihood function can avoid the above problems and the algorithm has high efficiency.In the third chapter,We study the problem of optimal control based on a Markov process individual model by spraying pesticides and releasing sterile insects.It is hoped to find a suitable ratio of pesticide spraying and release of sterile insects such that pest control effect is the best.Taking cotton aphids as an example,this paper presents optimal control problems governed by stochastic models with impulsive inter-ferences.A new computational approach is employed to solve this problem.The key of this method is to establish the functional relationship between the control variables and the corresponding state.In our study,we assume that there is a logarithmic linear regression relationship between them.Using training sample simulated from Gillespie algorithm,the regression coefficients for constraints and the objective function are es-timated by least squares method.Simulation shows the error of the prediction of this model is relatively low and control results based on regression model are superior to the method based on the moment closure equations in terms of the control cost.Final-ly the influence of the parameters in the objective function on the optimal strategy is discussed.