冰水界面海洋热通量的参数辨识系统

利用参数辨识和冰厚观测研究了固定冰冰底海洋热通量,建立了冰底薄层能量平衡系统,证明了系统解的存在与唯一性.以海洋热通量为辨识参数,观测和计算冰厚差值为目标函数,建立最优辨识模型.利用有界变差函数理论分析最优辨识模型最优解的存在性,通过改进遗传算法求得最优解.根据现场观测的2006-2007年冬季中山站附近固定冰冰厚数据进行了数值模拟,通过2005-2006年数值结果检验表明所建立的冰底薄层能量平衡系统及参数辨识模型是正确有效的.     

一类海冰-海水耦合热力学系统参数辨识问题的最优性

针对一维的海冰-海水耦合热力学系统,以该系统中的物理参数为辨识量,以温度偏差为目标函数,建立了一个参数辨识模型,并证明了该问题最优解的存在性,从而为这类海冰-海水耦合热力学系统参数辨识问题的数值计算提供数学理论依据.     

动力学系统参数辨识问题最优控制解的理论与方法(Ⅰ)--基本概念及确定性系统参数辨识

本文基于动力学系统参数辨识问题最优控制解的概念和确定性动力学系统的最优控制理论,建立了参数辨识研究与最优控制理论的对应关系.将最优控制的数学理论和算法应用于参数辨识问题的研究.依据Hamilton-Jacobi-Bellman (HJB)方程解的理论阐述了动力学系统参数辨识最优控制解的存在唯一性问题,并据此得到了解决确定性系统参数辨识问题的具体算法步骤.     

含有时滞资产投资模型的积累率的辨识问题

讨论了一类含有时滞的非线性资产投资模型的积累率的辨识问题.此模型为含有非局部和时滞边界条件的分布参数系统.利用Banach空间理论,得到了辨识问题解的存在唯一性.     

一类非光滑分布参数系统的可辨识性及最优性条件

变压器温度场参数辨识问题是一种分片光滑的分布参数辨识问题,以流速为辨识参数,针对传质传热的一类分布参数系统参数辨识问题,证明了系统最优参数的存在性和控制参数为最优的必要条件,为变压器温度场的数值模拟研究提供了理论基础.     

动力学系统参数辨识问题最优控制解的理论与方法(Ⅱ)——随机系统参数辨识及应用实例

基于文(Ⅰ)(《应用数学和力学》,1998,20(2))的内容和随机最优控制理论,本文首先介绍了随机动力学系统参数辨识问题最优控制解的概念.然后讨论了建立参数辨识问题HJB方程的过程以及参数辨识的算法.最后给出了一个应用实例:解决动力学系统局部非线性参数辨识问题的方法.     

动力学系统参数辨识问题最优控制解的理论与方法（I）—基本概 …

本文基于动力学系统参数辨识问题最优控制解的概念和确定性动力学系统的最优控制理论,建立了参数辨识研究与最优控制理论的对应关系。将最优控制的数学理论和算法应用于参数辨识问题的研究。依据Ｈａｍｉｌｔｏｎ－Ｊａｃｏｂｉ－Ｂｅｌｌｍａｎ（ＨＪＢ）方程解的理论阐述了动力学参数辨识最优控制解的存在唯一性问题,并据此得到了解决确定性系统参数辨识问题的具体算法步骤。     

AR模型辨识的稀疏结构迭代算法

模型估计是机器学习领域一个重要的研究内容,动态数据的模型估计是系统辨识和系统控制的基础.针对AR时间序列模型辨识问题,证明了在给定阶数下AR模型参数的最小二乘估计本质上也是一种矩估计.根据结构风险最小化原理,通过对模型拟合度和模型复杂度的折衷,提出了基于稀疏结构迭代的AR序列模型估计算法,并讨论了基于广义岭估计的最优正则化参数选取规则.数值结果表明,方法能以节省参数的方式有效地实现AR模型的辨识,比矩估计法结果有明显改善.     

关于HBV及其药物相互作用的反应扩散方程的参数识别

研究具有反应-扩散现象的HBV及其药物相互作用系统的参数识别问题,依该系统正问题解的性质,建立了参数识别问题的数学模型,论证了系统正问题解关于待识别参数的连续依赖性与参数识别问题最优解的存在性.     

Theory and Algorithm of Optimal Control Solution to Dynamic Systme Parameters Identification (

基于文(Ⅰ)(《应用数学和力学》,1998,20(2))的内容和随机最优控制理论,本文首先介绍了随机动力学系统参数辨识问题最优控制解的概念。然后讨论了建立参数辨识问题HJB方程的过程以及参数辨识的算法。最后给出了一个应用实例解决动力学系统局部非线性参数辨识问题的方法。     

Parameters identification of nonlinear system with impulse effect and its application on conversion from glycerol to 1,3-propanediol

Based on the continuous culture model we begin with introducing the nonlinear impulsive system to describe the fed-batch culture and some properties of its solution. And then the whole fermentation process is divided into two sub-processes, growth period and steady period according to the rule of the microorganisms fermentation. Instead of identifying all the uncertain parameters we only select several sensitive ones by analyzing their sensitivity to determine two pairs of parameters that are suitable for the two periods and to construct the control variable. In the end apart from establishing the identification system(PDP) of the sensitive parameters and discussing the existence of its solution we construct a algorithm and use it to obtain the optimal solution of PDP.     

Nonlinear impulsive system of microbial production in fed-batch culture and its optimal control

In this study the optimal control of fed-batch glycerol fermentation is investigated based on an impulsive dynamical system. Considering the sudden increase of the glycerol and alkali in fed-batch culture of biodissimilation of glycerol to 1,3-propanediol, this paper proposes a nonlinear impulsive system of fed-batch culture. The existence, uniqueness and regularity properties of piecewise solution for the system are proved. In view of the controllability of volumes of glycerol added to the reactor instantaneously, the paper constructs an optimal control model based on the nonlinear impulsive system and the existence of the optimal control is obtained. The control variables here are the moments and the sizes of jumps in the states at the discrete instants and the objective is to maximize the productivity of 1,3-propanediol over one cycle.     

Bilevel parameters identification for the multi-stage nonlinear impulsive system in microorganisms fed-batch cultures

Considering the abrupt jump of the substrate and different characters of the bacterial in the lag phase, the exponential phase and the stationary phase this paper proposes the multi-stage nonlinear impulsive system for the fed-batch fermentation from glycerol to 1,3-propanediol (1,3-PD) and establishes the bilevel identification system for its sensitive parameters. The properties of the solutions for the nonlinear multi-stage dynamical system are investigated and identifiability of the parameters is proved. Finally an optimal algorithm is constructed to obtain the optimal solution of the identification model and the numerical example is then discussed to illustrate the algorithm.     

Optimality condition of the nonlinear impulsive system in fed-batch fermentation

Based on the nonlinear impulsive system of fed-batch fermentation, which is used in the process of bio-dissimilation of glycerol to 1,3-propanediol by Klebsiella pneumoniae, this paper is concerned with the optimal control of the volumes of infused glycerol at impulsive moments. The optimal control model is developed. The authors study the properties of both the nonlinear impulsive system and the solution of it, and ascertain the existence of the optimal control. Then the optimality condition is obtained, which can be used as a necessary condition that the optimal control should satisfy.     

On period-$k$ solution for a population system with state-dependent impulsive effect

The period-$k$ solutions of population differential system with state-dependent impulsive effect are investigated by the theory of discontinuous dynamical system. Through $G$-function theory, the necessary and sufficient conditions are obtained for trajectory direction of a population differential system, and the results are better than the previous work. Also, the local stability of period-$k$ solutions is studied by the mapping structure and the theory of eigenvalue analysis. Furthermore, the existence of period-1 solution is investigated for a special impulsive population differential system, and the analytical condition is established. Finally, the trajectory of period-1 solution and the relationship between different parameters and the module of eigenvalues are illustrated.     

Vector measure as controls for explicit nonlinear impulsive system of fed-batch culture

In this paper, we consider an optimal control problem of microbial fermentation process in which glycerol is converted to 1,3-propanediol by Klebsiella pneumoniae in fed-batch culture. During the period of reaction, the variation of pH value is monitored to determine glycerol replenishment quantity, guaranteeing that microorganism can always keep growing fast under enough nutrition. Every time pH value is lower than seven, the quantity of glycerol added is such that pH value returns seven again. Glycerol is poured into reactor at discrete time instant and the quantity is controllable. The problem is to determine for each discrete time instant the glycerol quantity to add and maximize the final concentration of 1,3-propanediol. We present a controlled explicit nonlinear impulsive dynamical system of fed-batch culture with state independent vector measures as controls and study the existence, uniqueness, boundedness, continuous dependence and Gâteaux differentiability of its solution with respect to controls. We then propose a multiple objective programming model and demonstrate the regularity of cost functionals and weak compactness of admissible control set. Finally we discuss the existence of optimal control and implement a hybrid particle swarm optimization algorithm to solve the model optimally. Computational results are presented on a numerical example.     

Feasibility of time-limited control of a competition system with impulsive harvest

A kind of time-limited control model on a competition system with impulsive harvest, described by impulsive differential equation with the initial and boundary value problem, is presented. The existence of solution of the model, corresponding to the feasibility of the short-term control, is discussed. By the comparison principle, the conditions under which the model has a solution are found by a series of the upper solutions, and the conditions under which the model has no solution are also given by a series of the lower solutions. Finally, the practical meanings of those conditions are explained. As an example, if other parameters are given, the times of the impulsive control is estimated and the theoretical results are verified by numerical simulations.     

Optimal control and optimization algorithm of nonlinear impulsive delay system producing 1,3-Propanediol

According to the controllability of pulse times and the amount of jumps in the states at these times in the process of fed-batch culture producing 1,3-propanediol, this paper proposes a terminal optimal control model, whose constraint condition is the nonlinear impulsive delay system. The existence of optimal control is discussed and an optimization algorithm which is applied to each subinternal over one cycle for this optimal control problem is constructed. Finally, the numerical simulations show that the terminal intensity of producing 1,3-propanediol has been increased obviously.     

Dynamic behaviors of the periodic predator–prey model with modified Leslie-Gower Holling-type II schemes and impulsive effect

In this paper, a predator–prey system which based on a modified version of the Leslie–Gower scheme and Holling-type II scheme with impulsive effect are investigated, where all the parameters of the system are time-dependent periodic functions. By using Floquet theory of linear periodic impulsive equation, some conditions for the linear stability of trivial periodic solution and semi-trivial periodic solutions are obtained. It is proved that the system can be permanent if all the trivial and semi-trivial periodic solutions are linearly unstable. We use standard bifurcation theory to show the existence of nontrivial periodic solutions which arise near the semi-trivial periodic solution. As an application, we also examine some special case of the system to confirm our main results.     

Dynamic analysis of a turbidostat model with the feedback control

In this paper, a mathematical model with impulsive state feedback control is proposed for turbidostat system. The sufficient conditions of existence of positive order one periodic solution are obtained by using the existence criteria of periodic solution of a general planar impulsive autonomous system. It is shown that the system either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate and the initial concentration of microorganism and substrate. By investigating the periodic solution, the period and the initial point of the periodic solution are given. The results show that turbidostat with impulsive state feedback control tends to an order one periodic solution.