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Research on modulated control by embedding equilibrium point in null-cline of photosynthesis dynamics

光合作用动力学零斜线嵌入平衡点调制控制研究

基本信息

批准号：
21656108
负责人：
SUEMITSU Haruo
金额：
$ 2.01万
依托单位：
Oita University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Challenging Exploratory Research
财政年份：
2009
资助国家：
日本
起止时间：
2009 至 2011
项目状态：
已结题

项目摘要

Biological rhythm is characterized by free-running, endogenous rhythms, ranging from periods of seconds(e. g. heart beat) to years(e. g. population dynamics). They can adjust themselves in a certain entrainment range to varying external influences, which thereby gives them greater plasticity for adaptation to changes in the environment than a rigid coupling could accomplish. Blasius et al.\cite{blasius2} investigated the mechanism of endogenous circadian photosynthesis oscillations of plants performing crassulacean acid metabolism(CAM) in terms of a nonlinear theoretical model. They used throughout continuous time differential equations which modes adequately reflect the CAM dynamics. By incorporating results from both a complementary and a continuous membrane model, a detailed description of the molecular malate transport in and out of the vacuole through the tonoplast membrane was achieved. Their analysis showed that the membrane effectively acts as a hysteresis switch regulating the … More oscillations. It thus provided a molecular basis for the circadigan clock. The model showed regular endogenous limit cycle oscillations that were stable for a wide range of temperatures, in a manner that complies well with experimental data. In this research, the nonlinear dynamical model of CAM is discussed from the control theoretical viewpoint. The state-variables of the nonlinear dynamic equations are an internal CO2 concentration, a malate concentration in the cytoplasm, a malate concentration in the vacuole, and an order of the tonoplast membrane. The input variables are an external CO2 concentration, a light intensity and a temperature. The output is assumed to be a part of the state variables. We can define the following problems in the control theoretical points of view. We presented a dynamic estimator of the tonoplast order and a fuzzy identifier of the nonlinear function in the dynamics of the tonoplast order. Next, we analyzed the CAM dynamics as a slow/fast system and the P-type feedback controller with the adaptive observer. Moreover, we proposed two types of the feedback controllers with a constant gain. The feedback controllers allow us to reshape the nullcline of the fast system of the CAM dynamics. The simulation results were given to examine the performance of the proposed dynamic estimator and controller using MATLAB/Simulnk. Finally, we proposed an instantaneous decay/growth rate that is a kind of generalized Lyapunov exponent and call the instantaneous Lyapunov exponent with respect to a decay function. The instantaneous Lyapunov exponent is one of the measures that estimate the decay and growth rates of flows of nonlinear systems by assigning a comparison function and can apply a stable system whose decay rate is slower than an exponential function. Less

生物节律的特征是自由运行的内源性节律，范围从秒（e. G.年（年），年（年）。G.人口动态）。它们可以在一定的夹带范围内调整自己以适应不同的外部影响，从而使它们比刚性耦合能够实现更大的适应环境变化的可塑性。Blasius等人引用{blasius 2}根据非线性理论模型研究了进行景天科酸代谢（CAM）的植物的内源性昼夜光合作用振荡的机制。他们在整个连续时间中使用微分方程，这些微分方程的模式充分反映了CAM动态。通过将结果从一个互补的和一个连续的膜模型，通过液泡膜的分子苹果酸运输进出液泡的详细描述。他们的分析表明，膜有效地作为一个滞后开关调节 ...更多信息振荡因此，它为生物钟提供了分子基础。该模型表现出定期的内源性极限环振荡，在很宽的温度范围内是稳定的，符合实验数据的方式。本文从控制理论的角度出发，对凸轮的非线性动力学模型进行了研究。非线性动力学方程的状态变量是内部CO2浓度、细胞质中的苹果酸浓度、液泡中的苹果酸浓度和液泡膜的顺序。输入变量是外部CO2浓度、光强度和温度。假设输出是状态变量的一部分。我们可以从控制理论的角度来定义以下问题。我们提出了一个动态估计的液泡序和模糊识别器的非线性函数的动态液泡序。接下来，我们分析了CAM动态作为一个慢/快系统和P型反馈控制器与自适应观测器。此外，我们提出了两种类型的反馈控制器具有恒定的增益。反馈控制器使我们能够重塑零倾的快速系统的CAM动力学。使用MATLAB/Simulnk给出仿真结果来检验所提出的动态估计器和控制器的性能。最后，我们提出了一种广义的李雅普诺夫指数的瞬时衰减/增长率，并称之为关于衰减函数的瞬时李雅普诺夫指数。瞬时李雅普诺夫指数是通过分配比较函数来估计非线性系统流的衰减和增长速率的度量之一，并且可以应用于衰减速率比指数函数慢的稳定系统。少