基于不完全信息的生物网络随机非线性建模与控制研究
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摘要
在生物网络以及大型复杂工业系统中存在着大量的随机不确定性现象,例如基因调控网络中单个基因地产生、消亡,神经网络中介质传递过程以及周围环境中扰动地影响,都会引发网络的随机性和不确定性。对于这样的系统,受到物理条件以及知识地限制,其机理模型一般难以用准确的数学模型来描述,表现出强烈的随机特性。非线性在生物网络以及各类工业系统系统中普遍存在,所以针对随机非线性系统这类综合性问题地研究具有重大的应用价值,同时也是研究控制系统的难点所在。现代控制理论以状态空间为主,依赖系统精确的数学模型。但是由于被控系统复杂、受到各种随机扰动地影响,系统中的关键状态无法通过测量系统输出直接得到。因此需要设计合适的状态估计器对被控对象的状态进行估计,间接地获取被控系统状态,为后续地分析、设计控制系统作铺垫,例如利用估计状态设计状态反馈控制器等。系统测量输出的过程中不可避免地会发生一些无法预知的变化,例如测量数据延迟、信号量化、信号采样等。在这些不完全信息地影响下,控制系统的性能变差,甚至产生不稳定、震荡现象。考虑不完全信息影响下的随机非线性系统,设计合适的状态估计器以及控制器,使得控制系统取得优越的性能。
     因此,本论文以随机Lyapunov稳定性理论为基础、线性矩阵不等式为工具,研究了不完全信息影响下生物网络随机非线性建模与控制问题,提出了新的思路,给出了新的结果,主要工作如下:
     (1)针对测量数据概率延迟下的离散随机基因调控网络设计了鲁棒H∞状态估计器,其模型中考虑了参数的范数有界不确定性、随机扰动以及时变时滞的影响。测量延迟现象用条件概率分布的二进制开关序列来描述,激励函数满足扇形边界条件。通过Lyapunov稳定性理论和随机分析技术,得到了均方意义下的鲁棒指数稳定估计器以及在给定的H∞扰动衰减水平下随机鲁棒稳定估计器存在的充分条件,通过求解一组线性矩阵不等式得到。最后,通过一个数值例子来说明所提出方法的有效性。
     (2)考虑了随机中立型神经网络状态估计问题。常量时滞以及分布时滞影响下,估计误差系统均方指数稳定以及几乎必然指数稳定。激励函数以及非线性测量函数均满足Lipschitz条件,通过构造合适的Lyapunov-Krasovskii泛函得到了保证估计器存在的时滞相关判据,为一线性矩阵不等式的解。最后通过两个数值例子说明了理论结果的合理性,以及能够提供保守性更小的解。
     (3)针对离散通信以及节点时滞影响下的连续生物动态网络设计了自适应反馈同步控制器。网络中节点特性连续,节点之间只在离散瞬间进行通信,即通过离散通信方式交换信息。通信周期内的通信时间可以是变化不确定的。通过构造分段连续的Lyapunov-Krasovskii泛函来约束离散通信方式的特性,得到了自适应反馈控制器存在性的判据。在自适应更新律以及控制器的作用下,网络能够达到全局指数稳定同步。最后,通过两种不同耦合类型的生物动态网络,全局耦合动态网络以及最近邻连接动态网络来说明了自适应反馈同步控制器的有效性。
     (4)多级加工系统由单级系统串联而成,当扰动影响某级系统的生产时,多级系统最终的产品质量也会下降。本论文设计了基于基因调控网络的多级牵伸环节生物启发协同控制器,在扰动地影响下,维持产品性能指标稳定在期望值。对生物启发协同控制器的稳定性、收敛性进行了理论证明,利用多目标优化算法优化控制器参数,使得性能指标和期望值之间的误差以及调整时间最小,最后将生物启发协同控制器成功应用在了化纤生产的多级牵伸过程中。
     最后,对论文的研究内容进行了总结,讨论了将来需要进一步研究的方向。
The stochastic phenomena and uncertainty are quite commen in the biological networks and the industrial plants. Gene regulation is an intrinsically noisy process due to intracellular and extracellular noise perturbations, which are derived from random births and deaths of individual molecules and environmental fluctuations. In the neural systems, the synaptic transmission is a noisy process brought on by random fluctuation from the release of neuron transmitters and other probabilistic causes in real nervous systems. Subject to physical conditions and restrictions on the knowledge, it is imposible to obtain the deterministic model to describe the systems' dynamic characteristics, which show random characterics. The nonlinear systems are commonly encountered in the engineering fields and the nature. Therefore, it is of a great importance to investigate the stochastic nonlinear systems in theoretical and application, which is hard to be controlled. Based on the state space, the modern control theory utilizes the accurete mathematical model to design the controller. While, for the complexity of large-scale networks and the effects of disturbances, the states of the network are hard or even impossible to be obtained directly or completely. So, in order to make full use of the states, one may need to estimate the states through available outputs, and then utilize the estimated state to achieve certain objective, such as state feedback control. There are some inevitably and unpredictable changes in the measurement of the output, for example probabilistic measurement delays, signal sampling, and quantization effects, which are named as imcomplete information. The imcomplete information may induce instability, oscillations or poor performances, which should be taken into account in the control systems.
     In this thesis, we disuss the state estimation and control iusse for several typical stochastic nonlinear systems, genetic regulation systems, neural systems, and complex dynamical systems with the impletement information. Based on Lyapunov-Krasovskii functional mtheod, linear matrix inequalities, and so on, sufficient conditions are established to ensure the existence of the desired estimators and the controllers. The main contributions and the main contents are as follows:
     (1) The robust H∞state estimation problem is investigated for a class of discrete-time stochastic genetic regulatory networks (GRNs) with probabilistic measurement delays. Norm-bounded uncertainties, stochastic disturbances and time-varying delays are considered in the discrete-time stochastic GRNs. Meantime the measurement delays of GRNs are described by a binary switching sequence satisfying a conditional probability distribution. The main purpose is to design a linear estimator to approximate the true concentrations of the mRNA and the protein through the available measurement outputs. Based on Lyapunov stability theory and stochastic analysis techniques, sufficient conditions are first established to ensure the existence of the desired estimators in the terms of a linear matrix inequality (LMI). Then, the explicit expression of the desired estimator is shown to ensure the estimation error dynamics to be robustly exponentially stable in the mean square and a prescribed H∞disturbance rejection attenuation is guaranteed for the addressed system. Finally, a numerical example is presented to show the effectiveness of the proposed results.
     (2) The state estimation for stochastic neural networks of neutral type with discrete and distributed delays is considered. By using available output measurements, the state estimator can approximate the neuron states, and the asymptotic property of the state error is mean square exponential stable and also almost surely exponential stable in the presence of discrete and distributed delays. Under the Lipschitz assumptions for the activation functions and the measurement nonlinearity, a delay-dependent linear matrix inequality (LMI) criterion is proposed to guarantee the existence of the desired estimators by constructing an appropriate Lyapunov-Krasovskii function. It is shown that the existence conditions and the explicit expression of the state estimator can be parameterized in terms of the solution to a LMI. Finally, two numerical examples are presented to demonstrate the validity of the theoretical results and show that the theorem can provide less conservative conditions.
     (3) The synchronization of continuous complex dynamical networks with discrete-time communications and delayed nodes is investigated. The nodes in the dynamical networks act in the continuous manner. While the communications between nodes are discrete-time, that is, they communicate with others only at discrete time instants. The communication intervals in communication period can be uncertain and variable. By using a piecewise Lyapunov-Krasovskii function to govern the characteristics of the discrete communications instants, we investigate the adaptive feedback synchronization and a criterion is derived to guarantee the existence of the desired controllers. The globally exponentially synchronization can be achieved by the controllers under the updating laws. Finally, two numerical examples including globally coupled network and nearest-neighbour coupled networks are presented to demonstrate the validity and effectiveness of the proposed control scheme.
     (4) The multi-stage system in manufacture has a series structure of a single-stage production system. Once the vibrations in one stage affect the quality of its product, the performance of the finished products in the multi-stage system is degraded, too. A bio-inspired cooperative controller via evolution of gene regulatory network is presented to make the performance index of each stage stable over the whole study horizon and the overall performance index close to the desired value against vibrations simultaneously. A theoretical proof of the controller convergence to the desired overall performance index is also provided. This developmental controller is evolved using a multi-objective optimization algorithm subject to minimize the absolute value of the error between the desired overall performance index and the actual one and shorten the settling time. By using the bio-inspired cooperative controller, there is a decrease in scrap and eventually an improvement of the product quality. Furthermore, the implementation of the proposed bio-inspired cooperative controller is illustrated and examined through the multi-stage drafting system from the chemical fiber process industry. The experimental results demonstrate that the proposed controller should have wide application in similar multi-stage complex systems.
     At the end, we summarize the reselt of the thesis, and present some future works which required further investigation.
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