Stochastic Nonlinear Models Of Biological Networks With Incomplete Information

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.