Finite Time Synchronization for Complex System Modeling

The study of complex systems pervades all of sciences, from cell biology to ecology, from computer sciences to meteorology, from engineering to technology. A complex system involves the interactions of components (or subsystems), which are usually in a nonlinear fashion. Typical example of complex systems is the biological neural network or simply a set of coupling neurons, for which the complexity is governed by the topological structure, neuron model, dynamical evolution, and so on.The modeling a complex system is difficult as it involves the identification of subsystems and also their interactions, despite the fact that it is a common problem found in a broad spectrum of scientific fields. The difficulties further escalate, as those unknown parameters may not be fixed but have to be identified online under the constraints that only a limited number of system’s states are measurable.In this project, it is to develop a methodology to achieve finite time synchronization of a complex system in interest, such that the system model, including the model of the subsystems and their interactions, can be duly revealed. Unlike the common definition of synchronization, finite time synchronization implies that identical synchronization occurs when time approaches a finite value, instead of going to infinite. The fact that synchronization can be achieved in finite time is crucial for practical applications, especially in modeling complex systems.The core design is a sliding mode observer, which can adaptively identify the dynamics and the interactions of the subsystems, providing the necessity of finite time convergence of synchronization error, and the robustness in resisting the noise.In additional to the mathematical proof on its effectiveness, the proposed design will also be implemented for modeling several complex systems. That includes a network of chaotic oscillators and a biological neural system based on its numerical models and some available real data. Due to the nature of biological neural network, which is nonlinear, complex and high dimensional, this problem is considered to be challenging and important.The success of this project not only provides a general approach in modeling a complex system with finite time synchronization, but also facilitates the modeling of neurons and improves our understanding of their activities.