Controllability Of Stochastic Complex Networks

Our understanding and cognition of natural and engineering systems are often reflected in our ability to control them.Despite the fruitful achievements in control theory for engineering and natural systems,a general theoretical framework for controlling large-scale complex network systems is still lacking.According to classical control theory,a complex system is considered controllable if we can drive it from any initial state to the desired final state in finite time.However,a general theoretical framework for the controllability of complex network systems,particularly random complex network systems,is still lacking.This thesis mainly investigates the controllability of random complex network systems.Firstly,this thesis proposes a theoretical framework for controlling random nonlinear complex dynamic networks.In comparison with classical linear feedback controllers and finite-time controllers,the novel switching controller proposed in this paper combines the advantages of both.By using the stability theory of stochastic differential equations,sufficient conditions for system controllability are derived,along with upper bounds on the time and energy costs required for system control.Moreover,the research shows that there exists a trade-off between these two costs that depend on the control parameters.The research results indicate that for a given weighting criterion,there exists an optimal value of control parameters that minimizes the control cost.Numerical examples are provided to verify the correctness of the theoretical results,and the impact of network structure on time and energy costs is analyzed.Secondly,this thesis investigates the time and energy costs of controlling ecological networks with the Allee effects and analyzes environmental randomness through a noise term that affects population controllability.Using a real food-web network,this thesis verifies the theoretical results of the previous section.While taking into account both the time and energy costs of control,a comprehensive control cost index is proposed and used to select the optimal control parameters that minimize the total cost.Finally,this thesis studies the controllability of multi-layer networks.Based on the Kalman rank criterion and the PBH rank criterion,this thesis develops two controllability criteria for multi-layer complex networks.Additionally,this thesis analyzes a special model where the multi-layer system is configured as a single-layer input and derives some practical theorems.Findings suggest that the controllability of the entire system hinges on the first layer input and that,for a controllable system,the geometric multiplicity of any eigenvalue of the first and last layer network must be 1.When studying the controllability of a system,the spectrum of each layer is a key indicator,so a unidirectional interlayer coupled multi-layer network with different spectra is studied.In addition,this thesis also studied the controllability of unidirectional interlayer coupled multi-layer systems with the same structure.We find that the controllability of the homo-structure system in the first-layer input configuration is equivalent to the controllability of the first-layer network of the system and the eigenvalues of the single-layer network are different,and is also equivalent to the controllability of the first two-layer network subsystems of the system.