Research On Control And State Estimation Of Fractional-order Systems With Limited Communication

Fractional-order system is a class of dynamical systems described by fractionalorder differential equation,and its order is generally considered as a non-integer.Fractional-order control system generally refers to a kind of control systems whose controlled plant is a fractional-order system or whose controller is a fractional-order type.As a special complex system,fractional-order system has become a forefront research subject in current control science field,and related control problems have attracted wide attention of some scholars.On the other hand,due to the limitation of network bandwidth and some hardware facilities,the problem of limited communication has also attracted much attention in the study of networked systems.Therefore,it is very significant to study the stability and control synthesis problem for fractional-order systems with limited communication.Based on fractional-order differential equation,this thesis investigates the problems of control and state estimation respectively for fractional-order uncertain systems and fractional-order complex networked systems with limited communication,where the order satisfies 0 <? <1.The main research contents are as follows:(1)The robust control problem is investigated for a class of fractional-order nonlinear uncertain systems with control input saturation and state quantization,where the state measurements of the observer are quantized by a logarithmic quantizer.Firstly,considering the effects of state quantization and control input saturation,an observerbased closed-loop fractional-order control system model is proposed.Then,based on this system model and the continuous frequency distributed equivalent model of fractional integrator,a sufficient condition for the robust asymptotic stability of the closed-loop fractional-order control system is established via indirect Lyapunov approach.Moreover,by using matrix's singular value decomposition and LMI methods,the co-design of the observer and state estimated feedback controller is solved,which will be shown that the derived gains can guarantee the robust asymptotic stability of the closed-loop fractional-order control system.Finally,a numerical example is presented to demonstrate the usefulness of this proposed method.(2)Considering the influence of network attacks on signal transmission,the eventtriggered output feedback control problem is addressed for a class of fractional-order uncertain systems subject to cyber-attacks.An event-triggered scheme based on measurement output is proposed to update the observer input signals so as to reduce redundant data communications.Firstly,considering the effects of event-triggered transmission scheme and network attacks on signal transmission,an observer-based closed-loop fractional-order control system model is established.Then,in view of this system model and by making use of fractional-order Lyapunov indirect approach,some sufficient conditions that can guarantee the global stochastic asymptotic stability of the closed-loop fractional-order control system are established.Moreover,by utilizing of matrix's singular value decomposition technique,the gains of the observer and output feedback controller are derived in terms of solving the LMI.Finally,a simulation example is provided to illustrate the validity of the proposed method.(3)The adaptive event-triggered non-fragile state estimation problem is considered for a class of fractional-order complex networked systems subject to randomly occurring nonlinearities and adversarial network attacks.An adaptive eventtriggered scheme is proposed,which can dynamically adjust the trigger threshold parameter according to the output error to save more limited network resources while guaranteeing the desired estimated performance.Firstly,considering the effects of adaptive event-triggered scheme and antagonistic cyber-attacks on network nodes,a fractional-order state estimation error system model is established.Then,based on this model,a sufficient condition for guaranteeing the stochastic mean-square stability of the estimation error system is obtained by employing Lyapunov functional approach and some properties of Mittag-Leffler functions.Moreover,by making use of matrix's singular value decomposition technique,the design of the non-fragile state estimator is solved based on the LMI.Finally,a numerical example is given to verify the feasibility of the theoretical results.