Research On Intelligent Control Methods For Fractional Order System With Uncertainty

In recent years,fractional order system has attracted more and more attention of many researchers and engineers.The main reason is not only it is found that many practical systems are fractional order systems essentially,but also it is found that the better performance can be achieved by using fractional order controller than the integral order controller.In the actual system because of the influence of various external or internal factors the uncertainty is always happened,and it is inevitable.The intelligent control methods are the most important and effective methods to control of integer order systems with uncertainty,and many important results have been achieved.However,the intelligent control methods can not be extended to the fractional order system simply because of the complexity of fractional calculus,and there are a large number of relevant problems of control the fractional order uncertain system to be worth to study furtherly.Therefore,this paper discusses the intelligent control methods of fractional order uncertain system,and find an effective control method for the fractional order uncertain system by using the theory of fractional order system and intelligent algorithm.The main contents are discussed as follows:(1)The tracking problem is discussed for a kind of fractional order multiple input multiple output(MIMO)nonlinear system with disturbances(defined by RiemannLiouville and Caputo).First,the fractional order MIMO system has been decompounded into several of single input single output(SISO)systems by using the concept of “dominant input”,and then the improved Self-organizing adaptive fuzzy neural network is utilized to approximate the unknown function with the structure and parameters being tuned online.The adaptive controllers are proposed by using the indirect Lyapunov method and the fractional-order system stability method respectively.Sufficient conditions for the stability of the two systems are obtained.All the related variables in the closed-loop system are bounded and the tracking control of the system is realized.The controller is easy to design and the parameters of self-organizing fuzzy neural network are easy to choose.(2)The prescribed performance generalized synchronization of a class of fractional order chaotic systems with different dimensions and different orders(using Caputo definition)is discussed.First,the transformation function is introduced to the synchronization error system.By using the properties of the transformation function,the prescribed performance synchronization is achieved when the transformation error system is guaranteed bounded.Neural networks are utilized to approximate the unknown functions,and a robust control term and an error estimation term are utilized to compensate for the approximation errors.The adaptive synchronization controllers are proposed by using Lyapunov method and the prescribed performance generalized synchronization is obtained.So that the system has been synchronized with the specified synchronization speed,maximum overshoot and other indicators,and makes all variables of the closed-loop system bounded.(3)Based on RBF neural networks and backstepping control technique,the tracking control of a class of strict feedback fractional order nonlinear uncertain system under the Caputo definition is considered.Assuming that the state variables of the system are not measurable,the input drive filter is introduced to estimate the state variables,and then the RBF neural networks is used to approximate the virtual input,and the output feedback adaptive controller is designed to realize bounded of all the variables of the closed-loop system,and the tracking error can converge to a small residual set of zero.In the whole process of design controller,the calculus of the fractional order calculus is avoided,and the online adaptive parameters of the neural networks have only one,which reduces the calculation burden of the controller.(4)The control problem of fractional order systems with the positive real uncertainty(defined by Riemann-Liouville)is discussed.The asymptotic stability of a class of fractional order linear system with positive real uncertainty is realized by using the indirect Lapunov method,the LMI method and the singular value(SVD)decomposition method to design the state feedback controller,the output feedback controller,the based-on observer controller respectively.The sufficient conditions for system stability based on LMI are proposed.Then a class of fractional linear time delay system with positive real uncertainty is discussed,and the observer-based controller is designed.Finally,the asymptotic stability of a class of nonlinear fractional order system with positive real uncertainty and unknown nonlinear functions is presented by using the RBF neural network and the indirect Lapunov method.