Research On The Adaptive Control For Uncertain Fractional-Order Nonlinear Systems

As is well-known,most practical systems are inherently nonlinear and frequently affected by uncertain parameters and unknown disturbances.With the increase of system complexity,some existing theories and methods of nonlinear systems have certain limitations.On the other hand,along with the rapid development of industrial technology,higher requirements are put forward for system modeling and control in more and more situations.Fractional calculus,as the extension and generalization of integer-order calculus,provides a simpler and more accurate description of many complex systems.What's more,the introduction of fractional calculus can not only increase the degree of freedom for designing controller but also provide a solution for improving robustness and system performance.Besides,it is difficult for the original models to describe the dynamic characteristics of real-time systems influenced by some factors such as long-time running,the changes in a work environment,the loss of components,and so on.Therefore,studying the adaptive control problems for uncertain fractional-order nonlinear systems is of great theoretical significance and practical value in engineering.On the basis of the existing work,the adaptive control problems for fractional-order nonlinear systems with input saturation,input quantization,unknown control directions,unknown disturbances,timevarying delays,actuator failures,and malicious sensor deception attacks are investigated respectively by adopting some control methods such as adaptive backstepping control,intelligent control,fractional-order dynamic surface control(FODSC),fractional-order command filtered backstepping(FOCFB)control,Nussbaum function,Lyapunov direct method,Lyapunov indirect method,etc.The main contents are summarized as follows:1.The adaptive state-feedback and output feedback control problems for uncertain fractional-order nonlinear systems with input saturation are concerned.Firstly,by combining with fuzzy approximation and Lyapunov direct method,an adaptive fuzzy statefeedback controller is designed for uncertain fractional-order nonlinear systems with input saturation,where the modified FODSC technique and an auxiliary system are adopted to reduce the computational complexity and handle the saturation nonlinearity.The proposed controller guarantees that all signals in the closed-loop system are uniformly ultimately bounded and the tracking error converges to a neighborhood around the origin.Furthermore,by integrating with the FODSC technique and Lyapunov indirect method,a state observer-based adaptive fuzzy output-feedback control scheme is proposed for uncertain fractional-order nonlinear systems with input saturation and time-varying delays,where a fuzzy state observer is constructed to remove the restriction that all system states are assumed to be available a prior.The stability results prove that the proposed method guarantees that all signals in the closed-loop system are uniformly ultimately bounded and the system output can track the given reference signal.Finally,an application example is provided to verify the effectiveness of the proposed approaches.2.The adaptive dynamic surface control problems for uncertain fractional-order nonlinear systems with input quantization are considered.Firstly,by adopting the FODSC technique and Lyapunov indirect method,an adaptive fuzzy quantized controller is developed for a class of uncertain fractional-order nonlinear systems with unknown control directions,where the compensation signals are constructed to eliminate the filter errors between the input and output of the filter.In the procedure of recursive design,the Nussbaum gain technique is employed to remove the restriction that the control gains are assumed to be known and constant.Theoretical analysis proves that the designed controller guarantees that all signals in the closed-loop system are uniformly ultimately bounded.Furthermore,by using the FODSC technique and Lyapunov direct method,a disturbance observer-based adaptive fuzzy quantized controller is designed for uncertain fractional-order nonlinear systems with unknown disturbances,where a nonlinear disturbance observer is established in each step to enhance the anti-disturbance ability of the controlled system.Especially,an adjustable parameter and the event-driven control mechanism are incorporated into controller design for improving the flexibility of quantization design and reducing the communication burden.The stability results prove that the proposed quantized controller guarantees that all signals in the closed-loop system are uniformly ultimately bounded and the tracking error converges to a neighborhood around the origin.Finally,some simulation examples including the numerical example and practical example are provided to verify the effectiveness of the developed methods.3.The adaptive fault-tolerant control problem for incommensurate fractional-order nonlinear time-delay systems with actuator failures is studied.Firstly,a fuzzy state observer is constructed to estimate the unmeasurable system states,and LyapunovKrasovakii functional is adopted to overcome time-varying delays existing in the system.Different from most of the existing results,some compensation functions are added into controller design for handling the unknown disturbances and approximation errors.Furthermore,by combining with the FODSC technique and Lyapunov indirect method,an observer-based adaptive fuzzy output-feedback fault-tolerant controller is developed such that all signals in the closed-loop system are uniformly ultimately bounded and the system output can track with the given reference signal.Finally,a numerical example and an application example are given to verify the effectiveness of the proposed control approach.4.The adaptive secure control problems for uncertain incommensurate fractionalorder nonlinear time-delay systems with unknown sensor deception attacks are investigated.First,by using the Lyapunov indirect method and the FOCFB control technique,an attack compensator-based adaptive neural resilient controller is established for incommensurate fractional-order nonlinear time-delay systems subject to actuator failures and unknown sensor deception attacks.In the recursive procedure,the radial basis function neural networks are employed to approximate the unknown composite nonlinear terms,and an attack compensator is constructed to deal with unknown attacks.Stability results prove that the developed adaptive secure control scheme guarantees that all the signals in the closed-loop system are uniformly ultimately bounded.Nextly,by combing with Lyapunov indirect method,event-driven control method,and an improved FOCFB control technique,an adaptive event-triggered resilient controller is developed for uncertain incommensurate fractional-order nonlinear time-delay systems subject to unknown actuator failures,sensor deception attacks,and disturbances.In the recursive procedure,a novel coordinate of transformation is established to handle the unknown sensor deception attacks and the Nussbaum gain technique is employed to remove the limitations posted in the existing results on the sign of attack weight and some prior knowledge of actuator failures.Through stability analysis,it is proved that the proposed adaptive secure control scheme ensures that all the signals in the closed-loop system are uniformly ultimately bounded.Finally,simulation examples are presented to demonstrate the effectiveness of the proposed methods.