Fractional Order Adaptive Backstepping Control

The development of systems and control is full of challenges with complex prob-lems and difficult tasks.Adaptive methods are developed in demand,which solve the challenges from uncertain systems just in time.One of the adaptive control methods,named adaptive backstepping control,is quite popular for uncertain systems because of its simple control theory,straightforward design process and obvious effects.With the introduction of fractional order calculus,more and more control methods are improved by stronger robustness and more degree of freedom.Therefore,by the combination of fractional order calculus and adaptive backstepping control,not only are the adaptive backstepping controllers improved,but also the uncertain fractional order systems can be easily solved.The research on fractional order adaptive backstepping control is still at the prima-ry level.Although the theoretical framework is gradually constructed,there are many theoretical problems remaining.Additionally,it is difficult for fractional order adap-tive backstepping control to deal with complex systems or tasks.Therefore,on the one hand,this dissertation focuses on the improvement of fractional order adaptive back-stepping control for complex systems or tasks,such as dead zone,saturation,chattering and unobservable states.On the other hand,our research will also solve theoretical problems,such as backstepping control for non-strict feedback systems and asymptotic convergence of adaptive RBF neural networks backstepping control.Firstly,an auxiliary fractional order system is designed to compensate the input saturation of fractional order system,then the fractional order adaptive backstepping controller is developed on the basis of auxiliary fractional order system.When the system states are not observable,we design a fractional order observer and analyze its convergence,so the adaptive backstepping output feedback control can be realized for fractional order system with input saturation.What's more,after the linear feedback replaced by nonlinear one,the constraints on controller parameters are weakened and the control results are improved obviously.Secondly,besides saturation,dead zone is another difficult problem in practical engineering,especially when the systems are affected by saturation and dead zone simultaneously,there is no reliable solution.However,this dissertation proposes a projective decomposition method that transforms the problem of saturation and dead zone to the problem of saturation and bounded disturbance,even if all parameters of saturation and dead zone are unknown.Based on aforementioned auxiliary systems,fractional order adaptive backstepping controller is designed to compensate saturation and estimate disturbance.In order to eliminate chattering,we provide a strategy that could generate a series of nonlinear feedback functions to replace the traditional sign and power functions.Both theoretical and practical researches have demonstrated the chattering-free results.Thirdly,in terms of the combination of adaptive backstepping control and RBF neural networks,we are not satisfied with the objective that the signals of closed sys-tems are only bounded.To achieve asymptotic stability of closed systems,the con-troller design will consider estimated error and simplify parameters update law so that the convergence of Lyapunov function can be guaranteed.When RBF neural network-s and model transforming method are introduced,the non-strict feedback systems are changed into strict feedback forms,then the backstepping control will be applied at last.Finally,in order to verify the practical effect of theoretical research,fractional or-der adaptive backstepping control method will be applied for fractional order systems even integer order systems.The fractional order system is a heat conducting system and integer order systems are inverted pendulum and unmanned aerial vehicle.According to the theoretical research,the experiments will solve the problems of dead zone,sat-uration,unknown functions,non-strict feedback form and so on.After achieving the control objectives,the superiority of fractional order adaptive backstepping control is also demonstrated.