| Switched nonlinear systems,as a special class of hybrid systems,have a wide range of applications,such as robotic systems,switched circuit systems,and so on.With the progress of technology,the requirement of the tracking performance becomes higher and higher.Therefore,how to deal with the prescribed tracking performance control problem is a very important research topic.In this dissertation,the prescribed tracking performance control problem is studied for several complex nonlinear systems with arbitrary switching.By using the adaptive backstepping technique and neural network approximation method,several adaptive neural network control strategies are designed.On the other hand,to avoid the “the explosion of complexity” problem in the traditional backstepping design,several new adaptive neural network control schemes are developed.The proposed control algorithms achieve the control objective of prescribed tracking performance.The works of this dissertation are as follows:1.For a class of periodically time-varying linear parameterized switched nonlinear systems,by using the fourier series expansion and neural network approximation methods,the adaptive backstepping technique and combining two designed special switching functions related to the prescribed tracking accuracy,an adaptive neural network control strategy is developed to ensure that the tracking error converges to the prescribed small neighborhood of zero.And then,to deal with the problem of “the explosion of complexity”,a new command filterbased adaptive neural network control strategy is proposed for the considered system,so that the tracking error converges to a small neighborhood of zero.By taking the advantage of the Lyapunov stability theory,the boundedness theorem and Barbalat’s lemma,the boundedness of all the signals of the closed-loop system and the convergence of the tracking error are proved.2.An approximation algorithm,fourier series expansion-multi-layer neural network,is constructed to identify the unknown periodically time-varying nonlinear parameterized function.By using the adaptive backstepping method,an adaptive neural network control algorithm is designed for a class of periodically time-varying nonlinear parameterized switching systems,such that the tracking error converges to the prescribed small neighborhood of zero.Further,to avoid the “the explosion of complexity” problem,a novel adaptive neural network control strategy is proposed by utilizing the command filter technique,prescribed performance control method,and simplified approximation algorithm where fourier series expansion-radial basis function neural network.At the same time,it is ensured that the tracking error converges to the prescribed bound of the performance function.Finally,with the help of the Lyapunov stability theory and Barbalat’s lemma,it is proved that all the signals of the closed-loop system are bounded.And the obtained simulation results verify the effectiveness of the proposed algorithm.3.The fixed-time prescribed tracking performance control problem is addressed for a class of switched nonlinear systems with nonstrict-feedback form.The unknown continuous systems are identified by the radial basis function neural network method.Under the design framework of backstepping method,the properties of the Gaussian basis function of neural network are utilized to deal with the algebraic loop problem caused by the nonstrict-feedback structure.To obtain the good tracking performance,a new fixed-time performance function is first proposed which does not depend on the accurate initial value of the tracking error and has the property of convergence in fixed time.By using the prescribed performance control method and backstepping technique,an adaptive neural network control scheme is developed,to warrant that the tracking error converges to the prescribed domain of performance function in fixed time.Furthermore,to improve the above algorithm,a novel command filter-based adaptive neural network tracking control strategy is proposed,which can deal with the “the explosion of complexity” problem.And the prescribed performance of the tracking error is guaranteed within fixed time.Finally,based on the Lyapunov stability theory and boundedness theorem,it is proved that all the signals of the closed-loop system are bounded.At the same time,the two proposed algorithms ensure that the tracking error converges to the prescribed bounded by the performance function in fixed time.4.For a class of nonstrict-feedback multiple input multiple output switched nonlinear systems,the fixed-time prescribed performance problem is investigated.To deal with the control problem caused by the coupling between the input and output of each subsystem and the algebraic loop problem caused by the nonstrict-feedback structure,the properties of the Gaussian basis function of the neural network are used.And then,by using the adaptive backstepping method and the proposed fixed-time performance function,an adaptive neural network control strategy is designed to ensure the fixed-time prescribed performance of the tracking error.What’s more,to improve the above algorithm,by introducing the command filter technique,a new adaptive neural network tracking control strategy is developed to handle the “the explosion of complexity” problem.At the same time,the prescribed performance of the tracking error is warranted in fixed time.Finally,by combining the boundedness theorem and Lyapunov stability theory,it can be proved that all the signals are bounded.And the two proposed algorithms guarantee that the tracking error converges to the prescribed bounded by the performance function in fixed time. |
