Adaptive Control Of Nonlinear Systems Using Locally Weighted Learning

With the continuous iteration and update of science and technology,the systems existing in today's social life and industrial fields are becoming more and more complex,such as transportation systems,metallurgical systems,power systems,etc.These complex systems are often highly nonlinear,and it is difficult to establish accurate mathematical models.Therefore,how to overcome the problems caused by the unknown dynamics of the system and realize the control of the nonlinear system has become the focus of the majority of researchers.In recent years,a variety of intelligent control schemes for nonlinear systems based on neural networks have been proposed.Among them,the locally weighted learning neural network algorithm is favored by many scholars due to its good identification performance and flexibility for unknown nonlinear systems.Although there have been many research results in the research direction of locally weighted learning neural network,there are still some basic theoretical problems that have not been solved,including: 1.Most of the existing locally weighted learning neural network research results are only applicable to first-order system and n-order chain system;2.The approximation set of locally weighted learning neural network cannot be determined.Aiming at the above problems,this thesis will study the tracking control problem of unknown strict feedback nonlinear systems by combining techniques and theories such as locally weighted learning,neural network,adaptive control and barrier function.The main work contents are as follows:(1)For a class of n-order unknown strict feedback nonlinear systems,the adaptive tracking control problem based on locally weighted learning neural network is solved.First,by designing a new weighted function,the problem that the locally weighted learning neural network is difficult to apply to the n-order unknown strict feedback nonlinear system is solved.Then,by using the locally weighted learning neural network,the unknown nonlinearity of the system is identified without any prior knowledge of the system.Therefore,the system output can track the desired reference trajectory,and the designed locally weighted learning neural network controller can ensure that all closed-loop signals are bounded.Finally,an example simulation is carried out to verify the effectiveness of the control algorithm.(2)For a class of unknown strict feedback nonlinear systems,the adaptive tracking control problem of locally weighted learning neural network with predetermined approximation set is explored.First,the biquadratic kernel function is selected as the weighted function of the locally weighted learning neural network.By applying the barrier function and the qualitative theory of differential equations,the approximation set of the locally weighted learning neural network is preset to ensure the effectiveness of the locally weighted learning neural network to identify the nonlinearity of the system.Then the signal permutation technique is applied to solve the shortcoming that the weighted function designed in the first research content cannot meet the actual demand with the increase of the order.The proposed locally weighted learning neural network controller can make all signals of the closed-loop system bounded.Finally,the feasibility of the designed control algorithm is demonstrated through a numerical simulation,and the locally weighted learning neural network control strategy is compared with the radial basis function neural network control strategy to verify the superiority of the locally weighted learning neural network.(3)For a class of unknown strict feedback nonlinear systems,the adaptive tracking control problem based on self-organizing approximation is studied.Since the local area of the local weighted learning neural network covers the entire approximation set,and with the increase of the system order,the number of input signals of the local weighted learning neural network will increase greatly,resulting in a great increase in the amount of calculation,the existence of many unnecessary computations takes up too much computer computing power,making the computation time too long.In order to solve this problem,we first introduce a neuron self-growth strategy,design a self-organizing approximator,increase the number of local models according to needs,greatly reduce the amount of calculation,and avoid the waste of computer computing power.Then,by applying the qualitative theorem of barrier function and differential equation,without any prior knowledge,it is strictly proved that the input signal of the self-organizing approximator is always kept in a certain approximation set under the action of the designed control algorithm,and the proposed control algorithm can make all closed-loop signals uniformly bounded.Finally,a simulation example is given to verify the effectiveness of the control algorithm.