Abstract: This paper proposes an adaptive inverse control scheme based on linear networks for a class of perturbation-laden linear objects. The scheme consists of three parts: an identifier, a controller, and a perturbation canceller. By appropriately selecting the inputs of the three linear networks, the weights of the controller and the perturbation canceller are updated simultaneously through online learning of the identifier. The convergence and tracking performance of the scheme are investigated. Based on the convergence condition of variable step-size weights, an input-decorrelation variable step-size LMS algorithm is designed to adjust the identifier weights. The effectiveness of the inverse control method is studied through simulation. Keywords: linear network; LMS algorithm; adaptive inverse control Abstract: The linear neural network is applied of a class linear plant with Disturbance, and a LNN-based adaptive inverse control scheme is presented. The control scheme is composed of three parts: identifier, controller and disturbance canceller. Three LLN's respectively selected inputs are so reasonable that when on-line training is only in the identifier, three networks' weight values ​​are updated at the same time. 1 Introduction The adaptive inverse control method was proposed by Bernard The idea was first proposed by Widrow in 1960[1]. The basic idea is to regard the dynamic characteristics of the object as a mapping, and the controller approximates the inverse mapping so that the output of the object tracks the input of the command. This paper applies the dynamic linear network to the inverse control system, constructs a linear network controller that approximates the inverse control dynamic characteristics of the unknown linear object, reasonably selects the input of the three linear networks, learns online through the identifier, and updates the weights of the controller and the disturbance canceller at the same time. The paper studies the convergence of the scheme and the tracking performance of the control system. The identifier online learning uses the LMS algorithm, but theoretical analysis shows[1] that when the step size is fixed, the output convergence speed of the adaptive filtering algorithm depends on the minimum eigenvalue of the autocorrelation matrix of the input vector, while the total misalignment depends on the maximum eigenvalue. When the values ​​are severely dispersed, the output convergence speed is low and the misalignment is large. Moreover, the fixed step size LMS algorithm has contradictory requirements for adjusting the step size factor in terms of convergence speed, time-varying system tracking speed and convergence accuracy. Compared with the least squares algorithm, the residual (offset) and convergence speed of the LMS algorithm are more mutually constrained. The reason is that the step size of the least squares algorithm changes during the convergence process, while that of the LMS algorithm remains unchanged. Therefore, the variable step size algorithm performs better than the LMS algorithm. In order to overcome this contradiction, this influence is reduced in two ways. First, an adaptive filtering algorithm based on the optimized estimation gradient is adopted [2], which is actually a nonlinear transformation of the error [3]. Second, a variable step size factor [4-9] is adopted to reduce the steady-state offset noise of the adaptive filtering algorithm and improve the convergence accuracy of the algorithm. In fact, processing the error signal is equivalent to the variable step size measure, so the variable step size measure is equivalent to the optimized gradient estimation [10]. In order to make the control system suitable for adaptive applications, this paper designs a new input decorrelation [11, 12] variable step size LMS algorithm based on the convergence condition of variable step size weight. The paper presents a simulation study of the proposed inverse control method. For details, please click: Research on Inverse Control of a Class of Perturbed Linear Objects Based on Linear Networks