Abstract
In order to control a nonlinear dynamic system with unknown characteristics, the use of learning elements, i. e. multi-layer neural networks, has been studied.
A method that uses an acquired inverse model of the target system by learning is used by many researchers. However the conventional methods for learning an inverse model of the target system have many drawbacks. A method that uses an acquired forward model of the target system and calculates the input of the target system by using iterative methods, i. e. Newton's method, was proposed. However since iterative methods use only local information, they sometimes converge to local optimal solutions and can not calculate the precise solution for controlling the target system.
In order to solve a static system concerning inverse problems, we proposed a hybrid system that consists of an inverse model and the feedback system extended for the nonlinearity of the target system. The extended feedback system conducts a kind of iterative method from an enough number of initial values generated by random searches until a correct solution is obtained. Usually one of the correct solutions can be obtained by this procedure. However this configuration of the extended feedback system can not be applied for a dynamic system.
By using the acquired forward model of the target system instead of the target system, the proposed extended feedback system can control a nonlinear dynamic system.
The extended feedback system usually takes computation time. As the inverse model becomes accurate by learning, the required number of iterations for calculating the control value decreases and the computation time also decreases. The performance of the proposed system gets better by learning.
The performance of the proposed method is shown by numerical simulations.
