# Development of An Inverse Dynamic Model

## Abstract

In a controller design process, it is interesting to find the inverse model, in which the desired input signal of the system is determined by using a desired output of the system. In many cases, the inverse model problem is very difficult, and sometimes impossible to determine and implement. There are some methods to make an inverse dynamic model, such as computed torque control, which had been studied in the previous Chapters. The capability of the NNs to learn the inverse model of the plant has been investigated for many years; the NN can be used to learn an approximate inverse system. In this approach, the desired output of the dynamic system should be known, and the NN can be trained by the desired output of the dynamic system to obtain the inverse dynamic model. In early studies of adaptive learning control using an NN model, Barto *et al*. [1], Jordan [2], Miller *et al*. [3] and Psaltis *et al*. [4] addressed the problem of how to obtain the error signal for training the NN controller. Generally, the cost function, consisting of the squared norm of the output reference errors, can not correctly train the NN controller as an inverse dynamic model. Therefore, Jordan [2] proposed a *forward-inverse-modeling*, and Albus [5], Atkeson and Reinkensmeyer [6], Psaltis *et al*. [4], and Kuperstein and Rubinstein [7] used a *direct-inverse-modeling* to obtain the command-error for forming the inverse dynamic model as a feedforward controller. Moreover, Watanabe *et al*. [8] proposed a linear NN using feedforward NNs with two layers and a linear unit function in the output-layer. Kawato [9] proposed a learning method to obtain a feedforward controller, which uses the output of a feedback controller as the error for training an NN model. The conventional feedback controller is configured in parallel to the NN controller, in the same manner as reported by Gomi and Kawato [10], and Miyamoto *et al*. [11], but with a different SF and learning algorithm. In another work, Wada and Kawato [12] used a feedforward NN as an inverse dynamic model.

## Keywords

Connection Weight Uniform Random Number Cerebellar Model Articulation Controller Feedforward Controller Momentum Coefficient## Preview

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