Evaluation of robust control by universal learning networks

Abstract

The characteristics of control system design using a universal learning network (ULN) are such that both the controlled systems and their controller are represented in a unified framework, and that the learning stage of the ULN can be executed by using not only first-order derivatives (gradient) but also the higher order derivatives of the criterion function with respect to parameters. ULNs have the same generalization ability as neural networks. So the ULN controller is able to control the system in a favorable way under an environment which is little different from the environment of the control system at the learning stage. However, stability cannot be sufficiently realized. In this paper, we propose a robust control method using a ULN and second-order derivatives of that ULN. Robust control, as considered here, is defined as follows. Even though the initial values of the node outputs are very different from those at the learning stage, the control system is able to reduce its influence to other node outputs and can control the system as in the case of no variation. In order to realize such robust control, a new term concerning the variation is added to the usual criterion function, and the parameters are adjusted so as to minimize the above-mentioned criterion function using second-order derivatives of the criterion function with respect to the parameters. Finally, it is shown that the ULN controller constructed by the proposed method works effectively in a simulation study of a non-linear crane system.