Robust control using second order derivative of universal learning network

Characteristics of control system design using Universal Learning Network (U.L.N.) are such that a system to be controlled and a controller are both constructed by U.L.N. and that the controller is best tuned through learning, U.L.N. has the same generalization ability as N.N.. So the controller constructed by U.L.N. is able to control the system in a favorable way under the condition different from the condition at learning stage. But stability can not be realized sufficiently. In this paper, we propose a robust control method using U.L.N. and second order derivative of U.L.N.. The proposed method can realize more robustness than the commonly used Neural Network. Robust control considered here is defined as follows. Even though the system parameter variables in a nonlinear function of the system at control stage change from those at learning, the control system is able to reduce its influence to the system and can control the system in a preferable way as in the case of no variation. In order to realize such robust control, a new term concerning the variation is added to a usual criterion function. And control parameter variables are adjusted so as to minimize the above mentioned criterion function using the second order derivative of the criterion function with respect to the parameters. Finally it is shown that the controller constructed by the proposed method works in an effective way through a simulation study of a nonlinear crane system.