Method to obtain effective rule base for unknown nonlinear systems

In this paper, a new concept- the effective rule-base is proposed. Each rule in the rule-base can guarantee that the system state from its fire state transmits to a stabler state. A conclusion about the control stability is obtained by a way that differs from Lyapunov method. Furthermore, a method to find an effective rule-base is presented for unknown systems based on finite knowledge. First, an initial state set and a control input set of the plant are selected; then the output curves in its inertial time are recorded; third, the optimal control input-output couples set is picked out according to several optimal criterions; and finally, rule base is constructed based on that set. Analysis shows that the plant state can be kept in a very small range around the setpoint controlled by the fuzzy controller based on the rule-base. Simulation on a challenging nonlinear magnetic bearing system illustrates the method. The simulation results support the conclusions of this paper.