Monotone inertial system model for unknown nonlinear systems

In this paper, a qualitative mode and a quantitative control model for unknown system are proposed. Based on the system output process trend according to control input sequence, a qualitative model- monotone inertial system (MIS, for short) is proposed, which can be used to describe most MIMO plants with no exactly mathematical model or unknown systems in practical engineering. In a MIS, the relation between input and output is monotonic and the output process is of time inertial. In a quantitative way, we suggest a new concept- the effective rule-base. After getting some qualitative properties of the MIS, a conclusion about the control stability is obtained by a way, which differs from Lyapunov method. Furthermore, a method to find an effective rule-base is presented for an unknown MIS based on finite knowledge. Simulation results on a challenging nonlinear magnetic bearing system support the conclusions of this paper.