Output Tracking Control Based on Piecewise Multilinear Models for a Class of MIMO Discrete-Time Nonlinear Systems

Multi-input multi-output (MIMO) system controls are more difficult than single-input single-output (SISO) systems because any input change affects all outputs due to internal interference of MIMO systems. We proposed a regulator and output tracking controller for MIMO discrete-time nonlinear systems using piecewise multilinear (PML) system. The PML model is constructed using only the vertex values of piecewise hypercube regions. Input-output feedback linearization was used to transform each PML system into one linearized system represented by the Brunovsky canonical form. We showed that the proposed method was effective in some examples by computer simulations. The proposed design method can be applied to any nonlinear system whose relative degree is the same as the dimension of the state variable, and can control the wider regions of nonlinear control systems compared with conventional feedback linearization. Since the modeling is simple and independent of the characteristics of the system model, it may contribute to the realization of any nonlinear control system design.