Study on Nonlinear Internal Model Control Based Neural Networks: An Application to MIMO Non-Square Systems

This book chapter has been devoted to the Internal Model Control (IMC) of discrete under-actuated and over-actuated non-linear systems. The control of non-square systems presents many difficulties because of the complexity of this class of systems. Therefore, the synthesis of a non-linear internal controller is difficult to achieve. Then, the proposed solution consists on combining the IMC structure with neural networks, in order to facilitate the realization of an approximate inverse of the non-linear model of the process to be controlled.

In the basic IMC structure, a neural network can be introduced in the internal model controller with the two methods, direct and indirect. The learning of the neural network is done in the direct method with the input / output data of the system to represent its inverse dynamics. In the indirect method, the neural network represents the dynamics of the system. The simulation results obtained are satisfactory for the case of overactuated and underactuated systems and show the effectiveness of the proposed control strategy in ensuring satisfactory nominal and robust performance.