ANN generalised inversion for the linearisation and decoupling control of nonlinear systems

A generalised inverse system (or generalised inversion) method is developed for the linearisation and decoupling control of a general nonlinear dynamic continuous system. The existing condition for generalised inversion of a SISO or MIMO nonlinear system is discussed. Combining the generalised inversion and the original system creates a pseudo-linear composite system whose poles can be placed in the left-half complex plane so as to obtain an ideal open-loop frequency characteristic. To implement the generalised inversion for the control of an unmodelled or only poorly modelled dynamic nonlinear system, a dynamic artificial neural network (ANN) structure formed by connecting a number of linear components to a static ANN is proposed. The static ANN is responsible for approximating the static nonlinear mapping described by the analytical expression of the generalised inversion and the linear components are used to represent the dynamics of the generalised inversion. Simulation results are also presented to illustrate that the proposed control technique provides a practical approach to realise the linearisation and decoupling control of nonlinear SISO or MIMO systems.