MIMO system invertibility and decoupling control strategies based on ANN αth-order inversion

The theory of inverse systems is studied. A sufficient invertibility condition for the MIMO nonlinear continuous system described by input-output differential equations is established and demonstrated, and then an analytical expression of the corresponding inverse system is given. To overcome the difficulty of the practical implementation of inverse systems, two kinds of ANN ath-order inverse systems are proposed. Each of them consists of a static ANN and several integrators and forms a kind of continuous dynamic ANN structure. Both of them can be constructed even if the original nonlinear continuous system is poorly modelled or almost unknown. The proposal of two forms of ANN inversions provides a practical approach for the linearisation and decoupling control of real plants.