# 2-input 2-output nonlinear system

## Model description:

The suggested tracker scheme is tested with a 2-input 2-output nonlinear system given by:

\begin{align*} y_{1} (k) & = 0.21y_{1} (k-1)-0.12y_{2} (k-2) \\ & + 0.3y_{1} (k-1)u_{2} (k-1)-1.6u_{2} (k-1) \\ & + 1.2u_{1} (k-1), \\ y_{2} (k) & = 0.25y_{2} (k-1)-0.1y_{1} (k-2) \\ &- 0.2 y_{2} (k-1)u_{1} (k-1)-2.6u_{1} (k-1) \\ &-1.2u_{2} (k-1). \end{align*}

## Publication details:

 Title U-model Based Adaptive Tracking Scheme for Unknown MIMO Bilinear Systems Publication Type Conference Paper Year of Publication 2006 Authors Azhar, A.S.S., Al-Sunni F.M., and Shafiq M. Conference Name 1ST IEEE Conference on Industrial Electronics and Applications, 2006 Date Published 05/2006 Publisher IEEE Conference Location Singapore ISBN Number 0-7803-9513-1 Accession Number 9097014 Keywords bilinear systems, discrete time systems, linear systems, MIMO systems, neurocontrollers, radial basis function networks Abstract Bilinear systems are attractive candidates for many dynamical processes, since they allow a significantly larger class of behaviour than linear systems, yet retain a rich theory which is closely related to the familiar theory of linear systems. A new technique for the control of unknown MIMO bilinear systems is introduced. The scheme is based on the U-model with identification based on radial basis functions neural networks which is known for mapping any nonlinear function. U-model is a control oriented model used to represent a wide range of non-linear discrete time dynamic plants. The proposed tracking scheme is presented and verified using simulation examples DOI 10.1109/ICIEA.2006.257063