2-input 2-output nonlinear system

Model description: 

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

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



Time domain: 


Publication details: 

TitleU-model Based Adaptive Tracking Scheme for Unknown MIMO Bilinear Systems
Publication TypeConference Paper
Year of Publication2006
AuthorsAzhar, A.S.S., Al-Sunni F.M., and Shafiq M.
Conference Name1ST IEEE Conference on Industrial Electronics and Applications, 2006
Date Published05/2006
Conference LocationSingapore
ISBN Number0-7803-9513-1
Accession Number9097014
Keywordsbilinear systems, discrete time systems, linear systems, MIMO systems, neurocontrollers, radial basis function networks
AbstractBilinear 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