Model description: 

Consider the following unknown discrete nonlinear dynamic system:

$$\begin{align*} y(k+1)&=p[{\bf q}(k), u(k)]=0.2\cos[0.8(y(k)+y(k-1))] \\ & +0.4\sin[0.8(y(k)+y(k-1))+2u(k)+u(k-1)] \\ &+0.1[9+y(k)+y(k-1)]+\left[{2(u(k)+u(k-1))\over 1+\cos(y(k))}\right] \end{align*}$$

for $k=0,1,2,\ldots$ with $y(k)=0,u(k)=0$, for $k=0,-1,-2,\ldots$, $\Delta t := t(k+1)-t(k)=0.02sec$, for $k=0,1,2,\ldots$.



Model order: 


Time domain: 


Publication details: 

TitleRobust nonlinear adaptive control using neural networks
Publication TypeConference Paper
Year of Publication2001
AuthorsAdetona, O., Sathananthan S., and Keel L.H.
Conference NameProceedings of the 2001 American Control Conference, 2001
Date Published06/2001
Conference LocationArlington, VA
ISBN Number0-7803-6495-3
Accession Number7092721
Keywordsadaptive control, asymptotic stability, neurocontrollers, nonlinear control systems, radial basis function networks, robust control
AbstractThis paper provides a robust indirect adaptive control method for non-affine plants. Subject to some mild assumptions, the method can be applied to both minimum and non-minimum phase plants with operating regions of any finite size while avoiding a set of restrictions, at least one of which is imposed by all existing methods. The benefits are achieved under the following assumptions: 1) the operating region is limited to the basin of attraction of an asymptotically stable equilibrium point of the plant; 2) the desired output of the plant is sufficiently slowly varying; and 3) the output of the plant must be sufficiently sensitive to the input signal. It is shown that the adaptive control system will be stable in the presence of unknown bounded modeling errors