European Journal of Scientific Research - EuroJournals
European Journal of Scientific Research - EuroJournals
European Journal of Scientific Research - EuroJournals
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330 Amin Yazdanpanah Goharrizi and Mehdi Semin<br />
By employing the on-line Lyapunov exponents calculation strategy presented in section 2,<br />
figure 3 shows the simulation results for the given parameters variations.<br />
Figure 3: Henon Lyapunov exponents.<br />
Now, at each iteration the Lyapunov exponents are calculated with the RLS algorithm. Hence,<br />
if the maximum Lyapunov exponent becomes positive controller is applied to the system as discussed<br />
in pervious section. First the eigenvalues <strong>of</strong> matrix A is chosen as 1 , 2 1 = λ on the unit disk, so the<br />
output (state x) becomes periodic. The result is shown in figure 4.<br />
Figure 4: The closed loop response.<br />
The other simulation is performed as a regulation problem which the eigenvalues <strong>of</strong> matrix A is<br />
chosen as 1 , 2 0.<br />
5 = λ . The output <strong>of</strong> the Henon map (state x) is shown in figure 5 and figure 6 shows<br />
the estimation error for nonlinear observer.