European Journal of Scientific Research - EuroJournals

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