Theory and Modern Applications
Set | Non-optimal control | Optimal control |
---|---|---|
1 | \(\tau_{1}=3.23\), \(\tau_{2}=1.98\), \(\tau_{3}=1.44 \) | \(\tau_{1}^{*}=2.99\), \(\tau_{2}^{*}=1.77\), \(\tau_{3}^{*}=1.26\) |
\(\tau_{4}=1.13\), \(\tau_{5}=0.94 \) | \(\tau_{4}^{*}=0.98\), \(\tau _{5}^{*}=0.81\) | |
λ = 4.51, α = 0.8773, \(\varepsilon_{0}=0.1 \) | \(\lambda ^{*}=4.4\), \(\alpha^{*}=0.89\), \(\varepsilon^{*}=6.581e{-}5\) | |
\(J_{3}^{5}=18.2467\), \(x_{1}=0.49 \) | \(J_{3}^{5*}=14.1559\), \(x_{1}^{*}=0.6\) | |
2 | \(\tau_{1}=2.35\), \(\tau_{2}=1.27\), \(\tau_{3}=0.88 \) | \(\tau_{1}^{*}=2.34\), \(\tau_{2}^{*}=1.26\), \(\tau_{3}^{*}=0.876\) |
\(\tau_{4}=0.67\), \(\tau_{5}=0.54 \) | \(\tau_{4}^{*}=0.67\), \(\tau _{5}^{*}=0.54\) | |
λ = 4, α = 0.9028, \(\varepsilon_{0}=0.1 \) | \(\lambda ^{*}=3.99\), \(\alpha^{*}=0.9029\), \(\varepsilon^{*}=71e{-}5\) | |
\(J_{3}^{5}=13.5705\), \(x_{1}=1 \) | \(J_{3}^{5*}=10.6311\), \(x_{1}^{*}=4\) | |
3 | \(\tau_{1}=4.77\), \(\tau_{2}=3.82\), \(\tau_{3}=3.2 \) | \(\tau_{1}^{*}=4.74\), \(\tau_{2}^{*}=3.80\), \(\tau_{3}^{*}=3.17\) |
\(\tau_{4}=2.76\), \(\tau_{5}=2.44 \) | \(\tau_{4}^{*}=2.73\), \(\tau _{5}^{*}=2.40\) | |
λ = 4.8, α = 0.7724, \(\varepsilon_{0}=0.1 \) | \(\lambda ^{*}=4.79\), \(\alpha^{*}=0.7274\), \(\varepsilon^{*}=21e{-}4\) | |
\(J_{3}^{5}=24.2191\), \(x_{1}=0.2 \) | \(J_{3}^{5*}=21.30982\), \(x_{1}^{*}=0.21\) |