Theory and Modern Applications
Set | Non-optimal control | Optimal control |
---|---|---|
1 | T = 3.23, λ = 4.51 | \(T ^{*}=2.93\), \(\lambda ^{*}=4.37\) |
α = 0.5881, ε = 0.1 | \(\alpha ^{*}=0.62\), \(\varepsilon^{*}=1.57e{-}4\) | |
\(J_{3}^{1}=3.65\), \(x_{1}=0.49\) | \(J_{3}^{1*}=2.77\), \(x_{1}^{*}=0.63\) | |
2 | T = 2.35, λ = 4 | \(T ^{*}=2.31\), \(\lambda ^{*}=3.96\) |
α = 0.6501, ε = 0.1 | \(\alpha ^{*}=0.65\), \(\varepsilon^{*}=9e{-}5\) | |
\(J_{3}^{1}=2.71\), \(x_{1}=1\) | \(J_{3}^{1*}=2.01\), \(x_{1}^{*}=1.04\) | |
3 | T = 4.77, λ = 4.8 | \(T ^{*}=4.42\), \(\lambda ^{*}=4.76\) |
α = 0.2952, ε = 0.1 | \(\alpha ^{*}=0.41\), \(\varepsilon^{*}=2.64e{-}4\) | |
\(J_{3}^{1}=4.94\), \(x_{1}=0.2\) | \(J_{3}^{1*}=4.05\), \(x_{1}^{*}=0.24\) |