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Table 4 Results of simulation for \(n=1\)

From: Translation, solving scheme, and implementation of a periodic and optimal impulsive state control problem

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

\(\alpha ^{*}=0.41\), \(\varepsilon^{*}=2.64e{-}4\)

\(J_{3}^{1}=4.94\), \(x_{1}=0.2\)

\(J_{3}^{1*}=4.05\), \(x_{1}^{*}=0.24\)