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Theory and Modern Applications

Table 1 Results of simulation 1

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

Set

Non-optimal control

Optimal control

1

\(T_{0}=1.5\), \(e_{10}=0.7\)

\(T^{*}=1.6789\), \(e_{1}^{*}=0.6823\)

\(e_{20}=0.9\), \(\varepsilon_{0}=0.1\)

\(e_{2}^{*}=0.9075\), \(\varepsilon ^{*}=0.1\)

\(J_{3}=7931.6\), \(H_{0}=11.23 \)

\(J_{3}^{*}=8140.94\), \(H^{*}=14.49 \)

2

\(T_{0}=1.5\), \(e_{10}=0.4\)

\(T^{*}=1.8038\), \(e_{1}^{*}=0.4285\)

\(e_{20}=0.8\), \(\varepsilon_{0}=0.1\)

\(e_{2}^{*}=0.8429\), \(\varepsilon ^{*}=0.1\)

\(J_{3}=6291.7\), \(H_{0}=11 \)

\(J_{3}^{*}=7592.98\), \(H^{*}=16.44 \)

3

\(T_{0}=1\), \(e_{10}=0.7\)

\(T^{*}=1.8364\), \(e_{1}^{*}=0.7127\)

\(e_{20}=0.9\), \(\varepsilon_{0}=0.1\)

\(e_{2}^{*}=0.9665\), \(\varepsilon ^{*}=0.1\)

\(J_{3}=5333.51\), \(H_{0}=13.64 \)

\(J_{3}^{*}=8041.65\), \(H^{*}=16.84 \)