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Theory and Modern Applications

Table 2 Results of simulation 2

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

Set

Non-optimal control

Optimal control

1

T = 8, \(b_{2}=0.6\), \(\varepsilon_{0}=0.1 \)

\(T^{*}=6.5499\), \(b_{2}^{*}=0.6214\), \(\varepsilon^{*}=4.521e{-}5\)

\(e_{1}=0.8\), \(e_{2}=0.9 \)

\(e_{1}^{*}=0.1613\), \(e_{2}^{*}=0.4572\)

\(J_{1}=69.4267\), H = 0.7347

\(J^{*}=1.36176\), \(H^{*}=0.6632\)

2

T = 7, \(b_{2}=0.55\), \(\varepsilon_{0}=0.1 \)

\(T^{*}=6.1392\), \(b_{2}^{*}=0.6345\), \(\varepsilon^{*}=1.61e{-}6\)

\(e_{1}=0.7\), \(e_{2}=0.6 \)

\(e_{1}^{*}=0.1703\), \(e_{2}^{*}=0.4371\)

\(J_{1}=53.4043\), H = 0.7005

\(J^{*}=0.7111\), \(H^{*}=0.6396\)

3

T = 6, \(b_{2}=0.5\), \(\varepsilon_{0}=0.1 \)

\(T^{*}=5.9094\), \(b_{2}^{*}=0.5386\), \(\varepsilon^{*}=0.441e{-}7\)

\(e_{1}=0.2\), \(e_{2}=0.4 \)

\(e_{1}^{*}=0.1553\), \(e_{2}^{*}=0.4422\)

\(J_{1}=32.5521\), H = 0.6578

\(J^{*}=0.6984\), \(H^{*}=0.6454\)