Theory and Modern Applications
Table 1 Comparisons between objective functional values using N2LIM with and without control cases and \(T_{f} =100\)
α | J without control | \(J ( u_{A}^{*}, u_{M}^{*} )\) with two controls \(\phi ( h )=0.1(1 - e^{-h} )\) | \(J ( u_{A}^{*}, u_{M}^{*} )\) with two controls \(\phi ( h )=0.25(1 - e^{-h} )\) | \(J ( u_{A}^{*}, u_{M}^{*} )\) with two controls \(\phi ( h )=0.025(1 - e^{-h} )\) |
|---|---|---|---|---|
1 | 2.7175 × 108 | 3.4031 × 104 | 7.8020 × 104 | \( 2.1007 \times 1 0^{3}\) |
0.9 | 8.2497 × 108 | 2.0944 × 104 | 7.0124 × 104 | \( 1.2715 \times 1 0^{3}\) |
0.8 | 2.9802 × 109 | 6.4809 × 103 | 3.0513 × 104 | 327.5621 |
0.6 | 5.0357 × 108 | 4.1936 × 103 | 9.9418 × 103 | 119.6221 |
0.5 | 2.3932 × 107 | 8.4199 × 104 | 6.0894 × 104 | 105.3185 |