Stabilizing of Subspaces Based on DPGA and Chaos Genetic Algorithm for Optimizing State Feedback Controller

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left" rowspan="2">Method</td><td align="center" colspan="3">Feedback controller</td><td align="center" rowspan="2">Cost</td></tr><tr class="thead"><td align="center"><span style="width: 15.0125px;"><svg height="16.3125" id="M107" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 15.0125 16.3125" width="15.0125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,0,0,-.012,8.613,16.25)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
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<g transform="matrix(.012,0,0,-.012,8.613,16.25)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
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<g transform="matrix(.012,0,0,-.012,8.613,16.25)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
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</svg></span></td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left">GA</td><td align="center">−1.9</td><td align="center">−2.451</td><td align="center">−1.352</td><td align="center">
										71.9724
									</td></tr><tr><td align="left">Chaos GA</td><td align="center">−3.267</td><td align="center">−4.653</td><td align="center">−1.552</td><td align="center">
										69.6884
									</td></tr><tr><td align="left">DPGA + chaos GA</td><td align="center">−4.113</td><td align="center">−5.875</td><td align="center">−0.953</td><td align="center">
										52.3323
									</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

The parameters of controller for <svg height="16.275" id="M106" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 36.900002 16.275" width="36.900002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>.

Mathematical Problems in Engineering

tab5

Table 5

Table 5: Stabilizing of Subspaces Based on DPGA and Chaos Genetic Algorithm for Optimizing State Feedback Controller 