An Algorithm for Solving a Class of Multiplayer Feedback-Nash Differential Games

<table class="fixed-width table-group" id="tab4"><tr><td><table class="table"><colgroup><col style="width:5.30em"/><col style="width:3.07em"/><col style="width:3.74em"/><col style="width:3.91em"/><col style="width:3.53em"/><col style="width:3.59em"/><col style="width:3.92em"/><col style="width:3.40em"/><col style="width:3.71em"/></colgroup><tr><td class="thead-hr" colspan="9"><hr/></td></tr><tr class="thead"><td class="align_left"> </td><td class="align_center" colspan="4">CCF</td><td class="align_center" colspan="4">RaBVitG</td></tr><tr><td class="thead-hr" colspan="9"><hr/></td></tr><tr><td class="align_left"> <svg height="8.93365pt" id="M462" style="vertical-align:-0.2977505pt" version="1.1" viewbox="-0.0498162 -8.6359 20.5861 8.93365" width="20.5861pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 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364L153 550Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g></svg></span></td></tr><tr><td class="align_left" colspan="9"><hr/></td></tr><tr><td class="align_left">CPU time</td><td class="align_center">2140</td><td class="align_center">5140.3</td><td class="align_center">9623.6</td><td class="align_center">12854</td><td class="align_center">479.11</td><td class="align_center">603.08</td><td class="align_center">734.8</td><td class="align_center">1272.8</td></tr><tr><td class="align_left" colspan="9"><hr/></td></tr><tr><td class="align_left">Its</td><td class="align_center">333</td><td class="align_center">287</td><td class="align_center">266</td><td class="align_center">248</td><td class="align_center">542</td><td class="align_center">457</td><td class="align_center">397</td><td class="align_center">275</td></tr><tr class="table-tr"><td colspan="9"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Numerical Test 4 (non Scalar, Two Players): performance comparison between RaBVitG and CCF: mesh size <span class="nowrap"><svg height="8.68572pt" id="M461" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 12.9526 8.68572" width="12.9526pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 150 409 4H432L774 555H776L714 137C700 40 694 34 612 28L606 0H868L874 28C793 34 784 37 797 137L849 533C859 612 863 616 956 622L962 650Z"></path></g></svg>,</span> CPU time (s) and number of iterations (Its).</div>

Mathematical Problems in Engineering

tab4

Table 4

Table 4: An Algorithm for Solving a Class of Multiplayer Feedback-Nash Differential Games 