Event-Based Time Varying Formation Control for Multiple Quadrotor UAVs with Markovian Switching Topologies

<table class="fixed-width table-group" id="tab3"><tr><td><table class="table"><colgroup><col style="width:4.22em"/><col style="width:2.39em"/><col style="width:2.55em"/><col style="width:2.60em"/><col style="width:2.58em"/><col style="width:2.54em"/><col style="width:2.41em"/></colgroup><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left">Agent</td><td class="align_center"><span style="width: 10.9702ptpx;"><svg height="9.32509pt" id="M308" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -6.14359 10.9702 9.32509" width="10.9702pt" 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="M213 67C239 136 257 225 255 300C253 353 242 447 164 447C112 447 54 389 41 319L67 309C90 362 117 377 134 377C184 377 189 277 190 239C193 153 164 43 146 -12H176C278 73 450 253 450 390C450 439 410 463 396 463C384 463 380 459 382 449C385 440 389 415 389 402C389 284 312 146 216 67H213Z" id="g185-47"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.902,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g></svg></span></td><td class="align_center"><span style="width: 10.9702ptpx;"><svg height="9.32509pt" id="M309" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -6.14359 10.9702 9.32509" width="10.9702pt" 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="M213 67C239 136 257 225 255 300C253 353 242 447 164 447C112 447 54 389 41 319L67 309C90 362 117 377 134 377C184 377 189 277 190 239C193 153 164 43 146 -12H176C278 73 450 253 450 390C450 439 410 463 396 463C384 463 380 459 382 449C385 440 389 415 389 402C389 284 312 146 216 67H213Z" id="g185-47"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.902,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g></svg></span></td><td class="align_center"><span style="width: 10.9702ptpx;"><svg height="9.4347pt" id="M310" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -6.14359 10.9702 9.4347" width="10.9702pt" 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="M213 67C239 136 257 225 255 300C253 353 242 447 164 447C112 447 54 389 41 319L67 309C90 362 117 377 134 377C184 377 189 277 190 239C193 153 164 43 146 -12H176C278 73 450 253 450 390C450 439 410 463 396 463C384 463 380 459 382 449C385 440 389 415 389 402C389 284 312 146 216 67H213Z" id="g185-47"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.902,3.132)"><path d="M290 377C321 398 342 415 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440 389 415 389 402C389 284 312 146 216 67H213Z" id="g185-47"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.902,3.132)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z" id="g50-53"></path></g></svg></span></td><td class="align_center"><span style="width: 10.9702ptpx;"><svg height="9.4347pt" id="M312" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -6.14359 10.9702 9.4347" width="10.9702pt" 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="M213 67C239 136 257 225 255 300C253 353 242 447 164 447C112 447 54 389 41 319L67 309C90 362 117 377 134 377C184 377 189 277 190 239C193 153 164 43 146 -12H176C278 73 450 253 450 390C450 439 410 463 396 463C384 463 380 459 382 449C385 440 389 415 389 402C389 284 312 146 216 67H213Z" id="g185-47"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.902,3.132)"><path d="M158 548H390L417 615L410 623H122L83 318C105 326 143 337 185 337C296 337 350 275 350 188C350 116 308 42 225 42C164 42 122 74 100 93C90 101 82 99 72 92C60 82 51 68 50 59C48 46 52 38 66 24C82 9 125 -12 172 -12C225 -11 292 15 346 59C408 108 437 166 437 226C437 309 371 397 242 397C214 397 170 382 133 369L158 548Z" id="g50-54"></path></g></svg></span></td><td class="align_center"><span style="width: 10.9702ptpx;"><svg height="9.4347pt" id="M313" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -6.14359 10.9702 9.4347" width="10.9702pt" 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="M213 67C239 136 257 225 255 300C253 353 242 447 164 447C112 447 54 389 41 319L67 309C90 362 117 377 134 377C184 377 189 277 190 239C193 153 164 43 146 -12H176C278 73 450 253 450 390C450 439 410 463 396 463C384 463 380 459 382 449C385 440 389 415 389 402C389 284 312 146 216 67H213Z" id="g185-47"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.902,3.132)"><path d="M141 347C171 480 264 541 327 570C364 587 403 599 436 605L429 641C389 634 339 622 300 609C191 570 37 458 37 239C37 86 126 -12 245 -12C367 -12 454 89 454 210C454 314 380 397 272 397C252 397 230 390 208 380L141 347ZM231 338C323 338 366 257 366 174C366 108 340 27 263 27C180 27 129 123 129 244C129 268 130 292 135 310C158 323 193 338 231 338Z" id="g50-55"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left">Case <a href="https://static.hindawi.com/articles/complexity/volume-2018/8124861/figures/#casee1" target="_blank">1</a></td><td class="align_center">131</td><td class="align_center">123</td><td class="align_center">109</td><td class="align_center">126</td><td class="align_center">143</td><td class="align_center">115</td></tr><tr><td class="align_left">Case <a href="https://static.hindawi.com/articles/complexity/volume-2018/8124861/figures/#casee2" target="_blank">2</a></td><td class="align_center">62</td><td class="align_center">48</td><td class="align_center">67</td><td class="align_center">60</td><td class="align_center">61</td><td class="align_center">54</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Complexity

tab3

Table 3

Table 3: Event-Based Time Varying Formation Control for Multiple Quadrotor UAVs with Markovian Switching Topologies 