Predefined-Time Consensus of Nonlinear First-Order Systems Using a Time Base Generator

<div>Predefined-time TBG-tracking controller (<a href="https://static.hindawi.com/articles/mpe/volume-2018/1957070/figures/#EEq13">16</a>) for <span class="nowrap"><svg height="12.3524pt" id="M311" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -9.1709 15.9287 12.3524" width="15.9287pt" 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="M422 682C387 695 357 699 317 699C181 699 82 633 82 548C82 472 149 424 253 401C233 362 226 321 226 296C226 212 296 162 389 162C421 162 463 169 491 181L493 179C436 80 364 34 264 34C219 34 189 50 178 65V66C218 73 236 105 236 134C236 169 211 201 167 201C120 201 84 158 84 108C84 32 155 -21 272 -21C459 -21 585 56 641 209C664 269 678 309 707 336L668 368C537 250 498 217 406 217C371 217 360 244 360 279C360 318 375 364 390 391C485 394 576 415 649 448C738 488 799 543 799 602C799 662 746 687 665 687C543 687 382 600 284 457C220 472 173 496 173 548C173 609 232 644 324 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id="g113-54"></path></g></svg> sec., and the consensus value is <span class="nowrap"><svg height="16.3701pt" id="M313" style="vertical-align:-3.9435pt" version="1.1" viewbox="-0.0498162 -12.4266 116.267 16.3701" width="116.267pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,.007)"><path d="M697 -46L668 -39C637 -126 611 -142 545 -142H163L474 298L206 694H483C558 694 584 688 600 668C615 651 627 625 639 580L667 585L655 739H70V714L378 254L53 -203V-228H655L697 -46Z" id="g119-65"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.787,-6.394)"><path d="M870 650H622L613 619C694 615 708 606 708 559C708 531 702 477 686 396L636 136H633L281 650H127L120 619C180 616 198 611 212 592C227 572 232 558 220 503L166 254C148 169 139 131 126 89C112 43 85 35 33 32L24 0H280L286 32C208 37 189 44 189 93C189 124 198 179 212 250L267 526H271L622 -8H655L732 396C747 477 762 532 770 556C785 600 798 616 862 619L870 650Z" id="g50-79"></path></g><g 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Mathematical Problems in Engineering

fig2

Figure 2

Figure 2: Predefined-Time Consensus of Nonlinear First-Order Systems Using a Time Base Generator 