Dynamic Learning from Adaptive Neural Control of Uncertain Robots with Guaranteed Full-State Tracking Precision

<div>Function approximation: <svg height="12.4698pt" id="M454" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 32.9443 12.4698" width="32.9443pt" 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="M488 658H270V630C328 626 335 619 335 579C217 574 44 509 44 330C44 147 221 88 335 86C335 38 328 32 265 28V0H488V28C425 32 418 38 418 86C534 88 710 153 710 337C710 517 538 575 418 579C418 619 425 626 488 630V658ZM335 118C249 124 136 180 136 337C136 490 251 543 335 547V118ZM418 547C502 543 618 491 618 333S503 124 418 118V547Z" id="g113-150"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="754" vert-adv-y="754" xpluscharwidth="9.802"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,9.802,3.132)"><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><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="14.23368539"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.748,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346" xpluscharwidth="19.246"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,19.246,0)"><path d="M669 636L663 650H260C230 650 221 652 208 675H186C177 621 162 548 144 481L173 479C195 534 211 560 226 578C248 604 266 615 373 615H544C460 511 114 112 23 16L31 0H561C577 34 611 135 622 170L594 182C566 125 544 88 515 65C481 38 416 35 319 35C249 35 197 37 152 41C270 184 542 501 669 636Z" id="g113-91"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="692" vert-adv-y="692" xpluscharwidth="28.241999999999997"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,28.243,0)"><path d="M275 270C275 450 212 609 64 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transform="matrix(.0091,0,0,-0.0091,12.71,-8.606)"><path d="M655 676H628C608 656 600 650 571 650H156C118 650 114 651 102 676H77C63 615 45 548 24 485L60 486C81 531 97 562 114 580C134 603 148 611 252 611H308L217 127C201 41 196 38 105 32L98 0H384L393 32C300 38 288 41 304 127L393 611H466C553 611 571 604 582 580C592 559 597 530 595 485L630 489C636 548 645 624 655 676Z" id="g50-85"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="673" vert-adv-y="673" xpluscharwidth="18.83427981"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.71,3.784)"><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><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="17.14168539"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,19.099,0)"><path d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 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88 515 65C481 38 416 35 319 35C249 35 197 37 152 41C270 184 542 501 669 636Z" id="g113-91"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="692" vert-adv-y="692" xpluscharwidth="38.729"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,38.73,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346" xpluscharwidth="43.227999999999994"></glyph.data></g></svg> (-<svg height="4.18388pt" id="M456" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -4.13406 3.07474 4.18388" width="3.07474pt" 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="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z" id="g113-46"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228" xpluscharwidth="2.964"></glyph.data></g></svg>-<svg height="4.18388pt" id="M457" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -4.13406 3.07474 4.18388" width="3.07474pt" 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="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z" id="g113-46"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228" xpluscharwidth="2.964"></glyph.data></g></svg>).</div>

Complexity

fig9

Figure 9

Figure 9: Dynamic Learning from Adaptive Neural Control of Uncertain Robots with Guaranteed Full-State Tracking Precision 