Adaptive Control Using Neural Networks and Approximate Models for Nonlinear Dynamic Systems

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Controller</td><td class="align_center">MSE</td><td class="align_center">Nbr. of iterations</td><td class="align_center">Learning rate</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">FFRN</td><td class="align_center">0.0698</td><td class="align_center">100</td><td class="align_center">0.01</td></tr><tr><td class="align_left">NARX</td><td class="align_center"><span style="width: 75.3647ptpx;"><svg height="11.9413pt" id="M112" style="vertical-align:-0.3499002pt" version="1.1" viewbox="-0.0498162 -11.5914 75.3647 11.9413" width="75.3647pt" 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="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 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transform="matrix(.0091,0,0,-0.0091,65.695,-5.741)"><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"></path></g><g transform="matrix(.0091,0,0,-0.0091,70.127,-5.741)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"></path></g></svg></span></td><td class="align_center">300</td><td class="align_center">0.01</td></tr><tr><td class="align_left">NARMA-L2</td><td class="align_center"><span style="width: 58.3896ptpx;"><svg height="11.9413pt" id="M113" style="vertical-align:-0.3499002pt" version="1.1" viewbox="-0.0498162 -11.5914 58.3896 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602Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,47.655,-5.741)"><path d="M556 236V289H56V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,53.215,-5.741)"><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"></path></g></svg></span></td><td class="align_center">100</td><td class="align_center">0.01</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Comparison of the performance index of the proposed controller (example 2).</div>

Modelling and Simulation in Engineering

tab2

Table 2

Table 2: Adaptive Control Using Neural Networks and Approximate Models for Nonlinear Dynamic Systems 