Comparative Controlling of the Lorenz Chaotic System Using the SMC and APP Methods

<div>The change of adaptive control gain matrix <span class="nowrap"><svg height="14.5316pt" id="M59" style="vertical-align:-3.9384pt" version="1.1" viewbox="-0.0498162 -10.5932 68.5848 14.5316" width="68.5848pt" 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="M699 0V35C659 41 632 57 591 109C519 200 445 301 381 397C426 443 468 491 527 545C582 597 623 609 685 615V650H425V615L443 613C490 607 492 592 468 561C435 516 395 467 328 399C298 368 273 352 252 346V516C252 602 260 608 331 615V650H37V615C112 608 121 602 121 516V134C121 48 111 42 39 35V0H338V35C261 42 252 48 252 134V314C267 316 280 310 301 280C372 176 455 59 498 0H699Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.318,2.33939e-05)"><path d="M308 -259V-228H299C192 -219 190 -215 190 -109V616C190 755 193 759 299 768H308V799H127V-259H308Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.172,-.705)"><path d="M535 0V32C500 38 483 46 451 83C420 121 333 240 306 284C336 322 350 339 377 366C405 394 440 407 502 418V448L286 439V409C324 403 328 391 317 369C305 348 280 307 258 282C243 266 224 249 200 244V703C132 684 61 672 15 667V638C68 632 75 626 75 570V107C75 42 69 40 9 32V0H266V32C208 40 200 42 200 107V215C203 215 207 214 210 213C215 213 221 207 230 195C274 124 330 34 359 -1L535 0Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,22.841,2.427)"><path d="M415 0V41C335 46 327 62 327 127V635C236 611 161 593 93 583V547L150 544C187 541 192 535 192 483V127C192 59 182 46 102 41V0H415Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.973,-.705)"><path d="M535 0V32C500 38 483 46 451 83C420 121 333 240 306 284C336 322 350 339 377 366C405 394 440 407 502 418V448L286 439V409C324 403 328 391 317 369C305 348 280 307 258 282C243 266 224 249 200 244V703C132 684 61 672 15 667V638C68 632 75 626 75 570V107C75 42 69 40 9 32V0H266V32C208 40 200 42 200 107V215C203 215 207 214 210 213C215 213 221 207 230 195C274 124 330 34 359 -1L535 0Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,40.642,2.427)"><path d="M440 180C404 113 397 110 338 110H183L298 220C398 316 438 379 438 456C438 568 354 635 254 635C192 635 138 610 101 572L36 479L69 452C103 500 144 541 204 541C270 541 306 494 306 425C306 350 267 276 197 193C148 136 89 81 36 30V0H440C451 42 463 106 480 167L440 180Z"></path></g><g transform="matrix(.013,0,0,-0.013,51.774,-.705)"><path d="M535 0V32C500 38 483 46 451 83C420 121 333 240 306 284C336 322 350 339 377 366C405 394 440 407 502 418V448L286 439V409C324 403 328 391 317 369C305 348 280 307 258 282C243 266 224 249 200 244V703C132 684 61 672 15 667V638C68 632 75 626 75 570V107C75 42 69 40 9 32V0H266V32C208 40 200 42 200 107V215C203 215 207 214 210 213C215 213 221 207 230 195C274 124 330 34 359 -1L535 0Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,58.443,2.427)"><path d="M310 382C345 404 366 417 384 433C404 450 417 474 417 501C417 578 357 635 252 635H251C184 635 135 603 107 572L57 506L86 478C122 527 156 554 205 554C250 554 290 528 290 467S227 367 144 340L151 300C168 304 190 308 208 308C260 308 327 275 327 181C327 89 288 49 238 49C177 49 131 93 109 111C95 122 82 119 70 110C57 100 40 82 40 63C40 48 48 34 65 21C86 4 126 -12 177 -12C240 -12 460 60 460 222C460 298 409 363 310 380V382Z"></path></g><g transform="matrix(.013,0,0,-0.013,63.597,2.33939e-05)"><path d="M244 -259V799H63V768H72C178 759 181 755 181 616V-109C181 -215 179 -219 72 -228H63V-259H244Z"></path></g></svg>.</span></div>

Mathematical Problems in Engineering

fig14

Figure 14

Figure 14: Comparative Controlling of the Lorenz Chaotic System Using the SMC and APP Methods 