Stability Constraints for Robust Model Predictive Control

<div>RMPC-SC <svg height="7.56353pt" id="M292" style="vertical-align:-0.3629899pt" version="1.1" viewbox="-0.0498162 -7.20054 8.07242 7.56353" width="8.07242pt" 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="M547 55L345 261L547 468L508 508L306 301L104 508L65 468L267 261L65 55L104 14L306 221L508 14L547 55Z" id="g54-42"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data></g></svg> RGPC with Plant (<a href="https://static.hindawi.com/articles/mpe/volume-2015/870189/figures/#EEq30">36</a>) associated with each pair <svg height="11.4781pt" id="M293" style="vertical-align:-2.18977pt" version="1.1" viewbox="-0.0498162 -9.28833 27.6846 11.4781" width="27.6846pt" 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="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z" id="g50-41"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="358" vert-adv-y="358"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,4.654,0)"><path d="M490 97L476 124C442 96 405 70 398 70C392 70 390 78 396 114C419 243 448 379 463 432L457 436C446 436 431 439 418 442C393 447 368 451 343 451C281 451 204 418 155 381C74 320 24 206 24 107C24 23 59 -12 88 -12C118 -12 155 5 191 34C236 70 290 122 328 177H330L312 84C296 0 311 -12 331 -12C355 -12 425 24 490 97ZM374 387C371 367 360 299 347 264C323 202 187 53 142 53C128 53 113 73 113 120C113 224 157 332 221 380C241 395 274 403 303 403C330 403 360 395 374 387Z" id="g50-98"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="514" vert-adv-y="514"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,11.338,0)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" vert-adv-y="237"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,16.624,0)"><path d="M460 334C460 396 434 451 378 451C330 451 241 408 148 300H146L237 679C241 697 241 710 232 710C213 710 153 684 67 675L66 646H95C141 646 145 642 134 595L39 170C23 97 31 54 46 33C64 8 100 -12 137 -12C178 -12 234 3 298 43C391 101 460 222 460 334ZM371 320C371 204 316 89 248 51C230 41 208 37 192 37C143 37 102 72 119 166C124 194 129 215 135 235C202 323 298 392 335 392C353 392 371 372 371 320Z" id="g50-99"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="478" vert-adv-y="478"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,22.842,0)"><path d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z" id="g50-42"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="358" vert-adv-y="358"></glyph.data></g></svg>. RGPC with nominal model <svg height="11.4781pt" id="M294" style="vertical-align:-2.18977pt" version="1.1" viewbox="-0.0498162 -9.28833 95.6076 11.4781" width="95.6076pt" 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="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z" id="g50-41"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="358" vert-adv-y="358"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,4.654,0)"><path d="M490 97L476 124C442 96 405 70 398 70C392 70 390 78 396 114C419 243 448 379 463 432L457 436C446 436 431 439 418 442C393 447 368 451 343 451C281 451 204 418 155 381C74 320 24 206 24 107C24 23 59 -12 88 -12C118 -12 155 5 191 34C236 70 290 122 328 177H330L312 84C296 0 311 -12 331 -12C355 -12 425 24 490 97ZM374 387C371 367 360 299 347 264C323 202 187 53 142 53C128 53 113 73 113 120C113 224 157 332 221 380C241 395 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descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,63.187,0)"><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><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,69.518,0)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" vert-adv-y="237"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,74.805,0)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 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ascent="3443" descent="-2856" horiz-adv-x="358" vert-adv-y="358"></glyph.data></g></svg>. ○: satisfactory performance of RMPC-SC, <svg height="7.56353pt" id="M295" style="vertical-align:-0.3629899pt" version="1.1" viewbox="-0.0498162 -7.20054 8.07242 7.56353" width="8.07242pt" 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="M547 55L345 261L547 468L508 508L306 301L104 508L65 468L267 261L65 55L104 14L306 221L508 14L547 55Z" id="g54-42"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data></g></svg>: satisfactory performance of RGPC.</div>

Mathematical Problems in Engineering

Stability Constraints for Robust Model Predictive Control

Figure 11