HCDRNN-NMPC: A New Approach to Design Nonlinear Model Predictive Control (NMPC) Based on the Hyper Chaotic Diagonal Recurrent Neural Network (HCDRNN)

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Axis</td><td class="align_center"><span style="width: 6.38914ptpx;"><svg height="5.97156pt" id="M173" style="vertical-align:-0.04980993pt" version="1.1" viewbox="-0.0498162 -5.92175 6.38914 5.97156" width="6.38914pt" 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="M494 0V32C450 38 426 53 393 105L296 260C330 305 354 338 375 361C411 396 421 401 476 410V442H293V410C332 402 337 394 323 371C311 351 295 324 274 293L227 371C213 393 218 402 252 410V442H16V410C70 402 80 391 108 344L196 199C166 159 140 123 115 95C81 54 61 43 7 32V0H196V32C156 41 150 53 167 81C182 105 199 138 219 166L269 79C287 49 283 38 245 32V0H494Z"></path></g></svg></span></td><td class="align_center"><span style="width: 6.1673ptpx;"><svg height="9.16198pt" id="M174" 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<div>Tracking error range on <svg height="9.57302pt" id="M172" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -6.14359 31.7558 9.57302" width="31.7558pt" 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="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.267,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.41,0)"><path d="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.94,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,25.083,0)"><path d="M475 445L452 468C423 436 401 426 385 426S352 427 305 436C268 443 216 448 185 448C156 448 128 425 102 382C89 360 77 338 64 304L89 291C117 340 143 380 190 380C214 380 268 376 295 373C320 370 344 371 362 374L70 101C32 65 23 36 23 18C23 5 27 -3 31 -8C36 -8 39 -6 42 -1C52 15 67 31 80 40S110 49 143 33C195 8 257 -20 290 -20C339 -20 382 11 439 129L416 148C366 74 334 55 305 55C278 55 236 68 203 81C169 94 141 100 122 96C205 170 348 308 411 376L475 445Z"></path></g></svg> axis for two-frequency trajectory.</div>

Complexity

tab3

Table 3

Table 3: HCDRNN-NMPC: A New Approach to Design Nonlinear Model Predictive Control (NMPC) Based on the Hyper Chaotic Diagonal Recurrent Neural Network (HCDRNN) 

Table 3 | HCDRNN-NMPC: A New Approach to Design Nonlinear Model Predictive Control (NMPC) Based on the Hyper Chaotic Diagonal Recurrent Neural Network (HCDRNN) 