Adaptive Observer-Based Fault-Tolerant Control Design for Uncertain Systems

<div>Combined fault <svg height="12.0395pt" id="M385" style="vertical-align:-2.3616pt" version="1.1" viewbox="-0.0498162 -9.6779 19.6413 12.0395" width="19.6413pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M52 442L22 406L27 394H92V108C92 45 88 39 30 32V0H302V32C227 39 220 45 220 108V394H321C335 401 339 431 335 442H220L218 477C214 562 214 597 220 616C224 631 233 642 251 642C279 642 311 617 335 593C345 583 355 583 369 593C384 605 395 618 399 629C406 644 405 659 391 673C374 689 349 701 309 703C261 697 226 679 190 649C133 601 112 553 105 531C97 507 92 486 92 464V442H52Z" id="g13-100"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="331" vert-adv-y="331"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,5.477,0)"><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"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,10.165,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,14.785,0)"><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"></glyph.data></g></svg> (dotted line) and its estimation <svg height="15.3849pt" id="M386" style="vertical-align:-2.3616pt" version="1.1" viewbox="-0.0498162 -13.0233 19.6413 15.3849" width="19.6413pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,-.449,-3.617)"><path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 550 458 532L470 557Z" id="g119-17"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="470" vert-adv-y="470"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M52 442L22 406L27 394H92V108C92 45 88 39 30 32V0H302V32C227 39 220 45 220 108V394H321C335 401 339 431 335 442H220L218 477C214 562 214 597 220 616C224 631 233 642 251 642C279 642 311 617 335 593C345 583 355 583 369 593C384 605 395 618 399 629C406 644 405 659 391 673C374 689 349 701 309 703C261 697 226 679 190 649C133 601 112 553 105 531C97 507 92 486 92 464V442H52Z" id="g13-100"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="331" vert-adv-y="331"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,5.494,0)"><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"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,10.182,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,14.802,0)"><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"></glyph.data></g></svg> (solid line) using AFEA.</div>

Mathematical Problems in Engineering

fig9

Figure 9

Figure 9: Adaptive Observer-Based Fault-Tolerant Control Design for Uncertain Systems 