8873fc2ecc1d2971960c49022a013a1f mathematics_09_02175_v2.pdf e3a7a7fde95c90931fe2313dfe1817af9ca34cf1 mathematics_09_02175_v2.pdf 5989390991827cd4d2c9a8bffed23cc6b1056be6043341101bbfcc7739d95f24 mathematics_09_02175_v2.pdf Title: On the Reachability of a Feedback Controlled Leontief-Type Singular Model Involving Scheduled Production, Recycling and Non-Renewable Resources Subject: This paper proposes and studies the reachability of a singular regular dynamic discrete Leontief-type economic model which includes production industries, recycling industries, and non-renewable products in an integrated way. The designed prefixed final state to be reached, under discussed reachability conditions, is subject to necessary additional positivity-type constraints which depend on the initial conditions and the final time for the solution to match such a final prescribed state. It is assumed that the model may be driven by both the demand and an additional correcting control in order to achieve the final targeted state in finite time. Formal sufficiency-type conditions are established for the proposed singular Leontief model to be reachable under positive feedback, correcting controls designed for appropriate demand/supply regulation. Basically, the proposed regulation scheme allows fixing a prescribed final state of economic goods stock in finite time if the model is reachable. Keywords: Leontief economic model; Ghosh model; controllability; equilibrium points; singular systems; stability; positive systems Author: Manuel De la Sen, Asier Ibeas and Santiago Alonso-Quesada Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Thu Sep 9 09:10:08 2021 CEST ModDate: Thu Sep 9 09:14:48 2021 CEST Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 35 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 1461414 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- MXTWPO+VnURWPalladioL Type 1 Custom yes yes no 10 0 ADOAAZ+URWPalladioL-Ital Type 1 Custom yes yes no 15 0 ZFMABQ+URWPalladioL-Bold Type 1 Custom yes yes no 20 0 UQKLPL+URWPalladioL-Roma Type 1 Custom yes yes no 24 0 SOSTRQ+CMR10 Type 1 Builtin yes yes no 28 0 DVTHKG+TimesNewRomanPS-BoldItalicMT Type 1C WinAnsi yes yes no 36 0 MCBCCI+SourceSansRoman-Regular Type 1C Custom yes yes no 58 0 MCBCCM+SourceSansRoman.613wght Type 1C Custom yes yes no 62 0 MCBCCO+SourceSansRoman-Bold Type 1C Custom yes yes no 66 0 VUABVQ+CMMI10 Type 1 Builtin yes yes no 84 0 YVLJLA+URWPalladioL-BoldItal Type 1 Custom yes yes no 88 0 APXZNS+CMSY10 Type 1 Builtin yes yes no 92 0 GMPAHC+CMEX10 Type 1 Builtin yes yes no 99 0 TMHVPV+MSAM10 Type 1 Builtin yes yes no 112 0 HFDYRF+PazoMath Type 1 Builtin yes yes no 119 0 NFJBBW+PazoMath-Italic Type 1 Builtin yes yes no 129 0 GEJNTL+VnURWPalladioL-Italic Type 1 Custom yes yes no 277 0 Jhove (Rel. 1.22.1, 2019-04-17) Date: 2023-02-18 02:40:45 CET RepresentationInformation: mathematics_09_02175_v2.pdf ReportingModule: PDF-hul, Rel. 1.12.1 (2019-04-17) LastModified: 2023-02-16 01:34:27 CET Size: 1461414 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 430 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@44c8afef Item: Title: The Model and Its Solution Non-Negativity Properties under a Non-Singularity Constraint on the Re-Usable Goods Substate Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@7b69c6ba Item: Title: Reachability Properties under the Non-Singularity Constraint on the Re-Usable Goods Substate Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@46daef40 Item: Title: Extensions of the Results to the General Singular Regular Leontief Model Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@12f41634 Item: Title: Numerical Examples Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@13c27452 Item: Title: Conclusions Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@262b2c86 Item: Title: References Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@371a67ec Info: Title: On the Reachability of a Feedback Controlled Leontief-Type Singular Model Involving Scheduled Production, Recycling and Non-Renewable Resources Author: Manuel De la Sen, Asier Ibeas and Santiago Alonso-Quesada Subject: This paper proposes and studies the reachability of a singular regular dynamic discrete Leontief-type economic model which includes production industries, recycling industries, and non-renewable products in an integrated way. The designed prefixed final state to be reached, under discussed reachability conditions, is subject to necessary additional positivity-type constraints which depend on the initial conditions and the final time for the solution to match such a final prescribed state. It is assumed that the model may be driven by both the demand and an additional correcting control in order to achieve the final targeted state in finite time. Formal sufficiency-type conditions are established for the proposed singular Leontief model to be reachable under positive feedback, correcting controls designed for appropriate demand/supply regulation. Basically, the proposed regulation scheme allows fixing a prescribed final state of economic goods stock in finite time if the model is reachable. Keywords: Leontief economic model; Ghosh model; controllability; equilibrium points; singular systems; stability; positive systems Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Thu Sep 09 09:10:08 CEST 2021 ModDate: Thu Sep 09 09:14:48 CEST 2021 ID: 0x8498594e50de803adfeedfadbea78b21, 0x8498594e50de803adfeedfadbea78b21 Filters: FilterPipeline: FlateDecode Fonts: Type1: Font: BaseFont: NFJBBW+PazoMath-Italic FontSubset: true FirstChar: 35 LastChar: 115 FontDescriptor: FontName: NFJBBW+PazoMath-Italic Flags: Symbolic FontBBox: -70, -277, 902, 733 FontFile: true Font: BaseFont: GMPAHC+CMEX10 FontSubset: true FirstChar: 0 LastChar: 125 FontDescriptor: FontName: GMPAHC+CMEX10 Flags: Symbolic FontBBox: -24, -2960, 1454, 772 FontFile: true Font: BaseFont: MXTWPO+VnURWPalladioL FontSubset: true FirstChar: 161 LastChar: 225 FontDescriptor: FontName: MXTWPO+VnURWPalladioL Flags: Symbolic FontBBox: -166, -283, 1021, 943 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: ADOAAZ+URWPalladioL-Ital FontSubset: true FirstChar: 2 LastChar: 150 FontDescriptor: FontName: ADOAAZ+URWPalladioL-Ital Flags: Symbolic FontBBox: -170, -305, 1010, 941 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: TMHVPV+MSAM10 FontSubset: true FirstChar: 3 LastChar: 3 FontDescriptor: FontName: TMHVPV+MSAM10 Flags: Symbolic FontBBox: 8, -463, 1331, 1003 FontFile: true Font: BaseFont: ZFMABQ+URWPalladioL-Bold FontSubset: true FirstChar: 3 LastChar: 121 FontDescriptor: FontName: ZFMABQ+URWPalladioL-Bold Flags: Symbolic FontBBox: -152, -301, 1000, 935 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: VUABVQ+CMMI10 FontSubset: true FirstChar: 60 LastChar: 96 FontDescriptor: FontName: VUABVQ+CMMI10 Flags: Symbolic FontBBox: -32, -250, 1048, 750 FontFile: true Font: BaseFont: GEJNTL+VnURWPalladioL-Italic FontSubset: true FirstChar: 178 LastChar: 189 FontDescriptor: FontName: GEJNTL+VnURWPalladioL-Italic Flags: Symbolic FontBBox: -170, -305, 1010, 941 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: HFDYRF+PazoMath FontSubset: true FirstChar: 70 LastChar: 229 FontDescriptor: FontName: HFDYRF+PazoMath Flags: Symbolic FontBBox: -40, -283, 878, 946 FontFile: true Font: BaseFont: UQKLPL+URWPalladioL-Roma FontSubset: true FirstChar: 2 LastChar: 169 FontDescriptor: FontName: UQKLPL+URWPalladioL-Roma Flags: Symbolic FontBBox: -166, -283, 1021, 943 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: YVLJLA+URWPalladioL-BoldItal FontSubset: true FirstChar: 67 LastChar: 105 FontDescriptor: FontName: YVLJLA+URWPalladioL-BoldItal Flags: Symbolic FontBBox: -170, -300, 1073, 935 FontFile: true EncodingDictionary: Differences: true Font: BaseFont: SOSTRQ+CMR10 FontSubset: true FirstChar: 40 LastChar: 93 FontDescriptor: FontName: SOSTRQ+CMR10 Flags: Symbolic FontBBox: -40, -250, 1009, 750 FontFile: true Font: BaseFont: APXZNS+CMSY10 FontSubset: true FirstChar: 0 LastChar: 112 FontDescriptor: FontName: APXZNS+CMSY10 Flags: Symbolic FontBBox: -29, -960, 1116, 775 FontFile: true Pages: Page: Sequence: 1 Annotations: Annotation: Subtype: Link Rect: 35, 759, 173, 795 Annotation: Subtype: Link Rect: 515, 759, 560, 795 Annotation: Subtype: Link Rect: 130, 643, 141, 656 Annotation: Subtype: Link Rect: 202, 643, 213, 656 Annotation: Subtype: Link Rect: 358, 643, 369, 656 Annotation: Subtype: Link Rect: 35, 334, 152, 343 Annotation: Subtype: Link Rect: 35, 162, 97, 184 Annotation: Subtype: Link Rect: 153, 89, 154, 98 Annotation: Subtype: Link Rect: 35, 77, 147, 86 Annotation: Subtype: Link Rect: 366, 294, 373, 302 ActionDest: 274 Annotation: Subtype: Link Rect: 373, 294, 380, 302 ActionDest: 274 Annotation: Subtype: Link Rect: 291, 181, 298, 189 ActionDest: 274 Annotation: Subtype: Link Rect: 504, 130, 511, 139 ActionDest: 274 Annotation: Subtype: Link Rect: 507, 105, 514, 114 ActionDest: 274 Annotation: Subtype: Link Rect: 539, 105, 546, 114 ActionDest: 274 Annotation: Subtype: Link Rect: 127, 17, 265, 28 Annotation: Subtype: Link Rect: 389, 17, 558, 28 Annotation: Subtype: Link Rect: 35, 435, 87, 454 Page: Sequence: 2 Annotations: Annotation: Subtype: Link Rect: 549, 737, 556, 746 ActionDest: 274 Annotation: Subtype: Link Rect: 250, 712, 257, 721 ActionDest: 274 Annotation: Subtype: Link Rect: 237, 686, 244, 695 ActionDest: 274 Annotation: Subtype: Link Rect: 202, 636, 209, 645 ActionDest: 274 Annotation: Subtype: Link Rect: 518, 611, 530, 620 ActionDest: 274 Annotation: Subtype: Link Rect: 422, 599, 434, 608 ActionDest: 274 Annotation: Subtype: Link Rect: 181, 548, 193, 557 ActionDest: 274 Annotation: Subtype: Link Rect: 253, 511, 265, 520 ActionDest: 274 Annotation: Subtype: Link Rect: 448, 486, 460, 495 ActionDest: 274 Annotation: Subtype: Link Rect: 309, 435, 321, 444 ActionDest: 274 Annotation: Subtype: Link Rect: 525, 435, 537, 444 ActionDest: 274 Annotation: Subtype: Link Rect: 281, 398, 293, 407 ActionDest: 274 Annotation: Subtype: Link Rect: 461, 372, 473, 382 ActionDest: 274 Annotation: Subtype: Link Rect: 407, 297, 419, 306 ActionDest: 274 Annotation: Subtype: Link Rect: 422, 297, 434, 306 ActionDest: 274 Annotation: Subtype: Link Rect: 288, 272, 300, 281 ActionDest: 274 Annotation: Subtype: Link Rect: 300, 272, 312, 281 ActionDest: 274 Annotation: Subtype: Link Rect: 419, 272, 431, 281 ActionDest: 274 Annotation: Subtype: Link Rect: 432, 272, 444, 281 ActionDest: 274 Page: Sequence: 3 Page: Sequence: 4 Annotations: Annotation: Subtype: Link Rect: 377, 732, 384, 744 ActionDest: 81 Annotation: Subtype: Link Rect: 528, 682, 535, 694 ActionDest: 109 Annotation: Subtype: Link Rect: 477, 556, 484, 568 ActionDest: 140 Annotation: Subtype: Link Rect: 368, 544, 375, 556 ActionDest: 109 Annotation: Subtype: Link Rect: 334, 531, 340, 543 ActionDest: 168 Page: Sequence: 5 Page: Sequence: 6 Page: Sequence: 7 Page: Sequence: 8 Annotations: Annotation: Subtype: Link Rect: 529, 215, 541, 225 ActionDest: 274 Annotation: Subtype: Link Rect: 544, 215, 556, 225 ActionDest: 281 Annotation: Subtype: Link Rect: 530, 203, 541, 212 ActionDest: 281 Annotation: Subtype: Link Rect: 544, 203, 556, 212 ActionDest: 281 Page: Sequence: 9 Page: Sequence: 10 Page: Sequence: 11 Page: Sequence: 12 Page: Sequence: 13 Annotations: Annotation: Subtype: Link Rect: 314, 375, 326, 384 ActionDest: 281 Page: Sequence: 14 Annotations: Annotation: Subtype: Link Rect: 423, 735, 435, 744 ActionDest: 274 Annotation: Subtype: Link Rect: 436, 735, 448, 744 ActionDest: 281 Annotation: Subtype: Link Rect: 451, 735, 463, 744 ActionDest: 281 Annotation: Subtype: Link Rect: 384, 298, 391, 307 ActionDest: 274 Annotation: Subtype: Link Rect: 391, 298, 398, 307 ActionDest: 274 Annotation: Subtype: Link Rect: 399, 298, 411, 307 ActionDest: 274 Annotation: Subtype: Link Rect: 411, 298, 423, 307 ActionDest: 274 Annotation: Subtype: Link Rect: 427, 298, 438, 307 ActionDest: 281 Annotation: Subtype: Link Rect: 393, 285, 400, 295 ActionDest: 274 Annotation: Subtype: Link Rect: 415, 270, 422, 282 ActionDest: 81 Page: Sequence: 15 Annotations: Annotation: Subtype: Link Rect: 309, 640, 316, 649 ActionDest: 274 Annotation: Subtype: Link Rect: 316, 640, 328, 649 ActionDest: 281 Annotation: Subtype: Link Rect: 329, 640, 341, 649 ActionDest: 281 Annotation: Subtype: Link Rect: 214, 600, 221, 609 ActionDest: 274 Annotation: Subtype: Link Rect: 222, 600, 234, 609 ActionDest: 281 Annotation: Subtype: Link Rect: 234, 600, 246, 609 ActionDest: 281 Annotation: Subtype: Link Rect: 214, 477, 221, 486 ActionDest: 274 Annotation: Subtype: Link Rect: 222, 477, 234, 486 ActionDest: 281 Annotation: Subtype: Link Rect: 234, 477, 246, 486 ActionDest: 281 Annotation: Subtype: Link Rect: 212, 352, 224, 361 ActionDest: 281 Annotation: Subtype: Link Rect: 212, 311, 224, 320 ActionDest: 281 Annotation: Subtype: Link Rect: 388, 165, 395, 174 ActionDest: 274 Annotation: Subtype: Link Rect: 395, 165, 402, 174 ActionDest: 274 Annotation: Subtype: Link Rect: 324, 65, 331, 74 ActionDest: 274 Annotation: Subtype: Link Rect: 332, 65, 344, 74 ActionDest: 281 Page: Sequence: 16 Annotations: Annotation: Subtype: Link Rect: 185, 685, 197, 694 ActionDest: 281 Annotation: Subtype: Link Rect: 198, 685, 210, 694 ActionDest: 281 Page: Sequence: 17 Annotations: Annotation: Subtype: Link Rect: 373, 75, 380, 83 ActionDest: 274 Annotation: Subtype: Link Rect: 381, 74, 393, 83 ActionDest: 281 Page: Sequence: 18 Annotations: Annotation: Subtype: Link Rect: 398, 415, 410, 424 ActionDest: 274 Annotation: Subtype: Link Rect: 311, 331, 323, 341 ActionDest: 274 Annotation: Subtype: Link Rect: 363, 331, 375, 341 ActionDest: 281 Annotation: Subtype: Link Rect: 205, 319, 217, 328 ActionDest: 274 Page: Sequence: 19 Page: Sequence: 20 Page: Sequence: 21 Page: Sequence: 22 Page: Sequence: 23 Page: Sequence: 24 Annotations: Annotation: Subtype: Link Rect: 352, 682, 359, 694 ActionDest: 171 Annotation: Subtype: Link Rect: 466, 682, 473, 694 ActionDest: 171 Annotation: Subtype: Link Rect: 197, 644, 205, 656 ActionDest: 171 Annotation: Subtype: Link Rect: 319, 644, 326, 656 ActionDest: 171 Page: Sequence: 25 Annotations: Annotation: Subtype: Link Rect: 466, 403, 473, 420 ActionDest: 186 Annotation: Subtype: Link Rect: 197, 379, 204, 391 ActionDest: 193 Page: Sequence: 26 Annotations: Annotation: Subtype: Link Rect: 207, 126, 214, 138 ActionDest: 200 Annotation: Subtype: Link Rect: 368, 114, 375, 126 ActionDest: 200 Page: Sequence: 27 Page: Sequence: 28 Annotations: Annotation: Subtype: Link Rect: 219, 659, 231, 669 ActionDest: 281 Annotation: Subtype: Link Rect: 374, 644, 381, 656 ActionDest: 211 Annotation: Subtype: Link Rect: 242, 632, 249, 644 ActionDest: 211 Annotation: Subtype: Link Rect: 197, 619, 205, 631 ActionDest: 211 Annotation: Subtype: Link Rect: 325, 594, 332, 606 ActionDest: 222 Annotation: Subtype: Link Rect: 229, 581, 236, 594 ActionDest: 211 Page: Sequence: 29 Page: Sequence: 30 Annotations: Annotation: Subtype: Link Rect: 422, 649, 433, 661 ActionDest: 233 Annotation: Subtype: Link Rect: 493, 649, 505, 661 ActionDest: 233 Annotation: Subtype: Link Rect: 331, 636, 343, 648 ActionDest: 233 Page: Sequence: 31 Annotations: Annotation: Subtype: Link Rect: 303, 694, 315, 706 ActionDest: 244 Annotation: Subtype: Link Rect: 335, 694, 347, 706 ActionDest: 244 Page: Sequence: 32 Annotations: Annotation: Subtype: Link Rect: 319, 682, 332, 694 ActionDest: 256 Annotation: Subtype: Link Rect: 457, 669, 469, 682 ActionDest: 256 Annotation: Subtype: Link Rect: 455, 371, 467, 383 ActionDest: 256 Annotation: Subtype: Link Rect: 182, 320, 194, 346 ActionDest: 256 Annotation: Subtype: Link Rect: 302, 296, 315, 308 ActionDest: 267 Page: Sequence: 33 Annotations: Annotation: Subtype: Link Rect: 401, 168, 412, 177 ActionDest: 281 Annotation: Subtype: Link Rect: 329, 143, 341, 152 ActionDest: 281 Page: Sequence: 34 Annotations: Annotation: Subtype: Link Rect: 152, 492, 190, 503 Annotation: Subtype: Link Rect: 514, 480, 551, 491 Annotation: Subtype: Link Rect: 95, 458, 133, 468 Annotation: Subtype: Link Rect: 109, 435, 146, 445 Annotation: Subtype: Link Rect: 520, 423, 557, 434 Annotation: Subtype: Link Rect: 59, 400, 97, 410 Annotation: Subtype: Link Rect: 257, 376, 295, 387 Annotation: Subtype: Link Rect: 370, 342, 408, 353 Annotation: Subtype: Link Rect: 188, 296, 226, 307 Annotation: Subtype: Link Rect: 173, 273, 210, 284 Annotation: Subtype: Link Rect: 440, 261, 478, 272 Annotation: Subtype: Link Rect: 365, 250, 403, 261 Annotation: Subtype: Link Rect: 341, 238, 378, 249 Annotation: Subtype: Link Rect: 515, 204, 552, 215 Annotation: Subtype: Link Rect: 305, 158, 343, 169 Annotation: Subtype: Link Rect: 136, 136, 173, 146 Annotation: Subtype: Link Rect: 503, 123, 541, 134 Annotation: Subtype: Link Rect: 514, 112, 551, 123 Annotation: Subtype: Link Rect: 59, 90, 97, 100 Annotation: Subtype: Link Rect: 515, 77, 553, 88 Page: Sequence: 35 Annotations: Annotation: Subtype: Link Rect: 341, 698, 378, 709 Annotation: Subtype: Link Rect: 59, 664, 97, 674 Annotation: Subtype: Link Rect: 198, 629, 235, 640 Annotation: Subtype: Link Rect: 464, 617, 501, 628 Annotation: Subtype: Link Rect: 432, 606, 469, 617 Annotation: Subtype: Link Rect: 59, 572, 97, 582 Annotation: Subtype: Link Rect: 86, 549, 124, 559 Annotation: Subtype: Link Rect: 154, 503, 191, 513 Checksum: afe2ca0c Type: CRC32 Checksum: 8873fc2ecc1d2971960c49022a013a1f Type: MD5 Checksum: e3a7a7fde95c90931fe2313dfe1817af9ca34cf1 Type: SHA-1