Reach set computations using real quantifier elimination:
Abstract: "Reach set computations are of fundamental importance in control theory. We consider the reach set problem for open-loop systems described by parametric inhomogeneous linear differential systems and use real quantifier elimination methods to get exact and approximate solutions. For si...
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Passau
2000
|
| Series: | Universität <Passau> / Fakultät für Mathematik und Informatik: MIP
2000,12 |
| Subjects: | |
| Summary: | Abstract: "Reach set computations are of fundamental importance in control theory. We consider the reach set problem for open-loop systems described by parametric inhomogeneous linear differential systems and use real quantifier elimination methods to get exact and approximate solutions. For simple elementary functions we give an exact calculation of the cases where exact semialgebraic transcendental implicitization is possible. For the negative cases we provide approximate alternating using discrete point checking or safe estimations of reach sets and control parameter sets. The method employs a reduction of forward and backward reach set and control parameter set problem to the transcendental implicitization problem for the components of special solutions of simpler non-parametric systems. Numerous examples are computed using the REDLOG and QEPCAD packages." |
| Physical Description: | 54, 4 S. |
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| 490 | 1 | |a Universität <Passau> / Fakultät für Mathematik und Informatik: MIP |v 2000,12 | |
| 520 | 3 | |a Abstract: "Reach set computations are of fundamental importance in control theory. We consider the reach set problem for open-loop systems described by parametric inhomogeneous linear differential systems and use real quantifier elimination methods to get exact and approximate solutions. For simple elementary functions we give an exact calculation of the cases where exact semialgebraic transcendental implicitization is possible. For the negative cases we provide approximate alternating using discrete point checking or safe estimations of reach sets and control parameter sets. The method employs a reduction of forward and backward reach set and control parameter set problem to the transcendental implicitization problem for the components of special solutions of simpler non-parametric systems. Numerous examples are computed using the REDLOG and QEPCAD packages." | |
| 650 | 4 | |a Predicate calculus | |
| 650 | 4 | |a Set theory | |
| 700 | 1 | |a Weispfenning, Volker |d 1944- |e Verfasser |0 (DE-588)108063550 |4 aut | |
| 810 | 2 | |a Fakultät für Mathematik und Informatik: MIP |t Universität <Passau> |v 2000,12 |w (DE-604)BV000905393 |9 2000,12 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009168991 | |
Record in the Search Index
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| author | Anai, Hirokazu Weispfenning, Volker 1944- |
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| illustrated | Not Illustrated |
| indexdate | 2025-01-10T17:04:59Z |
| institution | BVB |
| language | English |
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| physical | 54, 4 S. |
| publishDate | 2000 |
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| series2 | Universität <Passau> / Fakultät für Mathematik und Informatik: MIP |
| spelling | Anai, Hirokazu Verfasser aut Reach set computations using real quantifier elimination Hirokazu Anai ; Volker Weispfenning Passau 2000 54, 4 S. txt rdacontent n rdamedia nc rdacarrier Universität <Passau> / Fakultät für Mathematik und Informatik: MIP 2000,12 Abstract: "Reach set computations are of fundamental importance in control theory. We consider the reach set problem for open-loop systems described by parametric inhomogeneous linear differential systems and use real quantifier elimination methods to get exact and approximate solutions. For simple elementary functions we give an exact calculation of the cases where exact semialgebraic transcendental implicitization is possible. For the negative cases we provide approximate alternating using discrete point checking or safe estimations of reach sets and control parameter sets. The method employs a reduction of forward and backward reach set and control parameter set problem to the transcendental implicitization problem for the components of special solutions of simpler non-parametric systems. Numerous examples are computed using the REDLOG and QEPCAD packages." Predicate calculus Set theory Weispfenning, Volker 1944- Verfasser (DE-588)108063550 aut Fakultät für Mathematik und Informatik: MIP Universität <Passau> 2000,12 (DE-604)BV000905393 2000,12 |
| spellingShingle | Anai, Hirokazu Weispfenning, Volker 1944- Reach set computations using real quantifier elimination Predicate calculus Set theory |
| title | Reach set computations using real quantifier elimination |
| title_auth | Reach set computations using real quantifier elimination |
| title_exact_search | Reach set computations using real quantifier elimination |
| title_full | Reach set computations using real quantifier elimination Hirokazu Anai ; Volker Weispfenning |
| title_fullStr | Reach set computations using real quantifier elimination Hirokazu Anai ; Volker Weispfenning |
| title_full_unstemmed | Reach set computations using real quantifier elimination Hirokazu Anai ; Volker Weispfenning |
| title_short | Reach set computations using real quantifier elimination |
| title_sort | reach set computations using real quantifier elimination |
| topic | Predicate calculus Set theory |
| topic_facet | Predicate calculus Set theory |
| volume_link | (DE-604)BV000905393 |
| work_keys_str_mv | AT anaihirokazu reachsetcomputationsusingrealquantifierelimination AT weispfenningvolker reachsetcomputationsusingrealquantifierelimination |