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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2103.08638 |
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| _version_ | 1866914845404692480 |
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| author | Khajenejad, Mohammad Yong, Sze Zheng |
| author_facet | Khajenejad, Mohammad Yong, Sze Zheng |
| contents | This paper proposes a tractable family of remainder-form mixed-monotone decomposition functions that are useful for over-approximating the image set of nonlinear mappings in reachability and estimation problems. Our approach applies to a new class of nonsmooth, discontinuous nonlinear systems that we call either-sided locally Lipschitz semicontinuous (ELLS) systems, which we show to be a strict superset of locally Lipschitz continuous (LLC) systems, thus expanding the set of systems that are formally known to be mixed-monotone. In addition, we derive lower and upper bounds for the over-approximation error and show that the lower bound is achieved with our proposed approach, i.e., our approach constructs the tightest, tractable remainder-form mixed-monotone decomposition function. Moreover, we introduce a set inversion algorithm that along with the proposed decomposition functions, can be used for constrained reachability analysis and guaranteed state estimation for continuous- and discrete-time systems with bounded noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_08638 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Tight Remainder-Form Decomposition Functions with Applications to Constrained Reachability and Guaranteed State Estimation Khajenejad, Mohammad Yong, Sze Zheng Optimization and Control Systems and Control This paper proposes a tractable family of remainder-form mixed-monotone decomposition functions that are useful for over-approximating the image set of nonlinear mappings in reachability and estimation problems. Our approach applies to a new class of nonsmooth, discontinuous nonlinear systems that we call either-sided locally Lipschitz semicontinuous (ELLS) systems, which we show to be a strict superset of locally Lipschitz continuous (LLC) systems, thus expanding the set of systems that are formally known to be mixed-monotone. In addition, we derive lower and upper bounds for the over-approximation error and show that the lower bound is achieved with our proposed approach, i.e., our approach constructs the tightest, tractable remainder-form mixed-monotone decomposition function. Moreover, we introduce a set inversion algorithm that along with the proposed decomposition functions, can be used for constrained reachability analysis and guaranteed state estimation for continuous- and discrete-time systems with bounded noise. |
| title | Tight Remainder-Form Decomposition Functions with Applications to Constrained Reachability and Guaranteed State Estimation |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2103.08638 |