LMI Framework for Set Reachability Inclusion in Discrete-Time LTI Systems
In this article, we present a convex optimization framework to verify the reachability of a desired set for discrete-time linear time-invariant systems. Given elliptically bounded inputs, the set of reachable states in N time steps is the Minkowski sum of a finite number of ellipsoids. We formulate...
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| Veröffentlicht in: | IEEE transactions on automatic control 2022-06, Vol.67 (6), p.2997-3004 |
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| container_title | IEEE transactions on automatic control |
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| creator | Hadizadeh Kafash, Sahand Ruths, Jusin |
| description | In this article, we present a convex optimization framework to verify the reachability of a desired set for discrete-time linear time-invariant systems. Given elliptically bounded inputs, the set of reachable states in N time steps is the Minkowski sum of a finite number of ellipsoids. We formulate the inclusion verification problem as a chain of constraints in the form of linear matrix inequalities. As the time horizon grows, the number of constraints becomes unwieldy, and we present a technique to achieve a similar level of accuracy with far fewer terms, significantly reducing the computational cost of the method. Numerical examples presented in this article show that the method is highly adaptable. |
| doi_str_mv | 10.1109/TAC.2021.3091412 |
| format | Article |
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Numerical examples presented in this article show that the method is highly adaptable.</description><identifier>ISSN: 0018-9286</identifier><identifier>EISSN: 1558-2523</identifier><identifier>DOI: 10.1109/TAC.2021.3091412</identifier><identifier>CODEN: IETAA9</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Computational geometry ; Convexity ; Discrete time systems ; Ellipsoidal approximation ; Ellipsoids ; Linear matrix inequalities ; linear matrix inequality (LMI) ; Linear systems ; linear time-invariant (LTI) systems ; Mathematical analysis ; Optimization ; reachable set ; Safety ; Shape ; System analysis and design ; Time invariant systems ; Trajectory</subject><ispartof>IEEE transactions on automatic control, 2022-06, Vol.67 (6), p.2997-3004</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. 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Numerical examples presented in this article show that the method is highly adaptable.</description><subject>Computational geometry</subject><subject>Convexity</subject><subject>Discrete time systems</subject><subject>Ellipsoidal approximation</subject><subject>Ellipsoids</subject><subject>Linear matrix inequalities</subject><subject>linear matrix inequality (LMI)</subject><subject>Linear systems</subject><subject>linear time-invariant (LTI) systems</subject><subject>Mathematical analysis</subject><subject>Optimization</subject><subject>reachable set</subject><subject>Safety</subject><subject>Shape</subject><subject>System analysis and design</subject><subject>Time invariant systems</subject><subject>Trajectory</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kFFLwzAUhYMoOKfvgi8BnztzkzRtHsd0WqgIrj6HJE0xc21n0jH27-3Y8Oly4DvnwofQPZAZAJFP1Xwxo4TCjBEJHOgFmkCa5glNKbtEE0IgTyTNxTW6iXE9RsE5TFBRvhd4GXTr9n34wU0f8MoN-NNp-62N3_jhgIvObnbR9x32HX720QY3uKTyrcNlVeDVIQ6ujbfoqtGb6O7Od4q-li_V4i0pP16LxbxMLJUwJNRZ0FqmdS4bw7TkGTNZDQ2YmvPMcJlq3QCjUhsQmrHaZiNSZxw45dwINkWPp91t6H93Lg5q3e9CN75UVGSEEsYYHylyomzoYwyuUdvgWx0OCog6ClOjMHUUps7CxsrDqeKdc_-45IILCewPw3tk-A</recordid><startdate>20220601</startdate><enddate>20220601</enddate><creator>Hadizadeh Kafash, Sahand</creator><creator>Ruths, Jusin</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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| language | eng |
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| subjects | Computational geometry Convexity Discrete time systems Ellipsoidal approximation Ellipsoids Linear matrix inequalities linear matrix inequality (LMI) Linear systems linear time-invariant (LTI) systems Mathematical analysis Optimization reachable set Safety Shape System analysis and design Time invariant systems Trajectory |
| title | LMI Framework for Set Reachability Inclusion in Discrete-Time LTI Systems |
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