A. Rajhans, S. Avadhanula, A. Chutinan, P. Mosterman, Fu Zhang
{"title":"Graphical Hybrid Automata with Simulink and Stateflow","authors":"A. Rajhans, S. Avadhanula, A. Chutinan, P. Mosterman, Fu Zhang","doi":"10.1145/3178126.3187007","DOIUrl":"https://doi.org/10.1145/3178126.3187007","url":null,"abstract":"","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125509104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This demo abstract presents ROCS, an algorithmic control synthesis tool for nonlinear dynamical systems. Different from other formal control synthesis tools, it guarantees to generate a control strategy with respect to a robustly realizable specification for a nonlinear system. The functionality and usability of ROCS will be illustrated through examples.
{"title":"ROCS: A Robustly Complete Control Synthesis Tool for Nonlinear Dynamical Systems","authors":"Yinan Li, Jun Liu","doi":"10.1145/3178126.3187006","DOIUrl":"https://doi.org/10.1145/3178126.3187006","url":null,"abstract":"This demo abstract presents ROCS, an algorithmic control synthesis tool for nonlinear dynamical systems. Different from other formal control synthesis tools, it guarantees to generate a control strategy with respect to a robustly realizable specification for a nonlinear system. The functionality and usability of ROCS will be illustrated through examples.","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127664138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we suggest a method based on convex programming for computing semi-algebraic under-approximations of reach sets for polynomial continuous systems with initial sets being the zero sub-level set of a polynomial function. It is well-known that the reachable set can be formulated as the zero sub-level set of a value function to a Hamilton-Jacobi partial differential equation (HJE), and our approach in this paper consequently focuses on searching for approximate analytical polynomial solutions to associated HJEs, of which the zero sub-level sets converge to the exact reachable set from inside in measure, without discretizing the state space. Such approximate solutions can be computed via a classical hierarchy of convex programs consisting of linear matrix inequalities, which are constructed by sum-of-squares decomposition techniques. In contrast to traditional numerical methods approximately solving HJEs, such as level-set methods, our method reduces HJE solving to convex optimization, avoiding the complexity associated to gridding the state space. Compared to existing approaches computing under-approximations, the approach described in this paper is structurally simpler as the under-approximations are the outcome of a single semi-definite program. Furthermore, an over-approximation of the reach set, shedding light on the quality of the constructed under-approximation, can be constructed via solving the same semi-definite program. Several illustrative examples and comparisons with existing methods demonstrate the merits of our approach.
{"title":"Under-Approximating Reach Sets for Polynomial Continuous Systems","authors":"Bai Xue, M. Fränzle, N. Zhan","doi":"10.1145/3178126.3178133","DOIUrl":"https://doi.org/10.1145/3178126.3178133","url":null,"abstract":"In this paper we suggest a method based on convex programming for computing semi-algebraic under-approximations of reach sets for polynomial continuous systems with initial sets being the zero sub-level set of a polynomial function. It is well-known that the reachable set can be formulated as the zero sub-level set of a value function to a Hamilton-Jacobi partial differential equation (HJE), and our approach in this paper consequently focuses on searching for approximate analytical polynomial solutions to associated HJEs, of which the zero sub-level sets converge to the exact reachable set from inside in measure, without discretizing the state space. Such approximate solutions can be computed via a classical hierarchy of convex programs consisting of linear matrix inequalities, which are constructed by sum-of-squares decomposition techniques. In contrast to traditional numerical methods approximately solving HJEs, such as level-set methods, our method reduces HJE solving to convex optimization, avoiding the complexity associated to gridding the state space. Compared to existing approaches computing under-approximations, the approach described in this paper is structurally simpler as the under-approximations are the outcome of a single semi-definite program. Furthermore, an over-approximation of the reach set, shedding light on the quality of the constructed under-approximation, can be constructed via solving the same semi-definite program. Several illustrative examples and comparisons with existing methods demonstrate the merits of our approach.","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"13 49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129678845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Session details: Abstracts for Demos and Posters","authors":"Jens Oehlerking","doi":"10.1145/3258033","DOIUrl":"https://doi.org/10.1145/3258033","url":null,"abstract":"","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126480051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Session details: Stabilization and Control Design","authors":"J. Kapinski","doi":"10.1145/3258027","DOIUrl":"https://doi.org/10.1145/3258027","url":null,"abstract":"","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115184163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a scalable algorithm to construct a polytopic underapproximation of the terminal hitting time stochastic reach-avoid set, for the verification of high-dimensional stochastic LTI systems with arbitrary stochastic disturbance. We prove the existence of a polytopic underapproximation by characterizing the sufficient conditions under which the stochastic reach-avoid set and the proposed open-loop underapproximation are compact and convex. We construct the polytopic underapproximation by formulating and solving a series of convex optimization problems. These set-theoretic properties also characterize circumstances under which the stochastic reach-avoid problem admits a bang-bang optimal Markov policy. We demonstrate the scalability of our algorithm on a 40D chain of integrators, the highest dimensional example demonstrated to date for stochastic reach-avoid problems, and compare its performance with existing approaches on a spacecraft rendezvous and docking problem.
{"title":"Scalable Underapproximative Verification of Stochastic LTI Systems using Convexity and Compactness","authors":"Abraham P. Vinod, Meeko Oishi","doi":"10.1145/3178126.3178148","DOIUrl":"https://doi.org/10.1145/3178126.3178148","url":null,"abstract":"We present a scalable algorithm to construct a polytopic underapproximation of the terminal hitting time stochastic reach-avoid set, for the verification of high-dimensional stochastic LTI systems with arbitrary stochastic disturbance. We prove the existence of a polytopic underapproximation by characterizing the sufficient conditions under which the stochastic reach-avoid set and the proposed open-loop underapproximation are compact and convex. We construct the polytopic underapproximation by formulating and solving a series of convex optimization problems. These set-theoretic properties also characterize circumstances under which the stochastic reach-avoid problem admits a bang-bang optimal Markov policy. We demonstrate the scalability of our algorithm on a 40D chain of integrators, the highest dimensional example demonstrated to date for stochastic reach-avoid problems, and compare its performance with existing approaches on a spacecraft rendezvous and docking problem.","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131951495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A polynomial continuous system S = (F,X0) is specified by a polynomial vector field F and a set of initial conditions X0. We study polynomial changes of bases that transform S into a linear system, called linear abstractions. We first give a complete algorithm to find all such abstractions that fit a user-specified template. This requires taking into account the algebraic structure of the set X0, which we do by working modulo an appropriate invariant ideal. Next, we give necessary and sufficient syntactic conditions under which a full linear abstraction exists, that is one capable of representing the behaviour of the individual variables in the original system. We then propose an approximate linearization and dimension-reduction technique, that is amenable to be implemented "on the fly". We finally illustrate the encouraging results of a preliminary experimentation with the linear abstraction algorithm, conducted on challenging systems drawn from the literature.
{"title":"Algorithms for exact and approximate linear abstractions of polynomial continuous systems","authors":"Michele Boreale","doi":"10.1145/3178126.3178137","DOIUrl":"https://doi.org/10.1145/3178126.3178137","url":null,"abstract":"A polynomial continuous system S = (F,X0) is specified by a polynomial vector field F and a set of initial conditions X0. We study polynomial changes of bases that transform S into a linear system, called linear abstractions. We first give a complete algorithm to find all such abstractions that fit a user-specified template. This requires taking into account the algebraic structure of the set X0, which we do by working modulo an appropriate invariant ideal. Next, we give necessary and sufficient syntactic conditions under which a full linear abstraction exists, that is one capable of representing the behaviour of the individual variables in the original system. We then propose an approximate linearization and dimension-reduction technique, that is amenable to be implemented \"on the fly\". We finally illustrate the encouraging results of a preliminary experimentation with the linear abstraction algorithm, conducted on challenging systems drawn from the literature.","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114837755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper tackles the problem of constructing finite abstractions for formal controller synthesis with high dimensional systems. We develop a theory of abstraction for discrete time nonlinear systems that are equipped with variables acting as interfaces for other systems. Systems interact via an interconnection map which constrains the value of system interface variables. An abstraction of a high dimensional interconnected system is obtained by composing subsystem abstractions with an abstraction of the interconnection. System abstractions are modular in the sense that they can be rearranged, substituted, or reused in configurations that were unknown during the time of abstraction. Constructing the abstraction of the interconnection map can become computationally infeasible when there are many systems. We introduce intermediate variables which break the interconnection and the abstraction procedure apart into smaller problems. Examples showcase the abstraction of a 24-dimensional system through the composition of 24 individual systems, and the synthesis of a controller for a 6-dimensional system with a consensus objective.
{"title":"Constructing Control System Abstractions from Modular Components","authors":"Eric S. Kim, M. Arcak, Majid Zamani","doi":"10.1145/3178126.3178144","DOIUrl":"https://doi.org/10.1145/3178126.3178144","url":null,"abstract":"This paper tackles the problem of constructing finite abstractions for formal controller synthesis with high dimensional systems. We develop a theory of abstraction for discrete time nonlinear systems that are equipped with variables acting as interfaces for other systems. Systems interact via an interconnection map which constrains the value of system interface variables. An abstraction of a high dimensional interconnected system is obtained by composing subsystem abstractions with an abstraction of the interconnection. System abstractions are modular in the sense that they can be rearranged, substituted, or reused in configurations that were unknown during the time of abstraction. Constructing the abstraction of the interconnection map can become computationally infeasible when there are many systems. We introduce intermediate variables which break the interconnection and the abstraction procedure apart into smaller problems. Examples showcase the abstraction of a 24-dimensional system through the composition of 24 individual systems, and the synthesis of a controller for a 6-dimensional system with a consensus objective.","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116814600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stochastic systems with rewards yield a generic stochastic model where both the state and the action space might be uncountable and where every action is decorated by a real-valued reward. For every deterministic stochastic system with rewards we prove that the bisimulation relation and the trace-distribution relation collapse. As a second result, we also establish a characterisation of the bisimulation relation in terms of an expressive action-based probabilistic logic and show that this characterisation is still maintained by a small fragment of this logic.
{"title":"Bisimulations, logics, and trace distributions for stochastic systems with rewards","authors":"Daniel Gburek, C. Baier","doi":"10.1145/3178126.3178139","DOIUrl":"https://doi.org/10.1145/3178126.3178139","url":null,"abstract":"Stochastic systems with rewards yield a generic stochastic model where both the state and the action space might be uncountable and where every action is decorated by a real-valued reward. For every deterministic stochastic system with rewards we prove that the bisimulation relation and the trace-distribution relation collapse. As a second result, we also establish a characterisation of the bisimulation relation in terms of an expressive action-based probabilistic logic and show that this characterisation is still maintained by a small fragment of this logic.","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127507214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Session details: Timed Systems","authors":"Vinayak S. Prabhu","doi":"10.1145/3258026","DOIUrl":"https://doi.org/10.1145/3258026","url":null,"abstract":"","PeriodicalId":131076,"journal":{"name":"Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130850203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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