Given a large homogeneous collection of switched systems, we consider a novel class of safety constraints, called mode-counting constraints, that impose restrictions on the number of systems that are in a particular mode. We propose an approach for synthesizing correct-by-construction switching protocols to enforce such constraints over time. Our approach starts by constructing an approximately bisimilar abstraction of the individual system model. Then, we show that the aggregate behavior of the collection can be represented by a linear system, whose system matrices are induced by the transition graph of the abstraction. Finally, the control synthesis problem with mode-counting constraints is reduced to a cycle assignment problem on the transition graph. One salient feature of the proposed approach is its scalability; the computational complexity is independent of the number of systems involved. We illustrate this approach on the problem of coordinating a large collection of thermostatically controlled loads while ensuring a bound on the number of loads that are extracting power from the electricity grid at any given time.
{"title":"Control Synthesis for Large Collections of Systems with Mode-Counting Constraints","authors":"Petter Nilsson, N. Ozay","doi":"10.1145/2883817.2883831","DOIUrl":"https://doi.org/10.1145/2883817.2883831","url":null,"abstract":"Given a large homogeneous collection of switched systems, we consider a novel class of safety constraints, called mode-counting constraints, that impose restrictions on the number of systems that are in a particular mode. We propose an approach for synthesizing correct-by-construction switching protocols to enforce such constraints over time. Our approach starts by constructing an approximately bisimilar abstraction of the individual system model. Then, we show that the aggregate behavior of the collection can be represented by a linear system, whose system matrices are induced by the transition graph of the abstraction. Finally, the control synthesis problem with mode-counting constraints is reduced to a cycle assignment problem on the transition graph. One salient feature of the proposed approach is its scalability; the computational complexity is independent of the number of systems involved. We illustrate this approach on the problem of coordinating a large collection of thermostatically controlled loads while ensuring a bound on the number of loads that are extracting power from the electricity grid at any given time.","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123580840","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: Reachability Computation","authors":"Alexandre Donzé","doi":"10.1145/3261117","DOIUrl":"https://doi.org/10.1145/3261117","url":null,"abstract":"","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116474298","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}
Safety analysis is important when designing and developing cyber-physical systems (CPS). An autonomous vehicle can be described as a complex CPS where the physical dynamics of the vehicle interact with the control systems. The challenge is ensuring safety despite nonlinearities, hybrid dynamics, and disturbances as well as complex cyber-physical interactions. In this paper, we present an approach for the safety analysis of automotive control systems using multimodal port-Hamiltonian systems (PHS). The approach uses the Hamiltonian function to represent the energy of the safe and unsafe states and employs passivity to prove that trajectories that begin in safe regions cannot enter unsafe regions. We first apply the approach to the safety analysis of a longitudinal vehicle dynamics composed with an adaptive cruise control (ACC) system. We then extend the results to the safety analysis of a combined longitudinal and lateral vehicle dynamics composed with an ACC and lane keeping control (LKC) system. Simulation results are presented to demonstrate the approach.
{"title":"Safety Analysis of Automotive Control Systems Using Multi-Modal Port-Hamiltonian Systems","authors":"Siyuan Dai, X. Koutsoukos","doi":"10.1145/2883817.2883845","DOIUrl":"https://doi.org/10.1145/2883817.2883845","url":null,"abstract":"Safety analysis is important when designing and developing cyber-physical systems (CPS). An autonomous vehicle can be described as a complex CPS where the physical dynamics of the vehicle interact with the control systems. The challenge is ensuring safety despite nonlinearities, hybrid dynamics, and disturbances as well as complex cyber-physical interactions. In this paper, we present an approach for the safety analysis of automotive control systems using multimodal port-Hamiltonian systems (PHS). The approach uses the Hamiltonian function to represent the energy of the safe and unsafe states and employs passivity to prove that trajectories that begin in safe regions cannot enter unsafe regions. We first apply the approach to the safety analysis of a longitudinal vehicle dynamics composed with an adaptive cruise control (ACC) system. We then extend the results to the safety analysis of a combined longitudinal and lateral vehicle dynamics composed with an ACC and lane keeping control (LKC) system. Simulation results are presented to demonstrate the approach.","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131919442","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}
Robots using distributed sensors in smart environments and smart infrastructure systems such as traffic and power systems are examples of networked cyber-physical systems where communication and/or computational resources are constrained. The scientific challenge is to design scheduling and control schemes taking into account such resource constraints and to preferably include fair resource sharing mechanisms among different control applications. In this talk we present a novel framework for the optimal co-design of scheduling and control for networked systems with resource constraints. In particular we consider multiple control loops, which transmit their measurements over a shared communication channel. Only a limited number of those control loops may close their feedback loop at a time. As a result the dynamics of the individual control loops are coupled through the resource constraint. The scientific question is, when a control loop should schedule the transmission of a measurement and what is the appropriate control law. We approach the problem from an optimality point of view with the scheduling and control policies being the optimization variables. We derive an efficient and tractable decomposition, which allows a distributed solution for control and scheduling decisions coordinated by a price-based mechanism. It turns out that an event-triggered control scheme is optimal and that certainty equivalence holds. In fact, our scheme exploits the adaptation ability of event-triggered control in terms of communication traffic elasticity. Furthermore, we provide stability results linking the resource constraints with the system dynamics.
{"title":"Optimal Co-Design of Scheduling and Control for Networked Systems","authors":"S. Hirche","doi":"10.1145/2883817.2883818","DOIUrl":"https://doi.org/10.1145/2883817.2883818","url":null,"abstract":"Robots using distributed sensors in smart environments and smart infrastructure systems such as traffic and power systems are examples of networked cyber-physical systems where communication and/or computational resources are constrained. The scientific challenge is to design scheduling and control schemes taking into account such resource constraints and to preferably include fair resource sharing mechanisms among different control applications. In this talk we present a novel framework for the optimal co-design of scheduling and control for networked systems with resource constraints. In particular we consider multiple control loops, which transmit their measurements over a shared communication channel. Only a limited number of those control loops may close their feedback loop at a time. As a result the dynamics of the individual control loops are coupled through the resource constraint. The scientific question is, when a control loop should schedule the transmission of a measurement and what is the appropriate control law. We approach the problem from an optimality point of view with the scheduling and control policies being the optimization variables. We derive an efficient and tractable decomposition, which allows a distributed solution for control and scheduling decisions coordinated by a price-based mechanism. It turns out that an event-triggered control scheme is optimal and that certainty equivalence holds. In fact, our scheme exploits the adaptation ability of event-triggered control in terms of communication traffic elasticity. Furthermore, we provide stability results linking the resource constraints with the system dynamics.","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116629611","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}
Given a dynamical system and a specification, assumption mining is the problem of identifying the set of admissible disturbance signals and initial states that generate trajectories satisfying the specification. We first introduce the notion of a directed specification, which describes either upper or lower sets in a partially ordered signal space, and show that this notion encompasses an expressive temporal logic fragment. We next show that the order preserving nature of monotone dynamical systems makes them amenable to a systematic form of assumption mining that checks numerical simulations of system trajectories against directed specifications. The assumption set is then located with a multidimensional bisection method that converges to the boundary from above and below. Typical objectives in vehicular traffic control, such as avoiding or clearing congestion, are directed specifications. In an application to a freeway flow model with monotone dynamics, we identify the set of vehicular demand profiles that satisfy a specification that congestion be intermittent.
{"title":"Directed Specifications and Assumption Mining for Monotone Dynamical Systems","authors":"Eric S. Kim, M. Arcak, S. Seshia","doi":"10.1145/2883817.2883833","DOIUrl":"https://doi.org/10.1145/2883817.2883833","url":null,"abstract":"Given a dynamical system and a specification, assumption mining is the problem of identifying the set of admissible disturbance signals and initial states that generate trajectories satisfying the specification. We first introduce the notion of a directed specification, which describes either upper or lower sets in a partially ordered signal space, and show that this notion encompasses an expressive temporal logic fragment. We next show that the order preserving nature of monotone dynamical systems makes them amenable to a systematic form of assumption mining that checks numerical simulations of system trajectories against directed specifications. The assumption set is then located with a multidimensional bisection method that converges to the boundary from above and below. Typical objectives in vehicular traffic control, such as avoiding or clearing congestion, are directed specifications. In an application to a freeway flow model with monotone dynamics, we identify the set of vehicular demand profiles that satisfy a specification that congestion be intermittent.","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116927274","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}
Hendrik Roehm, Jens Oehlerking, M. Woehrle, M. Althoff
Industrial-sized hybrid systems are typically not amenable to formal verification techniques. For this reason, a common approach is to formally verify abstractions of (parts of) the original system. However, we need to show that this abstraction conforms to the actual system implementation including its physical dynamics. In particular, verified properties of the abstract system need to transfer to the implementation. To this end, we introduce a formal conformance relation, called reachset conformance, which guarantees transference of safety properties, while being a weaker relation than the existing trace inclusion conformance. Based on this formal relation, we present a conformance testing method which allows us to tune the trade-off between accuracy and computational load. Additionally, we present a test selection algorithm that uses a coverage measure to reduce the number of test cases for conformance testing. We experimentally show the benefits of our novel techniques based on an example from autonomous driving.
{"title":"Reachset Conformance Testing of Hybrid Automata","authors":"Hendrik Roehm, Jens Oehlerking, M. Woehrle, M. Althoff","doi":"10.1145/2883817.2883828","DOIUrl":"https://doi.org/10.1145/2883817.2883828","url":null,"abstract":"Industrial-sized hybrid systems are typically not amenable to formal verification techniques. For this reason, a common approach is to formally verify abstractions of (parts of) the original system. However, we need to show that this abstraction conforms to the actual system implementation including its physical dynamics. In particular, verified properties of the abstract system need to transfer to the implementation. To this end, we introduce a formal conformance relation, called reachset conformance, which guarantees transference of safety properties, while being a weaker relation than the existing trace inclusion conformance. Based on this formal relation, we present a conformance testing method which allows us to tune the trade-off between accuracy and computational load. Additionally, we present a test selection algorithm that uses a coverage measure to reduce the number of test cases for conformance testing. We experimentally show the benefits of our novel techniques based on an example from autonomous driving.","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125277510","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}
K. Bae, P. C. Ölveczky, Soonho Kong, Sicun Gao, E. Clarke
This paper presents general techniques for verifying virtually synchronous distributed control systems with interconnected physical environments. Such cyber-physical systems (CPSs) are notoriously hard to verify, due to their combination of nontrivial continuous dynamics, network delays, imprecise local clocks, asynchronous communication, etc. To simplify their analysis, we first extend the PALS methodology---that allows to abstract from the timing of events, asynchronous communication, network delays, and imprecise clocks, as long as the infrastructure guarantees bounds on the network delays and clock skews---from real-time to hybrid systems. We prove a bisimulation equivalence between Hybrid PALS synchronous and asynchronous models. We then show how various verification problems for synchronous Hybrid PALS models can be reduced to SMT solving over nonlinear theories of the real numbers. We illustrate the Hybrid PALS modeling and verification methodology on a number of CPSs, including a control system for turning an airplane.
{"title":"SMT-Based Analysis of Virtually Synchronous Distributed Hybrid Systems","authors":"K. Bae, P. C. Ölveczky, Soonho Kong, Sicun Gao, E. Clarke","doi":"10.1145/2883817.2883849","DOIUrl":"https://doi.org/10.1145/2883817.2883849","url":null,"abstract":"This paper presents general techniques for verifying virtually synchronous distributed control systems with interconnected physical environments. Such cyber-physical systems (CPSs) are notoriously hard to verify, due to their combination of nontrivial continuous dynamics, network delays, imprecise local clocks, asynchronous communication, etc. To simplify their analysis, we first extend the PALS methodology---that allows to abstract from the timing of events, asynchronous communication, network delays, and imprecise clocks, as long as the infrastructure guarantees bounds on the network delays and clock skews---from real-time to hybrid systems. We prove a bisimulation equivalence between Hybrid PALS synchronous and asynchronous models. We then show how various verification problems for synchronous Hybrid PALS models can be reduced to SMT solving over nonlinear theories of the real numbers. We illustrate the Hybrid PALS modeling and verification methodology on a number of CPSs, including a control system for turning an airplane.","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"135 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120921959","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: Analysis of Switched Systems","authors":"M. Prandini","doi":"10.1145/3261109","DOIUrl":"https://doi.org/10.1145/3261109","url":null,"abstract":"","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121311840","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 present a hybridization method for stability analysis of switched linear hybrid system (LHS), that constructs a switched system with polyhedral inclusion dynamics (PHS) using a state-space partition that is specific to stability analysis. We use a previous result based on quantitative predicate abstraction to analyse the stability of PHS. We show completeness of the hybridization based verification technique for the class of asymptotically stable linear system and a subclass of switched linear systems whose dynamics are pairwise Lipschitz continuous on the state-space and uniformly converging in time. For this class of systems, we show that by increasing the granularity of the region partition, we eventually reach an abstract switched system with polyhedral inclusion dynamics that is asymptotically stable. On the practical side, we implemented our approach in the tool averist, and experimentally compared our approach with a state-of-the-art tool for stability analysis of hybrid systems based on Lyapunov functions. Our experimental results illustrate that our method is less prone to numerical errors and scales better than the traditional approaches. In addition, our tool returns a counterexample in the event that it fails to prove stability, providing feedback regarding the potential reason for instability. We also examined heuristics for the choice of state-space partition during refinement.
{"title":"Hybridization for Stability Analysis of Switched Linear Systems","authors":"P. Prabhakar, Miriam García Soto","doi":"10.1145/2883817.2883840","DOIUrl":"https://doi.org/10.1145/2883817.2883840","url":null,"abstract":"In this paper, we present a hybridization method for stability analysis of switched linear hybrid system (LHS), that constructs a switched system with polyhedral inclusion dynamics (PHS) using a state-space partition that is specific to stability analysis. We use a previous result based on quantitative predicate abstraction to analyse the stability of PHS. We show completeness of the hybridization based verification technique for the class of asymptotically stable linear system and a subclass of switched linear systems whose dynamics are pairwise Lipschitz continuous on the state-space and uniformly converging in time. For this class of systems, we show that by increasing the granularity of the region partition, we eventually reach an abstract switched system with polyhedral inclusion dynamics that is asymptotically stable. On the practical side, we implemented our approach in the tool averist, and experimentally compared our approach with a state-of-the-art tool for stability analysis of hybrid systems based on Lyapunov functions. Our experimental results illustrate that our method is less prone to numerical errors and scales better than the traditional approaches. In addition, our tool returns a counterexample in the event that it fails to prove stability, providing feedback regarding the potential reason for instability. We also examined heuristics for the choice of state-space partition during refinement.","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121121536","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: Time- and Event-based Models","authors":"N. Ozay","doi":"10.1145/3261113","DOIUrl":"https://doi.org/10.1145/3261113","url":null,"abstract":"","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134156006","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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