R. Wisniewski, Christoffer Sloth, Manuela L. Bujorianu, Nir Piterman
We consider the safety problem of piecewise-deterministic Markov processes (PDMP). These are systems that have deterministic dynamics and stochastic jumps, where both the time and the destination of the jumps are stochastic. Specifically, we solve a p-safety problem, where we identify the set of initial states from which the probability to reach designated unsafe states is at most 1 - p. Based on the knowledge of the full generator of the PDMP, we are able to develop a system of partial differential equations describing the connection between unsafe and initial states. We then show that by using the moment method, we can translate the infinite-dimensional optimisation problem searching for the largest set of p-safe states to a finite dimensional polynomial optimisation problem. We have implemented this technique on top of GloptiPoly and show how to apply it to a numerical example.
{"title":"Safety Verification of Piecewise-Deterministic Markov Processes","authors":"R. Wisniewski, Christoffer Sloth, Manuela L. Bujorianu, Nir Piterman","doi":"10.1145/2883817.2883836","DOIUrl":"https://doi.org/10.1145/2883817.2883836","url":null,"abstract":"We consider the safety problem of piecewise-deterministic Markov processes (PDMP). These are systems that have deterministic dynamics and stochastic jumps, where both the time and the destination of the jumps are stochastic. Specifically, we solve a p-safety problem, where we identify the set of initial states from which the probability to reach designated unsafe states is at most 1 - p. Based on the knowledge of the full generator of the PDMP, we are able to develop a system of partial differential equations describing the connection between unsafe and initial states. We then show that by using the moment method, we can translate the infinite-dimensional optimisation problem searching for the largest set of p-safe states to a finite dimensional polynomial optimisation problem. We have implemented this technique on top of GloptiPoly and show how to apply it to a numerical example.","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"48 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":"131018089","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: Safety and Stability Analysis","authors":"T. Johnson","doi":"10.1145/3261111","DOIUrl":"https://doi.org/10.1145/3261111","url":null,"abstract":"","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"276 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":"126055811","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}
Timing contracts for embedded controller implementation specify the constraints on the time instants at which certain operations are performed such as sampling, actuation, computation, etc. In this paper, we consider the problem of verifying the stability of embedded control systems under such timing contracts. Reformulating the problem in the framework of impulsive linear systems, we provide theoretical conditions for stability and a verification algorithm based on reachability analysis. In the second part of the paper, given a model of the plant and of the controller we propose an approach to synthesize timing contracts that guarantee stability.
{"title":"Verification and Synthesis of Timing Contracts for Embedded Controllers","authors":"M. A. Khatib, A. Girard, T. Dang","doi":"10.1145/2883817.2883827","DOIUrl":"https://doi.org/10.1145/2883817.2883827","url":null,"abstract":"Timing contracts for embedded controller implementation specify the constraints on the time instants at which certain operations are performed such as sampling, actuation, computation, etc. In this paper, we consider the problem of verifying the stability of embedded control systems under such timing contracts. Reformulating the problem in the framework of impulsive linear systems, we provide theoretical conditions for stability and a verification algorithm based on reachability analysis. In the second part of the paper, given a model of the plant and of the controller we propose an approach to synthesize timing contracts that guarantee stability.","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"18 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":"126000183","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 propose tools for the study of robust stabilizability and the design of robustly stabilizing feedback laws for a wide class of hybrid systems given in terms of hybrid inclusions with inputs and disturbances. We introduce notions of robust uniform global stabilizability and stabilization that capture the case when disturbances can be fully rejected, practically rejected, and when they induce a residual set that can be stabilized. Robust control Lyapunov functions are em- ployed to determine when stabilizing static state-feedback laws are available and also to synthesize robustly stabilizing feedback laws with minimum pointwise norm. Sufficient conditions on the data of the hybrid system as well as on the control Lyapunov function are proposed for the said properties to hold. An example illustrates the results throughout the paper.
{"title":"Robust Asymptotic Stabilization of Hybrid Systems using Control Lyapunov Functions","authors":"R. Sanfelice","doi":"10.1145/2883817.2883848","DOIUrl":"https://doi.org/10.1145/2883817.2883848","url":null,"abstract":"We propose tools for the study of robust stabilizability and the design of robustly stabilizing feedback laws for a wide class of hybrid systems given in terms of hybrid inclusions with inputs and disturbances. We introduce notions of robust uniform global stabilizability and stabilization that capture the case when disturbances can be fully rejected, practically rejected, and when they induce a residual set that can be stabilized. Robust control Lyapunov functions are em- ployed to determine when stabilizing static state-feedback laws are available and also to synthesize robustly stabilizing feedback laws with minimum pointwise norm. Sufficient conditions on the data of the hybrid system as well as on the control Lyapunov function are proposed for the said properties to hold. An example illustrates the results throughout the paper.","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"99 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":"114237205","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}
Timothy E. Wang, P. Garoche, P. Roux, Romain Jobredeaux, E. Feron
Robustness analyses play a major role in the synthesis and analysis of controllers. For control systems, robustness is a measure of the maximum tolerable model inaccuracies or perturbations that do not destabilize the system. Analyzing the robustness of a closed-loop system can be performed with multiple approaches: gain and phase margin computation for single-input single-output (SISO) linear systems, mu analysis, IQC computations, etc. However, none of these techniques consider the actual code in their analyses. The approach presented here relies on an invariant computation on the discrete system dynamics. Using semi-definite programming (SDP) solvers, a Lyapunov-based function is synthesized that captures the vector margins of the closed-loop linear system considered. This numerical invariant expressed over the state variables of the system is compatible with code analysis and enables its validation on the code artifact. This automatic analysis extends verification techniques focused on controller implementation, addressing validation of robustness at model and code level. It has been implemented in a tool analyzing discrete SISO systems and generating over-approximations of phase and gain margins. The analysis will be integrated in our toolchain for Simulink and Lustre models autocoding and formal analysis.
{"title":"Formal Analysis of Robustness at Model and Code Level","authors":"Timothy E. Wang, P. Garoche, P. Roux, Romain Jobredeaux, E. Feron","doi":"10.1145/2883817.2883824","DOIUrl":"https://doi.org/10.1145/2883817.2883824","url":null,"abstract":"Robustness analyses play a major role in the synthesis and analysis of controllers. For control systems, robustness is a measure of the maximum tolerable model inaccuracies or perturbations that do not destabilize the system. Analyzing the robustness of a closed-loop system can be performed with multiple approaches: gain and phase margin computation for single-input single-output (SISO) linear systems, mu analysis, IQC computations, etc. However, none of these techniques consider the actual code in their analyses. The approach presented here relies on an invariant computation on the discrete system dynamics. Using semi-definite programming (SDP) solvers, a Lyapunov-based function is synthesized that captures the vector margins of the closed-loop linear system considered. This numerical invariant expressed over the state variables of the system is compatible with code analysis and enables its validation on the code artifact. This automatic analysis extends verification techniques focused on controller implementation, addressing validation of robustness at model and code level. It has been implemented in a tool analyzing discrete SISO systems and generating over-approximations of phase and gain margins. The analysis will be integrated in our toolchain for Simulink and Lustre models autocoding and formal analysis.","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"2 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114018663","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 hybrid event-based control (HEBC) systems the controller influences a continuous plant $G$ through two input signals with different characteristics. A continuous input is used to attenuate disturbances and to force the plant to follow a reference signal, whereas a discrete-valued input is determined by an event-based component of the controller in order to adjust the operation point of the plant. HEBC systems have typical characteristics of hybrid dynamical systems including state jumps and switching dynamics. This paper analyses HEBC systems with linear components. It derives bounds on the event threshold in order to avoid Zeno behaviour and to guarantee a minimum inter-event time. The main result is a condition under which the closed-loop system is asymptotically stable and has an asymptotic set-point tracking behaviour. An application example illustrates the results.
{"title":"Event-Separation Properties and Asymptotic Behaviour of Hybrid Event-Based Control Systems","authors":"Tobias Noesselt, M. Schultalbers, J. Lunze","doi":"10.1145/2883817.2883835","DOIUrl":"https://doi.org/10.1145/2883817.2883835","url":null,"abstract":"In hybrid event-based control (HEBC) systems the controller influences a continuous plant $G$ through two input signals with different characteristics. A continuous input is used to attenuate disturbances and to force the plant to follow a reference signal, whereas a discrete-valued input is determined by an event-based component of the controller in order to adjust the operation point of the plant. HEBC systems have typical characteristics of hybrid dynamical systems including state jumps and switching dynamics. This paper analyses HEBC systems with linear components. It derives bounds on the event threshold in order to avoid Zeno behaviour and to guarantee a minimum inter-event time. The main result is a condition under which the closed-loop system is asymptotically stable and has an asymptotic set-point tracking behaviour. An application example illustrates the results.","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":"127586738","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: Temporal Logic Applications","authors":"S. Mitra","doi":"10.1145/3261108","DOIUrl":"https://doi.org/10.1145/3261108","url":null,"abstract":"","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"1 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":"131875280","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 consider the problem of translating a deterministic emph{simulation model} (like Matlab-Simunk, Modelica or Ptolemy models) into a emph{verification model} expressed by a network of hybrid automata. The goal is to verify safety using reachability analysis on the verification model. Simulation models typically use transitions with urgent semantics, which must be taken as soon as possible. Urgent transitions also make it possible to decompose systems that would otherwise need to be modeled with a monolithic hybrid automaton. In this paper, we include urgent transitions in our verification models and propose a suitable adaptation of our reachability algorithm. However, the simulation model, due to its imperfections, may be unsafe even though the corresponding hybrid automata are safe. Conversely, set-based reachability may not be able to show safety of an ideal formal model, since complex dynamics necessarily entail overapproximations. Taken as a whole, the formal modeling and verification process can both falsely claim safety and fail to show safety of the concrete system. We address this inconsistency by relaxing the model as follows. The standard semantics of hybrid automata is a mathematical idealization, where reactions are considered to be instantaneous and physical measurements infinitely precise. We propose semantics that relax these assumptions, where guard conditions are sampled in discrete time and admit measurement errors. The relaxed semantics can be translated to an equivalent relaxed model in standard semantics. The relaxed model is realistic in the sense that it can be implemented on hardware fast and precise enough, and in a way that safety is preserved. Finally, we show that overapproximative reachability analysis can show safety of relaxed models, which is not the case in general.
{"title":"From Simulation Models to Hybrid Automata Using Urgency and Relaxation","authors":"Stefano Minopoli, Goran Frehse","doi":"10.1145/2883817.2883825","DOIUrl":"https://doi.org/10.1145/2883817.2883825","url":null,"abstract":"We consider the problem of translating a deterministic emph{simulation model} (like Matlab-Simunk, Modelica or Ptolemy models) into a emph{verification model} expressed by a network of hybrid automata. The goal is to verify safety using reachability analysis on the verification model. Simulation models typically use transitions with urgent semantics, which must be taken as soon as possible. Urgent transitions also make it possible to decompose systems that would otherwise need to be modeled with a monolithic hybrid automaton. In this paper, we include urgent transitions in our verification models and propose a suitable adaptation of our reachability algorithm. However, the simulation model, due to its imperfections, may be unsafe even though the corresponding hybrid automata are safe. Conversely, set-based reachability may not be able to show safety of an ideal formal model, since complex dynamics necessarily entail overapproximations. Taken as a whole, the formal modeling and verification process can both falsely claim safety and fail to show safety of the concrete system. We address this inconsistency by relaxing the model as follows. The standard semantics of hybrid automata is a mathematical idealization, where reactions are considered to be instantaneous and physical measurements infinitely precise. We propose semantics that relax these assumptions, where guard conditions are sampled in discrete time and admit measurement errors. The relaxed semantics can be translated to an equivalent relaxed model in standard semantics. The relaxed model is realistic in the sense that it can be implemented on hardware fast and precise enough, and in a way that safety is preserved. Finally, we show that overapproximative reachability analysis can show safety of relaxed models, which is not the case in general.","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"23 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":"125261217","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}
Benoît Barbot, M. Kwiatkowska, A. Mereacre, Nicola Paoletti
We develop a novel model-based hardware-in-the-loop (HIL) framework for optimising energy consumption of embedded software controllers. Controller and plant models are specified as networks of parameterised timed input/output automata and translated into executable code. The controller is encoded into the target embedded hardware, which is connected to a power monitor and interacts with the simulation of the plant model. The framework then generates a power consumption model that maps controller transitions to distributions over power measurements, and is used to optimise the timing parameters of the controller, without compromising a given safety requirement. The novelty of our approach is that we measure the real power consumption of the controller and use thus obtained data for energy optimisation. We employ timed Petri nets as an intermediate representation of the executable specification, which facilitates efficient code generation and fast simulations. Our framework uniquely combines the advantages of rigorous specifications with accurate power measurements and methods for online model estimation, thus enabling automated design of correct and energy-efficient controllers.
{"title":"Building Power Consumption Models from Executable Timed I/O Automata Specifications","authors":"Benoît Barbot, M. Kwiatkowska, A. Mereacre, Nicola Paoletti","doi":"10.1145/2883817.2883844","DOIUrl":"https://doi.org/10.1145/2883817.2883844","url":null,"abstract":"We develop a novel model-based hardware-in-the-loop (HIL) framework for optimising energy consumption of embedded software controllers. Controller and plant models are specified as networks of parameterised timed input/output automata and translated into executable code. The controller is encoded into the target embedded hardware, which is connected to a power monitor and interacts with the simulation of the plant model. The framework then generates a power consumption model that maps controller transitions to distributions over power measurements, and is used to optimise the timing parameters of the controller, without compromising a given safety requirement. The novelty of our approach is that we measure the real power consumption of the controller and use thus obtained data for energy optimisation. We employ timed Petri nets as an intermediate representation of the executable specification, which facilitates efficient code generation and fast simulations. Our framework uniquely combines the advantages of rigorous specifications with accurate power measurements and methods for online model estimation, thus enabling automated design of correct and energy-efficient controllers.","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"46 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":"124155669","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: Invited Speaker","authors":"A. Abate","doi":"10.1145/3261115","DOIUrl":"https://doi.org/10.1145/3261115","url":null,"abstract":"","PeriodicalId":337926,"journal":{"name":"Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control","volume":"1 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":"125191097","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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