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Claire J. Tomlin - One of the best experts on this subject based on the ideXlab platform.
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A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems
2019 American Control Conference (ACC), 2019Co-Authors: Margaret P. Chapman, Marco Pavone, Jonathan Lacotte, Aviv Tamar, Kevin M. Smith, Victoria Cheng, Jaime F. Fisac, Claire J. TomlinAbstract:A classic Reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of Reachability analysis and risk measures to devise a risk-sensitive Reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set asa set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk(CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set and provide arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive Reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi Reachability analysis) to risk-neutral (which is the case for stochastic Reachability analysis).
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a risk sensitive finite time Reachability approach for safety of stochastic dynamic systems
arXiv: Systems and Control, 2019Co-Authors: Margaret P. Chapman, Marco Pavone, Jonathan Lacotte, Aviv Tamar, Kevin M. Smith, Victoria Cheng, Jaime F. Fisac, Donggun Lee, Susmit Jha, Claire J. TomlinAbstract:A classic Reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of Reachability analysis and risk measures to devise a risk-sensitive Reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set as a set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk (CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set, and provide theoretical arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive Reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi Reachability analysis) to risk-neutral (which is the case for stochastic Reachability analysis).
Margaret P. Chapman - One of the best experts on this subject based on the ideXlab platform.
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A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems
2019 American Control Conference (ACC), 2019Co-Authors: Margaret P. Chapman, Marco Pavone, Jonathan Lacotte, Aviv Tamar, Kevin M. Smith, Victoria Cheng, Jaime F. Fisac, Claire J. TomlinAbstract:A classic Reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of Reachability analysis and risk measures to devise a risk-sensitive Reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set asa set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk(CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set and provide arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive Reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi Reachability analysis) to risk-neutral (which is the case for stochastic Reachability analysis).
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a risk sensitive finite time Reachability approach for safety of stochastic dynamic systems
arXiv: Systems and Control, 2019Co-Authors: Margaret P. Chapman, Marco Pavone, Jonathan Lacotte, Aviv Tamar, Kevin M. Smith, Victoria Cheng, Jaime F. Fisac, Donggun Lee, Susmit Jha, Claire J. TomlinAbstract:A classic Reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of Reachability analysis and risk measures to devise a risk-sensitive Reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set as a set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk (CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set, and provide theoretical arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive Reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi Reachability analysis) to risk-neutral (which is the case for stochastic Reachability analysis).
Marco Pavone - One of the best experts on this subject based on the ideXlab platform.
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A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems
2019 American Control Conference (ACC), 2019Co-Authors: Margaret P. Chapman, Marco Pavone, Jonathan Lacotte, Aviv Tamar, Kevin M. Smith, Victoria Cheng, Jaime F. Fisac, Claire J. TomlinAbstract:A classic Reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of Reachability analysis and risk measures to devise a risk-sensitive Reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set asa set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk(CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set and provide arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive Reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi Reachability analysis) to risk-neutral (which is the case for stochastic Reachability analysis).
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a risk sensitive finite time Reachability approach for safety of stochastic dynamic systems
arXiv: Systems and Control, 2019Co-Authors: Margaret P. Chapman, Marco Pavone, Jonathan Lacotte, Aviv Tamar, Kevin M. Smith, Victoria Cheng, Jaime F. Fisac, Donggun Lee, Susmit Jha, Claire J. TomlinAbstract:A classic Reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of Reachability analysis and risk measures to devise a risk-sensitive Reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set as a set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk (CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set, and provide theoretical arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive Reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi Reachability analysis) to risk-neutral (which is the case for stochastic Reachability analysis).
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signal temporal logic meets Reachability connections and applications
International Workshop Algorithmic Foundations Robotics, 2018Co-Authors: Mo Chen, Scott C Livingston, Marco PavoneAbstract:Signal temporal logic (STL) and Reachability analysis are effective mathematical tools for formally analyzing the behavior of robotic systems. STL is a specification language that uses logic and temporal operators to precisely express real-valued and time-dependent requirements on system behaviors. While recursively defined STL specifications are extremely expressive and controller synthesis methods exist, there has not been work that quantifies the set of states from which STL formulas can be satisfied. Reachability analysis, on the other hand, involves computing the reachable set – the set of states from which a system is able to reach a goal while satisfying state and control constraints. While reasoning about system requirements through sets of states is useful for predetermining the possibility of satisfying desired system properties and obtaining state feedback controllers, so far the application of Reachability has been limited to reach-avoid specifications. In this paper, we merge STL and time-varying Reachability into a single framework that combines the key advantage of both methods – expressiveness of specifications and set quantification. To do this, we establish a correspondence between temporal and Reachability operators, and use the idea of least-restrictive feasible controller sets (LRFCSs) to break down controller synthesis for complex STL formulas into a sequence of Reachability and elementary set operations. LRFCSs are crucial for avoiding controller conflicts among different Reachability operations. In addition, the synthesized state feedback controllers are guaranteed to satisfy STL specifications if determined to be possible by our framework, and violate specifications minimally if not. For simplicity, Hamilton-Jacobi Reachability will be used in this paper, although our method is agnostic to the time-varying Reachability method. We demonstrate our method through numerical simulations and robotic experiments.
Gennaro Parlato - One of the best experts on this subject based on the ideXlab platform.
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reducing context bounded concurrent Reachability to sequential Reachability
Computer Aided Verification, 2009Co-Authors: Salvatore La Torre, P Madhusudan, Gennaro ParlatoAbstract:We give a translation from concurrent programs to sequential programs that reduces the context-bounded Reachability problem in the concurrent program to a Reachability problem in the sequential one. The translation has two salient features: (a) the sequential program tracks, at any time, the local state of only one thread (though it does track multiple copies of shared variables), and (b) all reachable states of the sequential program correspond to reachable states of the concurrent program. We also implement our transformation in the setting of concurrent recursive programs with finite data domains, and show that the resulting sequential program can be model-checked efficiently using existing recursive sequential program Reachability tools.
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CAV - Reducing Context-Bounded Concurrent Reachability to Sequential Reachability
Computer Aided Verification, 2009Co-Authors: Salvatore La Torre, P Madhusudan, Gennaro ParlatoAbstract:We give a translation from concurrent programs to sequential programs that reduces the context-bounded Reachability problem in the concurrent program to a Reachability problem in the sequential one. The translation has two salient features: (a) the sequential program tracks, at any time, the local state of only one thread (though it does track multiple copies of shared variables), and (b) all reachable states of the sequential program correspond to reachable states of the concurrent program. We also implement our transformation in the setting of concurrent recursive programs with finite data domains, and show that the resulting sequential program can be model-checked efficiently using existing recursive sequential program Reachability tools.
Jonathan Lacotte - One of the best experts on this subject based on the ideXlab platform.
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A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems
2019 American Control Conference (ACC), 2019Co-Authors: Margaret P. Chapman, Marco Pavone, Jonathan Lacotte, Aviv Tamar, Kevin M. Smith, Victoria Cheng, Jaime F. Fisac, Claire J. TomlinAbstract:A classic Reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of Reachability analysis and risk measures to devise a risk-sensitive Reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set asa set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk(CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set and provide arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive Reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi Reachability analysis) to risk-neutral (which is the case for stochastic Reachability analysis).
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a risk sensitive finite time Reachability approach for safety of stochastic dynamic systems
arXiv: Systems and Control, 2019Co-Authors: Margaret P. Chapman, Marco Pavone, Jonathan Lacotte, Aviv Tamar, Kevin M. Smith, Victoria Cheng, Jaime F. Fisac, Donggun Lee, Susmit Jha, Claire J. TomlinAbstract:A classic Reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of Reachability analysis and risk measures to devise a risk-sensitive Reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set as a set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk (CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set, and provide theoretical arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive Reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi Reachability analysis) to risk-neutral (which is the case for stochastic Reachability analysis).
