Discrete Reachability Analysis With Bounded Error Sets

Siefert, Jacob A.; Leister, Daniel D.; Koeln, Justin P.; Pangborn, Herschel C.

doi:10.1109/lcsys.2021.3131607

Cited by 2 publications

(3 citation statements)

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“…To handle growth in set memory complexity over time steps, set propagation methods often utilize over-approximations to reduce complexity. Using techniques from [21], overapproximations of the reachable set are taken periodically every three time steps beginning at k = 3, resulting in 4 total approximations that took an average of 49 seconds each to compute, in a manner similar to [34]. At the time steps corresponding to over-approximations, the set is first saved and analyzed before being over-approximated.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Table II compares the complexity of the three methods, demonstrating how Proposition 1 enables more scalable overapproximations of the bilinear function as sampling is increased and over-approximations become more accurate. Figure 4 plots over-approximation of the bilinear function using all three methods corresponding to Case (6,17,34) in Table II. The partitioning in Figure 4(a) and Figure 4(c) corresponds to sampling in the (x, y) space while the partitioning in Figure 4(b) corresponds to sampling in the (u, v) space.…”

Section: B Reduced Memory Complexity For Bilinear Functionmentioning

confidence: 99%

“…17,34) ng = 73 n b = 26 nc = 38 ng = 40 n b = 18 nc = 22 ng = 73 n b = 18 nc = 38 (9,26,52) ng = 163 n b = 65 nc = 83 ng = 56 n b = 26 nc = 30 ng = 105 n b = 26 nc = 54 (12,34,68) ng = 289 n b = 122 nc = 146 ng = 72 n b = 34 nc = 38 ng = 137 n b = 34 nc = 70…”

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Robust Successor and Precursor Sets of Hybrid Systems Using Hybrid Zonotopes

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et al. 2023

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This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition, and special ordered set approximations to enable linear growth in both reachable set memory complexity and computational complexity with time. Facilitating this combination are new identities for constructing nonconvex sets that contain nonlinear functions and for efficiently converting a collection of polytopes from vertex representation to hybrid zonotope representation. Numerical examples demonstrate reachability analysis of a continuous-time nonlinear system in closed loop with a neural network controller trained using nonlinear model predictive control and a high-dimensional logical system.

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Section: Numerical Examplesmentioning

confidence: 99%

Section: B Reduced Memory Complexity For Bilinear Functionmentioning

confidence: 99%

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Robust Successor and Precursor Sets of Hybrid Systems Using Hybrid Zonotopes

Siefert

Bird

Koeln

et al. 2023

IEEE Control Syst. Lett.

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Control Performance Analysis of Automotive Cyber-physical Systems: A Study on Efficient Formal Verification

Panahi

Kargahi

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2024

ACM Trans. Cyber-Phys. Syst.

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Automotive cyber-physical systems consist of multiple control subsystems working under resource limitations, and the trend is to run the corresponding control tasks on a shared platform. The resource requirements of the tasks are usually variable at runtime due to the uncertainties in the environment, necessitating some kinds of adaptation to deal with the resource limitations. Such adaptations may positively or negatively affect the control performance of several subsystems. Since there might be some thresholds on the control performances as quality constraints, this matter should be considered carefully to avoid any quality attribute constraint violation. This paper proposes a scalable control performance constraint verification method for such a system that works based on a feedback scheduler. The scalability is the result of a control-aware pruning method. In case of a constraint violation, the designer may change the system configuration and perform re-verification. Our evaluations show that the proposed method scales well while preserving the verification soundness.

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Discrete Reachability Analysis With Bounded Error Sets

Cited by 2 publications

References 12 publications

Robust Successor and Precursor Sets of Hybrid Systems Using Hybrid Zonotopes

Robust Successor and Precursor Sets of Hybrid Systems Using Hybrid Zonotopes

Control Performance Analysis of Automotive Cyber-physical Systems: A Study on Efficient Formal Verification

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