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Überwachungsinstanz zur Trennung des Missionssystems und des Flugkontrollsystems in dem unbemannten Luftfahrtsystem SAGITTA
No full textUnderapproximative Methods for the Order Reduction of Zonotopes
No full textZonotopes are a widely used set representation in set-based computations due to their compact representation size and their closure under many relevant set operations. However, certain set operations, such as the Minkowski sum, increase the zonotope order, which in turn increases the computational cost of further computations. To address this issue, various order reduction techniques have been proposed, most of which focus on overapproximating the original zonotope. While overapproximations are crucial for safety verification, some applications – such as reachset-conformant identification and backward reachability analysis – require underapproximations (also referred to as inner-approximations). Besides providing a comprehensive survey of existing underapproximative order reduction methods, we propose four novel reduction methods in this letter. We analyze the computational cost of all methods and evaluate the tightness of the resulting underapproximations through numerical experiments on more than 2000 randomly generated zonotopes. The results demonstrate that our proposed methods achieve a favorable balance between computational efficiency and approximation accuracy, making them well-suited for applications in control, estimation, and system identification
Computing Non-Convex Inner-Approximations of Reachable Sets for Nonlinear Continuous Systems
No full textReachability Analysis for Linear Systems with Uncertain Parameters using Polynomial Zonotopes
No full textReachability of Koopman Linearized Systems Using Random Fourier Feature Observables and Polynomial Zonotope Refinement
No full textKoopman operator linearization approximates nonlinear systems of differential equations with higher-dimensional linear systems. For formal verification using reachability analysis, this is an attractive conversion, as highly scalable methods exist to compute reachable sets for linear systems. However, two main challenges are present with this approach, both of which are addressed in this work. First, the approximation must be sufficiently accurate for the result to be meaningful, which is controlled by the choice ofobservable functionsduring Koopman operator linearization. By using random Fourier features as observable functions, the process becomes more systematic than earlier work, while providing a higher-accuracy approximation. Second, although the higher-dimensional system is linear, simple convex initial sets in the original space can become complex non-convex initial sets in the linear system. We overcome this using a combination of Taylor model arithmetic and polynomial zonotope refinement. Compared with prior work, the result is more efficient, more systematic and more accurate
ARCH-COMP19 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics
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Electromyography-Based Validation of a Musculoskeletal Hand Model
Full text linkRegarding the prevention of injuries and rehabilitation of the human hand, musculoskeletal simulations using an inverse dynamics approach allow for insights of the muscle recruitment and thus acting forces on the hand. Currently, several hand models from various research groups are in use, which are mainly validated by the comparison of numerical and anatomical moment arms. In contrast to this validation and model-building technique by cadaver studies, the aim of this study is to further validate a recently published hand model [1] by analyzing numerically calculated muscle activities in comparison to experimentally measured electromyographical signals of the muscles. Therefore, the electromyographical signals of 10 hand muscles of five test subjects performing seven different hand movements were measured. The kinematics of these tasks were used as input for the hand model, and the numerical muscle activities were computed. To analyze the relationship between simulated and measured activities, the time difference of the muscle on- and off-set points was calculated, which resulted in a mean on- and off-set time difference of 0.58 s between the experimental data and the model. The largest differences were detected for movements that mainly addressed the wrist. One major issue comparing simulated and measured muscle activities of the hand is cross-talk. Nevertheless, the results show that the hand model fits the experiment quite accurately despite some limitations and is a further step toward patient-specific modeling of the upper extremity