Computing differential invariants of hybrid systems as fixedpoints
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ICFEM '09 Proceedings of the 11th International Conference on Formal Engineering Methods: Formal Methods and Software Engineering
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CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
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Stochastic differential dynamic logic for stochastic hybrid programs
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Differential dynamic logics: automated theorem proving for hybrid systems
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LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
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Proceedings of the 16th international conference on Hybrid systems: computation and control
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ACM Computing Surveys (CSUR)
Synthesizing switching controllers for hybrid systems by generating invariants
Theories of Programming and Formal Methods
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We generalize dynamic logic to a logic for differential-algebraic (DA) programs, i.e. discrete programs augmented with first-order differential-algebraic formulas as continuous evolution constraints in addition to first-order discrete jump formulas. These programs characterize interacting discrete and continuous dynamics of hybrid systems elegantly and uniformly. For our logic, we introduce a calculus over real arithmetic with discrete induction and a new differential induction with which DA programs can be verified by exploiting their differential constraints algebraically without having to solve them. We develop the theory of differential induction and differential refinement and analyse their deductive power. As a case study, we present parametric tangential roundabout maneuvers in air traffic control and prove collision avoidance in our calculus.