We demonstrate our approach by verifying safety, controllability, liveness, and collision avoidance properties in case studies ranging from train control applications in the European Train Control System to air traffic control, where we prove collision avoidance in aircraft roundabout maneuvers.
For our logic, we further complement discrete induction with differential induction as a new continuous generalization of induction, with which hybrid systems can be verified by exploiting their differential constraints algebraically without having to solve them.
Our main result proves that this calculus axiomatises the transition behaviour of hybrid systems completely relative to differential equations. Our "Ordinary Differential Equations" researchers are highly-educated specialists with impeccable research and writing skills who have vast experience in preparing doctoral-level research materials.
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Finally, we develop a fixedpoint algorithm for computing the differential invariants required for differential induction, and we introduce a differential saturation procedure that refines the system dynamics successively with differential invariants until correctness becomes provable. The calculus is compositional, i.
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Systematically, we develop automated theorem proving techniques for our calculus and present proof procedures to tackle the complexities of integrating decision procedures for real arithmetic.
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Automated Theorem Proving for Hybrid Systems Abstract Hybrid systems are models for complex physical systems and are defined as dynamical systems with interacting discrete transitions and continuous evolutions along differential equations. As a verification technique that is suitable for automation, we introduce a free variable proof calculus with a novel combination of real-valued free variables and Skolemisation for lifting quantifier elimination for real arithmetic to dynamic logic.
With the goal of developing a theoretical and practical foundation for deductive verification of hybrid systems, we introduce differential dynamic logic as a new logic with which correctness properties of hybrid systems with parameterized system dynamics can be specified and verified naturally.
As a systematic combination of logic-based techniques, we obtain a sound verification procedure that is particularly suitable for parametric hybrid systems.WEINSTEIN, Mills B., Sturm Transformations and Singular Perturbation Problems for Hyperbolic Differential Equations in Two Independent VariablesDonald R.
Smith (Chair) WU, Lang-Fang, The Ricci Flow of 2-dimensional Orbifolds with Positive Curvature. Our "Ordinary Differential Equations" experts can research and write a NEW, ONE-OF-A-KIND, ORIGINAL dissertation, thesis, or research proposal—JUST FOR YOU—on the precise "Ordinary Differential Equations" topic of your choice.
David STRÜTT: - "Asymptotic Decay for a One-Dimensional Nonlinear Wave Equation". For centuries, differential equations have been the key to unlocking nature's deepest secrets. Over years ago, Isaac Newton invented differential equations to understand the problem of motion, and he developed calculus in order to solve differential equations.
STOCHASTIC DIFFERENTIAL EQUATIONS WITH APPLICATION TO MANIFOLDS AND NONLINEAR FILTERING by Rajesh Rugunanan A thesis submitted in fulﬁllment of the requirements for. Weerawarana, Sanjiva, "Problem Solving Environments for Partial Differential Equation Based Applications (Ph.D.
Thesis)" (). Department of Computer Science Technical Reports. PaperDownload