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Lecture Structure
- II Foundations (01:30:07)
- Semantics (01:23:32)
- A hybrid automaton described by a 6 tuple (01:23:32)
- 7 and continuous sets VI V (01:23:32)
- Definition A hybrid automaton described by a 6 tuple (01:23:32)
- Semantic Problem Time (01:22:21)
- Semantic Problem Zeno (01:22:18)
- 47 D execution sequence 6 m 0 1 (01:22:18)
- i 6 finite but not zero (01:22:18)
- An unbound sequence E instantaneous (01:22:18)
- Semantic Problem Time Stopping Deadlocks (01:22:14)
- Semantic Problem Zeno Behavior (01:18:23)
- Formal Semantics (01:16:48)
- Basic idea (01:17:31)
- Also allow changes in the sets of input state and (01:17:31)
- output variables (01:17:31)
- Motivation Reconfiguration across multiple (01:17:31)
- is otherwise impossible (01:17:31)
- and 1 6 L For s 6 L we P quire that (01:16:48)
- Formal Semantics (01:16:22)
- with L a of locations D a L assigns to (01:16:22)
- non instantaneous transition see block for (01:16:22)
- Parallel Composition (01:16:19)
- For two hybrid All and M the parallel (01:16:19)
- The composition of hybrid is only when the resulting (01:16:19)
- Formal Semantics (01:15:25)
- Hybrid Semantics (01:14:37)
- Formal Semantics (01:13:31)
- Hybrid (01:12:48)
- Composition (01:11:37)
- Definition The composition of AI V y G denoted by again a continuous model M V F G C X u w w V u V V V u (01:11:37)
- 2 is only when (01:11:37)
- Formal Semantics (01:10:30)
- Example Block (01:09:57)
- B Semantics (01:09:10)
- Simple Blocks (01:09:09)
- Formal Semantics (01:08:33)
- i V denotes the set 01 all equations the form p (01:08:36)
- f n and right hand side s of th (01:08:36)
- denotes the set of all conditions over variables of V (01:08:36)
- The set of possible operations and constants is named OP (01:08:36)
- For any g y I j 6 IT holds that l 4 is he (01:08:33)
- Timed Semantics (01:07:46)
- Formal Semantics i A timed automaton as described by a 7 tuple V It O T C (01:07:09)
- Timed Semantics (01:06:53)
- Formal Semantics i A timed automaton is described by a 7 tuple V I O T C (01:04:46)
- Timed (01:04:34)
- Formal Semantics (01:03:31)
- Timed Semantics (01:02:42)
- Formal Semantics (00:58:08)
- Considered Model Types (00:56:34)
- I State Machine (00:56:34)
- I Timed (00:56:34)
- I Continuous Behavior (00:56:34)
- 1 Hybrid (00:56:34)
- I Hybrid Reconfiguration (00:56:34)
- Mathematical Prerequisites (00:56:23)
- denotes the set of the real greater or equal 0 (00:56:23)
- the natural numbers including O (00:56:23)
- the power 01 1 (00:56:23)
- B denotes the set of all total functions from 4 to B and (00:56:23)
- and g 3 A (00:56:23)
- II 3 Model Semantics (00:55:01)
- II Foundations (00:53:06)
- II 1 Terminology (00:53:06)
- II 2 Model Types (00:53:06)
- II 4 Model Properties (00:53:06)
- II S Probabilistic Models (00:53:06)
- II 6 Discussion Summary (00:53:06)
- II 7 Bibliography (00:53:06)
- Extended Example (00:51:41)
- Example (00:49:27)
- Variable Structure (00:51:05)
- V Static Structure (00:51:05)
- I Map structure (00:49:27)
- I Behavior (00:49:27)
- I Map behavior (00:49:27)
- Rule (00:49:27)
- Graph Transformation Systems (00:48:24)
- Petri Nets (00:47:28)
- Variable Structure (00:46:49)
- State space s E S (00:46:56)
- S is an unstructured set of possible states (00:46:56)
- Limitation no change of S is possible (00:46:56)
- Variable Structure (00:46:49)
- Bouncing Ball Examples (00:42:08)
- Hybrid (00:40:26)
- Basic extension to timed (00:40:26)
- Continuous equations per state (00:40:26)
- Clock continuous variable z with (00:40:26)
- Falling Ball Example (00:37:39)
- Continuous Behavior (00:34:50)
- Timed (00:29:26)
- State (00:28:29)
- Considered Model Types (00:27:52)
- Types (00:26:56)
- II Foundations (00:24:48)
- II 1 Terminology (00:24:48)
- II 2 Model Types (00:24:48)
- II 4 Model Properties (00:24:48)
- II S Probabilistic Models (00:24:48)
- II 6 Discussion Summary (00:24:48)
- II 7 Bibliography (00:24:48)
- Refinement vs (00:19:43)
- Stepwise Refinement (00:17:25)
- Models Preservation of Properties (00:16:18)
- Formal Relations (00:16:17)
- n Refinement M is a refinement of M (00:16:17)
- Approximation approx M is an approximation of M (00:16:17)
- Different Kind of Models (00:12:28)
- Models vs Specifications (00:08:17)
- II 1 Terminology (00:04:42)
- A Of L l A simplified representation of something may be physical or abstract and may be restricted properties of me referent In computing models are and are represented in a notation such as functional R a data or state transition diagrams a model (00:04:42)
- A formal description of a system or a component of a system intended as a basis for further of he specification may be in text in a natural 1 in a specification which may be a language and by the use 0 stages of that inc a diagrammatic technique Characteristics of a good specification are that it should comp consistent modifiable traceable and after development (00:04:42)
- II Foundations (00:00:48)
- II 2 Model Types (00:00:48)
- II 3 Model Semantics (00:00:48)
- II 4 Model Properties (00:00:48)
- II 5 Probabilistic Models (00:00:48)
- II 7 Bibliography (00:00:48)
- Outline (00:00:47)
- Introduction (00:00:47)
- IV Requirements (00:00:47)
- VI Implementation (00:00:47)
- VII Verification Validation (00:00:47)
- and Outlook (00:00:47)
- Plattner (00:00:01)
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