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Lecture Structure
- II Foundations (00:00:01)
- II 3 Model Semantics (00:00:01)
- II 5 Probabilistic Models (00:00:01)
- II 6 Discussion Summary (00:00:01)
- Bibliography (00:00:01)
- Terminology (00:00:01)
- To access this computer you need to enter password (00:07:44)
- II Foundations (00:07:49)
- II 1 Terminology (00:07:49)
- II 3 Model Semantics (00:07:49)
- II 5 Probabilistic Models (00:07:49)
- II 6 Discussion Summary (00:07:49)
- Bibliography (00:07:49)
- f Preview File Edit View Bookmarks Window Help E SHE Chapter 2 S1 of 941 (00:07:51)
- Preview File Edit View Go Tools Bookmarks Window Help I (00:07:52)
- Preview File Edit Go Tools Bookmarks Window Help IE Display (00:08:01)
- II Foundations (00:08:04)
- II 4 Model Properties (00:08:17)
- State and Sequence (00:09:06)
- IR such that for 6 (00:09:06)
- u with l and u (00:09:06)
- l t holds that (00:09:06)
- A property for a hybrid D I QT S (00:09:06)
- with L with W x Mm van (00:09:06)
- Temporal Logics (00:12:03)
- Linear Temporal Logic (00:15:03)
- Additional temporal operators G E U (00:15:03)
- For p q propositions with a free time and trajectory variables we define (00:15:03)
- Example val 3 (00:15:03)
- For a temporal logic with a time and trajectory variables we (00:15:03)
- TYPES of SEQ (00:15:47)
- Linear Temporal Logic (00:15:49)
- Additional temporal operators G E U (00:15:49)
- For p q propositions with a free time and trajectory variables we define (00:15:49)
- Example 3 lg (00:15:49)
- For a temporal logic with a free time and trajectory variables we (00:15:49)
- write p p (00:15:49)
- Types of Sequence (00:16:22)
- Example Light Controller (00:18:41)
- Specifications (00:19:30)
- Example Traffic Light Controller (00:19:34)
- Specifications (00:19:37)
- Safety Properties (00:24:17)
- A sequence property p is a safety it is (00:24:17)
- for any infinite sequence of with p a prefix of holds (00:24:17)
- Safety Property Examples (00:26:02)
- Bouncing Ball Examples (00:28:10)
- Liveness Properties (00:28:51)
- A sequence property p is a liveness property for every finite sys (00:28:51)
- p is a prefix of p and (00:28:51)
- Something good will eventually happen (00:28:51)
- Liveness Property Examples (00:30:01)
- Completeness of Safety (00:31:35)
- Theorem For any non empty sequence property p exists a safety (00:31:35)
- property p and prop p v (00:31:35)
- Remark But ensemble properties which are a property of the (00:31:35)
- whole family of so are no e prop (00:31:35)
- Stability (00:33:18)
- Stability for Hybrid Systems (00:37:24)
- A trajectory p for Al is stable any other trajectory (00:37:24)
- If further l p 0 fort ac the trajectory is called (00:37:24)
- Distance (00:43:04)
- r Controllability (00:44:37)
- State is usually taken to mean that it is inputs to steer the states from any initial to any some time window (00:44:37)
- Output means by admissible inputs (00:44:37)
- Player Game (00:48:34)
- N Player Game (00:50:32)
- In a large system you do not only have one active controller and (00:50:32)
- Assuming n agents M the (00:50:32)
- becomes whether M M the (00:50:32)
- goals of all agents a g for each (00:50:32)
- If the agents adjust their goals at run time we have to consider (00:50:32)
- state dependent control goal for each agent (00:50:32)
- u Observability (00:52:12)
- In control theory observability is a measure for how cf a system can be inferred by knowledge of its ext (00:52:12)
- that their value to the add that it (00:52:12)
- Robustness (00:54:38)
- II 5 Probabilistic Models (00:56:42)
- N Player Game (01:00:52)
- e large system you do not only have one active controller and (01:00:52)
- Assuming n control agents behavior Al a plant AI (01:00:52)
- s whether A reaches the (01:00:52)
- goals of all agents a g u fur each (01:00:52)
- If the agents adjust their goals at run we have to consider (01:00:52)
- state control goal of for each agent (01:00:52)
- Stability for Hybrid Systems (01:00:53)
- Completeness of Liv Safety (01:00:54)
- Theorem For any non empty sequence property p exists a safety (01:00:54)
- Remark But which are a property of the (01:00:54)
- whole family of are no e (01:00:54)
- Stability (01:00:55)
- Stability for Hybrid Systems (01:00:56)
- A trajectory p for Al is stab e tor any other trajectory (01:00:56)
- p of AI holds (01:00:56)
- If further p 0 for the trajectory is called (01:00:56)
- table (01:00:56)
- To access this computer you need to enter your password (01:11:47)
- Stability for Hybrid Systems (01:11:55)
- A trajectory p for AI is stable tor any other trajectory (01:11:55)
- p of Al holds (01:11:55)
- If further p O for c the trajectory is called (01:11:55)
- is stable if is (01:11:55)
- r Controllability (01:11:56)
- State is usually taken to mean that it is inputs to steer the states from any initial to any some time window (01:11:56)
- Output means by admissible inputs (01:11:56)
- Observability (01:11:57)
- In theory i a for well (01:11:57)
- outputs and a system are (01:11:57)
- Formally a system is said to be observable if fur any possible (01:11:57)
- If a system in nut observable this means the current values cf some (01:11:57)
- II 5 Probabilistic Models (01:11:58)
- A man SAP 1 Robust M M es From The key and (01:15:04)
- File Edit Go Tools Window Help E SUB Gum mun41ann f Sn (01:15:20)
- Alarm Pm man Cordon A (01:15:22)
Keyword
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