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MelodyyyYin committed Jan 10, 2024
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Expand Up @@ -25,7 +25,7 @@ The purpose of this function is linearized state-space model for general LCC sys

**General System Model Formula:**
![General System Model Formula](img/General_System_Model_Formula1.jpg)
where ![F](img/F.png) and ![P](img/P.png) shown in [LCC figure](https://github.com/soc-ucsd/LCC/blob/main/docs/img/LCC.png)
where <img src="img/F.png" alt="F" width="100"> and <img src="img/P.png" alt="P" width="125"> shown in [LCC figure](https://github.com/soc-ucsd/LCC/blob/main/docs/img/LCC.png)



Expand All @@ -39,10 +39,12 @@ The purpose of this function is linearized state-space model for Car-following s

**Output:**
- state-space model: [A, B]
![state_model_formula](img/state_model_formula.png)
<img src="img/state_model_formula.png" alt="state_model_formula" width="90">

**Car-following system model formula:**
![Car-following_system_model_formula](img/Car-following_system_model_formula.png)

<img src="img/Car-following_system_model_formula.png" alt="Car-following_system_model_formula" width="600">

> (For more information of how to derive from general formula to car-following formula, please check the [LCC paper](https://arxiv.org/abs/2012.04313))
#### SystemModel_FD[.m](https://github.com/soc-ucsd/LCC/blob/main/_model/SystemModel_FD.m) / [.py](https://github.com/soc-ucsd/LCC/blob/main/Python%20Implementation/_model/SystemModel_FD.py)
Expand All @@ -54,11 +56,11 @@ The purpose of this function is linearized state-space model for free-driving sy

**Output:**
- state-space model: [A, B]
![state_model_formula](img/state_model_formula.png)
<img src="img/state_model_formula.png" alt="state_model_formula" width="90">

**Free-driving system model formula:**

![Free-driving_system_model_formula](img/Free-driving_system_model_formula.png)
<img src="img/Free-driving_system_model_formula.png" alt="Free-driving_system_model_formula" width="500">

>(For more information of how to derive from general formula to free-driving formula, please check the [LCC paper](https://arxiv.org/abs/2012.04313))
Expand Down Expand Up @@ -238,11 +240,15 @@ The purpose of this file is to find the head-to-tail string stable regions when
When only monitoring one HDV the transfer function is slightly different for each different cases.

Case 1: id < 0 Monitoring the preceding vehicle
![ID_less_zero](img/ID_less_zero.png)

<img src="img/ID_less_zero.png" alt="ID_less_zero" width="300" >



Case 2: id > 0 Monitoring the following vehicle
![ID_greater_zero](img/ID_greater_zero.png)

<img src="img/ID_greater_zero.png" alt="ID_greater_zero" width="300" >



Besides the Gamma function formula, the rest formula stays the same.
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