diff --git a/docs/Implementations.md b/docs/Implementations.md index 078b7d5..4c78a36 100644 --- a/docs/Implementations.md +++ b/docs/Implementations.md @@ -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 F and P shown in [LCC figure](https://github.com/soc-ucsd/LCC/blob/main/docs/img/LCC.png) @@ -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) +state_model_formula **Car-following system model formula:** -![Car-following_system_model_formula](img/Car-following_system_model_formula.png) + +Car-following_system_model_formula + > (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) @@ -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) +state_model_formula **Free-driving system model formula:** -![Free-driving_system_model_formula](img/Free-driving_system_model_formula.png) +Free-driving_system_model_formula >(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)) @@ -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) + +ID_less_zero + Case 2: id > 0 Monitoring the following vehicle -![ID_greater_zero](img/ID_greater_zero.png) + +ID_greater_zero + Besides the Gamma function formula, the rest formula stays the same.