
Shams Karimkhan
Guaranteed Hybrid Simulations 
Weekly Updates

Week 1
The first week I read up on different mathematical approximations for solving differential equations. Euler’s method, the trapezoidal approximation and Rungekutta were among the subjects I reviewed. I also refreshed my memory on basic MATLAB and C++ programming.

Week 2
The second week I started developing programs for the mathematical approximations. I also started learning how to use ODE45 in MATLAB for solving ordinary differential equations. The ODE45 uses the Rungekutta 4 and 5 to calculate the solution for a given differential equation.

Week 3
This week I started reading about errors in Euler and RungeKutta methods. Also I read some material on hybrid systems and got more familiar with the concept and examples of hybrid systems. I’m currently trying to learn how to implement the event detection properties for the ODE45 solver.

Week 4
This week I familiarized myself more with the event detection function in MATLAB. I came up with my own example of a hybrid system with 2 domains and 1 guard between them and simulated it. I also read a manuscript on error handling that my mentor, Alessandro Abate sent me. I’m currently trying to write code to keep track of the errors in integration.

Week 5
This week I worked with RelTol and Abstol, the error tolerance properties of the options for ODE solvers. I also read more about global error propagation. On Friday I started reading papers on TCP (TransmissionControlProtocol). My goal will be to develop our error methods for a TCP flow control problem.

Week 6
This week I worked on modeling a simple network congestion problem in MATLAB. The network consists of two users and two links. One of the links is used by both and the other is only used by one of the users. I also started working with LaTeX and worked on generating the final paper template.

Week 7
After modeling the simple network, we were interested in finding a Zeno behavior. A Zeno behavior in simple terms is when we have infinite events in a finite amount of time. With the help of my mentor Alessandro Abate I was able to come up with the code that simulated the network and drove it into a Zeno behavior. I’m currently working on simulating a more complex network with 3 links and two users, where the first user uses the first and second links while the second user uses the second and third link. Meaning the two users share the middle link and the two outer links are each used only by one of the user.

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