Week 2:
Started reading papers on Hybrid Systems focusing on Stochastic Hybrid Systems.
So started having the probabilistic flavor of it. Worked on the MATLAB code
for Wiener Process and Poisson Process as they will be used in the
future works. Started writing the report of my project using LATEX.
Paper read:
- Reachability Analysis for Controlled Discrete Time Stochastic Hybrid System
by Saurabh Amin, Alessandro Abate, Maria Prandini, John Lygeros and
Shankar Sastry.
- Electric Load Model Synthesis by Diffusion Approximation of a High-Order
Hybrid-State Stochastic System by Roland Malhame and Chee-Yee Chong.
Attended the control paper reading group of Mechanical Engineering.
Attended the SHS(Stochastic Hybrid System) work group weekly meeting where
the following paper was presented
X. Koutsoukos, D. Riley. Computational methods
for reachability analysis of stochastic hybrid systems
Week 3:
Wrote programs for Multi Room thermostat. First one is for randomly generated
temperaures. Second one is for Controlled system in which I tried to control
the temperature of both room when they started going to the unsafe set.
Paper read:
- On the Fokker-Plank Equation for Stochastic Hybrid Systems: Application
to a Wind Turbine Model by Julien Bect, Yannick Phulpin, Hana Baili,
Gilles Fleury.
In weekly SHS work group I. Hwang, H. Balakrishnan, and C. J.
Tomlin, State Estimation for Hybrid Systems: Applications to Aircraft
Tracking was presented.
Met with Beatriz Lopez-Flores for graduate school advising.
Attended Lessons Unlearned in Wireless presented by Rajiv Laroia.
Week 4:
Presented a power point presentation based on first
three weeks works in the weekly CHESS meeting. Started working on the reachability
problem. Wrote a program for the safe set and the indicator function.
Paper read:
- Benchmarks for Hybrid Systems Verification by Ansgar Fehnker and Franjo
Ivancic .
SHS workgroup paper was Rakovic, Kerrigan, Mayne, Lygeros. Reachability
analysis of discrete-time systems with disturbances.
Attended presentation on TRUST group by Shankar Sastry.
Week 5:
Started working on the probability calculation problem
for the two room one heater system. I am using dynamic programming to calculate
that. This will give the probability of both room to be in the safe set together.
SHS workgroup paper was A.A. Julius.Approximate abstraction of stochastic
hybrid automata
Attended presentation on CHESS group by Professor Shankar Sastry.
Attended talk about Secure Sensor Networks given by Professor Shankar Sastry
with Tanya Roosta and
Marci Meingast in the WISE computer security workshop.
Met with Shelia Humphrys and Patrick Hernan for graduate school advising
Week 6:
Kept on working on the probability calculation problem
for the two room one heater system and started working on the optimal control
calculation. This will give the optimal probability and optimal control actions
for both room to be in the safe set together.
SHS workgroup paper was Haas, Frei, Osorio, Pasik-Duncan, Radel.
EEG ocular artifact removal through ARMAX model system identification using
extended least squares
Visited IBM Research Laboritories in San Jose
Attended presentation on fellowships by Shelia Humphrys.
Week 7:
Working on the optimal safe set probability calculation.
The program takes hours to run. So I increased the spatial resolution from
.1 to .25. Kept on changing the values of some parameters to have a good result.
Started working on the poster and report.
Week 8:
Finished writing the code for optimal safety policy
and got the graphs for value function and all the optimal actions. Applied
those optimal actions in the heater. It worked. the temperatures of both of
the rooms were in between 20-25 degree F. Finished the final poster and final
report. Attended the final poster session and closing ceremony.
Attended the SHS workgroup meeting. The paper read
was the following
A Unified Framework for Hybrid Control: Model and Optimal Control Theory
Michael S. Branicky, Member, IEEE, Vivek S. Borkar, Senior Member, IEEE,
and Sanjoy K. Mitter.
