## Weekly review: week from 2012-04-22 to 05-05

### Last week

• Work
• [-] Continue to work on robust schedulability, try to finish, including coding.
• [X] Set up files for thesis (LaTeX, orgmode,…)
• [-] Work on/Write safe set computation & robust.
• [ ] Habit of reviewing, updating, backing up my plan, results, data for thesis.
• [ ] Habit of writing a bit each day.
• [X] MLE+ plan (with R’s students).
• [X] RTSS plan (with R and M).
• [ ] Read RL & continue to develop ML-based scheduling.
• [X] Update BibTeX of papers & docs.
• Later: attracting set for schedulability of more general dynamics, ML – bandit, tech report for CDC paper, mechanism design.
• Personal
• [-] Keep healthy lifestyle and exercise.
• [ ] Brainstorm and Plan.

### Plan for next week

• Work
• [ ] RTSS
• [ ] Finish robust schedulability, coding and example.
• [ ] Finish safe set computation & robust on paper & mindmap.
• [ ] Import all papers on desktop to BibTex & mindmap.
• [ ] Gather & organize all my hand writings.
• [ ] Habit of reviewing, updating, backing up my plan, results, references, data for thesis.
• [ ] Habit of writing a bit each day.
• [ ] Check on MLE+ progress.
• Later: attracting set for schedulability of more general dynamics, ML – bandit, tech report for CDC paper, mechanism design, ML-based scheduling.
• Personal
• [ ] Keep healthy lifestyle and exercise.
• [ ] Insurance & credit card for wife.
• [ ] Financial management.
• [ ] Clean up house.
• [ ] Brainstorm and Plan.

## Weekly review: week from 2012-04-15 to 04-21

### Last week

I decided not going to Germany.

• Work
• [X] Work on robust optimization & robust schedulability.
• [-] Work on/Write safe set computation & robust.
• [ ] Set up files for thesis (LaTeX, orgmode,…)
• [-] Read RL & continue to develop ML-based scheduling.
• [ ] Habit of reviewing, updating, backing up my plan, results, data for thesis.
• [ ] Habit of writing a bit each day.
• [ ] Update BibTeX of papers & docs.
• [0/10] Update ideas on mindmaps/outline:
• [ ] ML scheduling
• [ ] hybrid computation: maximal safe set, approximation
• [ ] robust schedulability: how to solve optim
• [ ] multi-agent view (cf. the other thesis)
• [ ] hierarchical scheduling
• [ ] performance of periodic sched (J’s paper, my TECS)
• [ ] multiple modes
• [ ] system ID???
• [ ] adaptive???
• [ ] applications, implementation/simulation: need to update weekly
• Later: write up proofs and results I have so far, Update literature (BibTeX), attracting set for schedulability of more general dynamics, ML – bandit, tech report for CDC paper, mechanism design, brainstorm MLE+.
• Personal
• [ ] Try to keep healthy lifestyle, exercise.
• [X] Make appointment for US visa in Canada.
• [X] Check out German visa requirements & procedure.
• [X] VEF DS-2019.
• [X] Preparation for H to US.

### Plan for next week

• Work
• [ ] Continue to work on robust schedulability, try to finish, including coding.
• [ ] Set up files for thesis (LaTeX, orgmode,…)
• [ ] Work on/Write safe set computation & robust.
• [ ] Habit of reviewing, updating, backing up my plan, results, data for thesis.
• [ ] Habit of writing a bit each day.
• [ ] MLE+ plan (with R’s students).
• [ ] RTSS plan (with R and M).
• [ ] Read RL & continue to develop ML-based scheduling.
• [ ] Update BibTeX of papers & docs.
• [0/11] Update ideas on mindmaps/outline:
• [ ] ML scheduling
• [ ] hybrid computation: maximal safe set, approximation
• [ ] robust schedulability
• [ ] robust periodic scheduling
• [ ] multi-agent view (cf. the other thesis)
• [ ] hierarchical scheduling
• [ ] performance of periodic sched (J’s paper, my TECS)
• [ ] multiple modes
• [ ] system ID???
• [ ] adaptive???
• [ ] applications, implementation/simulation: need to update weekly
• Later: attracting set for schedulability of more general dynamics, ML – bandit, tech report for CDC paper, mechanism design.
• Personal
• [ ] Keep healthy lifestyle and exercise.
• [ ] Brainstorm and Plan.

Posted in Weekly | 1 Comment

## Geometric computation and plotting with Yalmip

Yalmip is modeling language in Matlab for mathematical optimization (or programming in the language of Operation Research). There are many excellent optimization solvers out there, for Matlah or not, commercial or free or open source. However, each of them uses a different programming and modeling interface. Some are quite difficult to use. Most require you to transform your optimization problems into a standard form to be able to solved by the solver. Thus, it is unintuitive. Furthermore, in many practical applications, you must apply many technical tricks to transform or approximate your problems just to be able to solve them (efficiently). Manually doing this is both time-consuming and error-prone, and you may not know all the tricks, especially if you are not an expert.

Yalmip solves these difficulties by providing a consistent, well-designed, intuitive, and easy-to-use modeling language. The language is symbolic and uses a syntax very close to the mathematical languge used to formulate optimization problems. It also transforms your problems automatically, applies many useful tricks accurately, then calls external solvers to solve them for you. More information can be found on its website.

I have just discovered that Yalmip can also plot (constraint) sets. Basically, it samples the variable space with a grid and solves a sequence of optimization problems to calculate the feasible points. Then a (bounded convex) representation of the constraint set can be formed and plotted. This has been available in Yalmip for quite a while, but I only discovered it when I needed to plot a complex set and MPT could not handle the task. This feature is very helpful. To plot standard geometric objects such as a polytope or an ellipsoid, Yalmip is much slower than a specialized toolbox like MPT, but it is more flexible and more powerful. Therefore, you should stick to specialized toolboxes for standard objects, and use Yalmip for the rest.

Another more useful feature of Yalmip is the ability to perform geometric computation, such as Minkowski sum/difference and contracting/expanding sets. Examples can be found here. Although these computations can be performed by specialized toolboxes (MPT, ellipsoid), they are limited in capability. For example, using the polytope class in MPT, you can only compute the Minkowski difference between polytopic sets. Minkowski difference between a polytope and an ellipsoid (essentially shifting and contracting the polytope in a metric defined by the ellipsoid) can however be carried out by Yalmip, using its robust optimization framework and the robustify command. Another example is the range computation of a polytopic set, i.e. $\{ y | y = A x + b, x \in P\}$ where $P$ is a polytope, $A$ and $b$ are given matrix and vector. MPT can only compute this set if $A$ is non-singular (and of course, square). With Yalmip, you are able to compute this set when $A$ is singular and even non-square. Depending on the set and the dimensions you are working on, the computation can be very heavy and time-consuming, but at least it is possible.

All these computations will be implemented in a collection of Matlab functions for my research, and will be published on my github account.

## Weekly review: week from 2012-04-08 to 04-14

### Last week

• Work
• [X] Develop ML-based scheduling: finish experiment(s).
• [ ] Set up files for thesis (LaTeX, orgmode,…)
• [X] Code and plan for RTSS, delegate tasks to M.
• [-] Habit of reviewing, updating, backing up my plan, results, data for thesis.
• [ ] Habit of writing a bit each day.
• [ ] Start writing up hybrid computation.
• [2/10] Update ideas on mindmaps/outline:
• [X] ML scheduling
• [ ] hybrid computation: maximal safe set, approximation
• [ ] robust schedulability: how to solve optim
• [ ] multi-agent view (cf. the other thesis)
• [ ] hierarchical scheduling
• [X] performance of periodic sched (J’s paper, my TECS)
• [ ] multiple modes
• [ ] system ID???
• [ ] adaptive???
• [ ] applications, implementation/simulation: need to update weekly
• [ ] (Optional) Work on robust optimization & robust schedulability.
• Later: write up proofs and results I have so far, Update literature (BibTeX), attracting set for schedulability of more general dynamics, ML – bandit, tech report for CDC paper, mechanism design, brainstorm MLE+.
• Personal
• [-] Try to keep healthy lifestyle, exercise.
• [-] Make appointment for US visa in Canada, pay if necessary.
• [ ] Check out German visa requirements & procedure.
• [X] List of docs for wife’s visa, e.g. letter, bank statement, etc.
• [ ] Develop vision & plan (Hyatt).

### Plan for next week

• Work
• [ ] Work on robust optimization & robust schedulability.
• [ ] Work on/Write safe set computation & robust.
• [ ] Set up files for thesis (LaTeX, orgmode,…)
• [ ] Read RL & continue to develop ML-based scheduling.
• [ ] Habit of reviewing, updating, backing up my plan, results, data for thesis.
• [ ] Habit of writing a bit each day.
• [ ] Update BibTeX of papers & docs.
• [0/10] Update ideas on mindmaps/outline:
• [ ] ML scheduling
• [ ] hybrid computation: maximal safe set, approximation
• [ ] robust schedulability: how to solve optim
• [ ] multi-agent view (cf. the other thesis)
• [ ] hierarchical scheduling
• [ ] performance of periodic sched (J’s paper, my TECS)
• [ ] multiple modes
• [ ] system ID???
• [ ] adaptive???
• [ ] applications, implementation/simulation: need to update weekly
• Later: write up proofs and results I have so far, Update literature (BibTeX), attracting set for schedulability of more general dynamics, ML – bandit, tech report for CDC paper, mechanism design, brainstorm MLE+.
• Personal
• [ ] Try to keep healthy lifestyle, exercise.
• [ ] Make appointment for US visa in Canada.
• [ ] Check out German visa requirements & procedure.
• [ ] VEF DS-2019.
• [ ] Preparation for H to US.