Beda Teorema dan Lemma??

Teorema adalah pernyataan matematis yang telah dibuktikan secara logis sesuai dengan kaidah matematika dengan menggunakan asumsi - asumsi matematis yang telah diketahui

Lemma adalah suatu pernyataan matematis di dalam pembuktian suatu teorema. Dengan kata lain, lemma adalah "teorema kecil" yang digunakan untuk membuktikan suatu teorema. Lemma adalah alat bantu untuk membuktikan suatu teorema

Tampilan Desktop Windows 7 to be More Beautiful

Kali ini saya ingin berbagi sedikit tentang bagaimana cara memaksimalkan tampilan Windows 7 agar terlihat lebih cantik.
Berikut ini adalah contoh tampilan Windows 7 Ultimate yang saya modifikasi dengan software untuk mempercantik tampilan

Mau tau gimana caranya?? Gampang kok, pertama cari software yang namanya "xwidget" bisa lewat Google, kemudian download dan install. Software "xwidget" ini gratis, free, alias ga berbayar. Nah setelah terinstal, nanti kamu bisa memilih widget2 apa aja yg kamu sukai.. Lengkap dan banyak, dijamin tampilan Windows kamu ga mati gaya.. hehe

Resolution of This Year #2013

Mungkin agak telat kalo ngomongin soal resolusi di tahun ini.. But, anyway ga ada salahnya terlambat daripada ga sama sekali.
"Bukan tentang tajamnya parang sehingga pohon bisa tumbang, tetapi tentang kesungguhan dan kerja keras untuk membuatnya terbelah. Bermimpilah besar, bermimpilah tinggi. Letakkan cinta dalam mengejar mimpi-mimpimu, dan cinta akan meminta segalanya dari dirimu"
Resolusi itu ibarat kalo kita aktif di salah satu kegiatan organisasi mahasiswa, dimana di awal kepengurusan kita pasti diminta untuk membuat semacam rancangan program kerja beserta dengan TUK nya (Tolok Ukur Kegiatan, red). Alright here we go!
Resolusiku tahun ini adalah :

1. Ikut 5 international conference dan 2 jurnal published
2. Dapat LoA dari universitas di Jerman (ex : RWTH Aachen, TU Darmstadt, TU Munchen)
3. Dapat menguasai LaTex dan mempublish tutorial LaTeX
4. Membuat template tesis dalam LaTeX untuk ITS
5. Berat badan lebih proporsional (sekitar 61an)
6. Mendapatkan nilai terbaik (A) untuk semua mata kuliah di NTUST
7. Tesis S2 kelar di Taiwan
8. Bisa mengunjungi 2 negara yang berbeda (selain Taiwan)
9. Aktif menulis blog minimal 1 bulan sekali
10. Punya 200 teman baru dari seluruh dunia
11. Waktu untuk olahraga minimal 1 minggu sekali
12. Memiliki penghasilan sendiri selain dari beasiswa
13. TOEFL min 580
14. Mampu bicara bahasa mandarin secara oral dan lancar
15. Menjaga puasa Senin-Kamis.. mulai dari 14 Januari 2013

Tak akan selamanya matahari terbit dari timur, tak akan selamanya langit berwarna biru, tak akan selamanya mimpi-mimpimu berdiam dalam angan kejenuhanmu. Ia akan segera datang dengan aura hangat nan menenangkan, hingga kau sadar ia telah memelukmu.. Semoga resolusi tahun ini tercapai.. Aminnn Ya Robbal Alamin

Pseudo Inverse Matrix

Matriks yang tidak persegi membutuhkan suatu metode khusus untuk menginverskan, yang biasa disebut pseudo inverse matriks.

Properti 1
Suppose that A is mn real matrix
If m<n, then the inverse of A^TA does not exist
If mn and if the inverse of A^TA exists
A⁺=(A^TA)^-1A^T satisfies the definition of pseudoinverse
Here, A⁺A=I holds. I is identity matrix.
A: mn, A^T: nm, A⁺: nm, A^TA: nn, I: nn
The rank of A and A⁺ is n

Properti 2
Suppose that A is mn real matrix
If m>n, then the inverse of AA^T does not exist
If mn and if the inverse of AA^T exists
A⁺=A^T(AA^T)^-1 satisfies the definition of pseudoinverse
Here, AA⁺=I holds. I is identity matrix.
A: mn, A^T: nm, A⁺: nm, AA^T: mm, I: mm
The rank of A and A⁺ is m

Pseudoinverse dengan Teknik Singular Decomposition Value (SVD)
Suppose A is mn matrix. If m<n, attach the row of 0 and make the size m=n, a priori. Here, mn.
A=UWV^T is supposed to be the result of SVD
Assume that the left-upper part of W has larger number, and the right-lower part of W has smaller number
If the component of W is less than a threshold, set it to be 0, and define such matrix as W'
When W'=diag(w₁,w₂,...,w_k,0,0,...,0), we define
W''=diag(1/w₁,1/w₂,...,1/w_k,0,0,...,0)
Define A⁺=VW''U^T
A⁺A is nn matrix. Left-upper kk is identity matrix. Otherwise 0.
AA⁺ is mm matrix
If the rank of A is n, A⁺ satisfies the above property 1
Even if the rank of A is less than n, A⁺ satisfies the definition of pseudoinverse
Suppose that we want to solve Ax=b. Calculate x=VW''U^Tb
If the rank of A is n, then x is the value where the error is minimum
If the rank of A is less than n, then x is the solution where the norm ||x|| is minimum

Definition of Moore - Penrose generalized matrix inverse
Given mn real matrix A, nm matrix pseudoinverse A⁺ is defined as follows
AA⁺A=A
A⁺AA⁺=A⁺
(AA⁺)^T=AA⁺
(A⁺A)^T=A⁺A


Reference : Diktat Mata Kuliah Teknik Numerik Sistem Linier, ITS Surabaya

Model Predictive Control (MPC) - Preface

Model Predictive Control (MPC), variously known as rolling-horizon control, receding-horizon control, etc, is a powerful technique employed in diverse engineering applications, and valued for its inherent ability to handle constraints while minimizing some cost (or maximizing some reward). The underlying idea of MPC is to approximate an infinite horizon constrained optimization problem by a finite horizon one, and then an optimal control law is calculated at every time step and applied in a rolling-horizon fashion. In most applications uncertainty in the model is involved, either due to some external disturbances or due to imprecise modeling of the controlled process. Uncertainty is commonly addressed in literature by formulating a robust MPC problem, assuming that the uncertainty is bounded and adopting a worst-case approach. Although there has been some major advances in this field, this approach is often too pessimistic.

But what happens if the uncertainty is not bounded? Or when it is not uniformly distributed? A less conservative approach would clearly be to take these possibilities into account, identifying appropriate distributions of the uncertainties and formulating a stochastic MPC problem instead. In this context, there are several points one should take into consideration for the problem formulation:  

• Probabilistic Constraints:
In the context of unbounded stochastic disturbances, satisfying all constraints with probability one is impossible, as at any time the system might encounter a very big disturbance that forces it to violate its constraints. It is important thus, to substitute the hard constraints with soft, probabilistic ones, ensuring that they are respected with a desired probability

• Expected Value Constraints:
  Another alternative for dealing with constraints is to make sure that they are respected on an average for the optimization problem considered. Depending on the nature of the problem such expected value constraints may be more meaningful than the probabilistic ones.
  
  
• Cost (Reward):  
  The simplest cost (reward) is perhaps an expected cost (reward), formulated as the expected value of the sum of discounted cost-per-stage functions. Depending on the application, alternative and more difficult formulations may be to consider long-run expected average cost (reward), or long-run pathwise cost (reward).

Internal Combustion Engine Vehicle (ICEV) vs Electric Vehicle (EV)

Nowadays, many countries develop EV in order to reduce the polution caused by ICEV. Several advatages of EV over ICEV are :

1. Quick torque response
    The electric motor's torque response is 100 - 500 times faster than ICEVs

2. Motor torque can be measured easily
    In ICEVs, it is difficult to accurately measure their output. On the other hand, the output torque motor can be easily measured by using observer

3. Individual wheels
    Electric motors like in-wheels motors are very small. Therefore, a motor can be attached to each wheel. In conventional automobile, individual control is very complicated

4. Reduce mechanical layout
    In ICEVs, there is required complicated mechanical layout so that need big space of its vehicle. On the other hand, by using individual wheel of EV, it does not need mechanical transmission, so that reduce mechanical layout of its vehicle.

Electric Vehicle developed in Indonesia