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T. BAKHTIAR
Bogor Agricultural University
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Earth & Planetary Sciences Mathematics

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MODEL MATEMATIKA SIS-SI DALAM PENYEBARAN PENYAKIT MALARIA DENGAN VAKSINASI TAKSEMPURNA N. FAJRI; P. SIANTURI; T. BAKHTIAR
MILANG Journal of Mathematics and Its Applications Vol. 15 No. 2 (2016): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (798.222 KB) | DOI: 10.29244/jmap.15.2.51-62

Abstract

Dalam penelitian ini, dibahas sebuah model penyebaran penyakit malaria tipe SIS-SI. Model ini membahas tentang penyebaran penyakit malaria dengan memperhatikan vaksin taksempurna (e). Vaksin dikatakan berhasil jika 1 e=0, dan dikatakan tidak berhasil jika e=1. Model SIS-SI mempunyai dua titik tetap yaitu, titik tetap tanpa penyakit dan titik tetap endemik. Dengan menggunakan bilangan reproduksi dasar (R0), maka diperoleh bahwa  titik tetap tanpa penyakit bersifat stabil global, jika R0<1 dan titik tetap endemik bersifat stabil global, jika R0>1 Selain itu, digunakan juga analisis bifurkasi yang bertujuan untuk mengetahui eksistensi dan jumlah titik tetap endemik pada model untuk setiap parameter yang diberikan. Jika pada model terjadi bifurkasi maju, maka titik tetap endemik bersifat stabil, dan jika terjadi bifurkasi mundur maka titik tetap endemik bersifat takstabil. Selanjutnya, jika efektivitas vaksin ditingkatkan, maka manusia terinfeksi akan menurun.
MODEL GOAL PROGRAMMING DAN PENGOPTIMUMAN TAKLINEAR PADA PENJADWALAN PERAWAT L. HAKIM; T. BAKHTIAR; J. JAHARUDDIN
MILANG Journal of Mathematics and Its Applications Vol. 15 No. 1 (2016): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (582.459 KB) | DOI: 10.29244/jmap.15.1.23-32

Abstract

Penjadwalan perawat merupakan pekerjaan penting dalam operasional sebuah rumah sakit. Jika manajemen rumah sakit melakukan penjadwalan dengan baik maka akan berdampak pada kinerja perawat yang semakin baik. Salah satu indikator penjadwalan yang baik adalah tercapainya distribusi beban kerja yang merata bagi seluruh perawat. Namun demikian, adanya keterbatasan sumber daya untuk memenuhi kebutuhan rumah sakit menjadi kendala tersendiri dalam upaya mencapai keadilan. Dalam hal ini, goal programming dapat menjadi salah satu solusi untuk mengatasi kendala tersebut. Dalam penelitian ini, nonpreemptive goal programming digunakan untuk memecahkan masalah penjadwalan perawat. Tujuan model ini adalah untuk meminimumkan beberapa simpangan preferensi perawat terhadap banyaknya shift kerja dan libur. Kami juga memberikan alternatif penyelesaian penjadwalan perawat menggunakan model optimasi taklinear dengan meminimumkan ragam beban kerja pada setiap shift kerja dan libur. Model ini diaplikasikan pada penjadwalan perawat ruang rawat inap Rumah Sakit Umum Daerah Kota Bogor.
APLIKASI KONTROL OPTIMUM PADA MODEL PEMANENAN IKAN DI ZONA NONCADANGAN DENGAN MEMPERTIMBANGKAN ZONA CADANGAN R. NURBAYAN; T. BAKHTIAR; A. KUSNANTO
MILANG Journal of Mathematics and Its Applications Vol. 13 No. 2 (2014): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (494.432 KB) | DOI: 10.29244/jmap.13.2.35-48

Abstract

Tulisan ini akan membahas analisa model matematika tentang sistem dinamika sumber daya perikanan pada suatu wilayah perairan. Wilayah perairan yang dipertimbangkan terdiri dari dua zona: zona noncadangan (ikannya boleh ditangkap) dan zona cadangan (ikannya tidak boleh ditangkap), di mana kepadatan populasi ikan di masing-masing zona dinyatakan dalam bentuk persamaan diferensial taklinear. Berdasarkan model tersebut, ingin diketahui bagaimana kebijakan penangkapan ikan yang optimal. Oleh karena itu, sebuah kebijakan penangkapan ikan yang optimal telah dianalisis menggunakan prinsip maksimum Pontryagin. Suatu contoh ilustratif telah diberikan dengan mempertimbangkan studi kasus penangkapan Sardinella lemuru di Selat Bali. Simulasi numerik tersebut memberikan informasi bahwa secara umum model dapat mengambarkan dinamika populasi ikan yang mempertimbangkan dua zona di atas.
IDENTIFIKASI KONDISI KETERKONTROLAN BEBERAPA SISTEM PENDULUM S. SAKIRMAN; T. BAKHTIAR; A. KUSNANTO
MILANG Journal of Mathematics and Its Applications Vol. 13 No. 2 (2014): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (285.153 KB) | DOI: 10.29244/jmap.13.2.63-71

Abstract

Dalam teori pengendalian (control theory), keterkontrolan (controllability) merupakan isu penting, di mana dalam masalah pengendalian yang dihadapi, input kendali harus dicari sedemikian sehingga keadaan sistem (system state) atau output sistem bergerak 
MOBIUS AND DELTA TRANSFORMS IN THE UNIFICATION OF CONTINUOUS-DISCRETE SPACES T. BAKHTIAR; S. SAMSURIZAL; N. ALIATININGTYAS
MILANG Journal of Mathematics and Its Applications Vol. 12 No. 2 (2013): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (272.914 KB) | DOI: 10.29244/jmap.12.2.15-24

Abstract

It is well-known that in control theory the stability region of continuous- time system is laid in the left half plane of complex space, while that of discrete-time system is dwelled inside a unit circle. The former fact might be shown by exploiting the Laplace transform and the later by utilizing the corresponding zeta transform. In this paper we revealed the connectivity of both regions by employing M¨obius transform. We also used the same transform to derive continuous/discrete-time counterpart of several existing results, including Bode integral and Poisson-Jensen formula. We then demonstrated their unification property by using delta transform. Some numerical examples were provided to verify our results.
OPTIMAL TRACKING AND REGULATION ACCURACY OF FEEDBACK CONTROL SYSTEMS T. BAKHTIAR
MILANG Journal of Mathematics and Its Applications Vol. 4 No. 1 (2005): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (180.795 KB) | DOI: 10.29244/jmap.4.1.41-50

Abstract

This paper deals with intrinsic performance limits achievable by feedback control. We give analytical expressions of the optimal tracking and regulation problems for linear shift- invariant single-input and multiple-output (SIMO) discrete-time systems. For the former, we modify the existing results by means of the delta operator and show that the continuous-time counter- part results can be properly recovered from this point. For the latter, we derive a discrete-time result first and show the conver- gence property.
REGULATION LIMITS UNDER CONTROL EFFORT OF SIMO LTI SYSTEMS AND ITS EXTENSION TO DELAY-TIME SYSTEMS T. BAKHTIAR
MILANG Journal of Mathematics and Its Applications Vol. 5 No. 1 (2006): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (148.627 KB) | DOI: 10.29244/jmap.5.1.33-42

Abstract

In this paper, we investigate regulation properties pertaining to SIMO LTI systems, in which objective function of regulated response is minimized jointly with the control effort. We provide the closed-form solution of the H2 optimal regulation performance for unstable/non-minimum phase continuous-time and discrete-time systems. A direct implication of our main result in- cludes the energy regulation performance of minimum phase time delay systems.
PERFORMANCE LIMITATION OF SYSTEMS UNDER SIGNAL-TO-NOISE CONSTRAINED CHANNEL T. BAKHTIAR
MILANG Journal of Mathematics and Its Applications Vol. 5 No. 2 (2006): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (173.008 KB) | DOI: 10.29244/jmap.5.2.1-12

Abstract

This paper re-discusses [1] and [11], where the prob- lems of feedback stabilization over a signal-to-noise ratio (SNR) constrained channel are studied. The first paper considers both continuous and discrete-time minimum phase systems, while the second extends the results to non-minimum phase ones and pro- poses a linear time-varying feedback strategies to eliminate the effect of non-minimum phase zeros in SNR limited stabilization. In general, the limitations on the ability to stabilize a plant over an SNR constrained channel are imposed mainly by unstable poles and non-minimum phase zeros of the plant.
OPTIMAL ENERGY REGULATION PERFORMANCE OF DELAY-TIME SYSTEMS T. BAKHTIAR
MILANG Journal of Mathematics and Its Applications Vol. 6 No. 1 (2007): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (298.071 KB) | DOI: 10.29244/jmap.6.1.1-10

Abstract

This paper studies the regulation performance limi- tation of delay-time systems. The performance is measured by the energy of the control input with respect to an impulse dis- turbance function. We first provide the analytical closed-form expression of the optimal performance for minimum phase case by reviewing the existing result. We then extend the problem to non-minimum phase case by exploiting the results of linear time- invariant discrete-time and delta domain cases.
MASALAH GALAT PENJEJAKAN MINIMUM PADA SISTEM PENDULUM TERBALIK T. BAKHTIAR
MILANG Journal of Mathematics and Its Applications Vol. 9 No. 1 (2010): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (297.838 KB) | DOI: 10.29244/jmap.9.1.15-22

Abstract

This paper studies the optimal tracking error control problem on an inverted pendulum model. We characterize the optimal tracking error in term of pendulum’s parameters. Particularly, we derive the closed form expression for the pendulum length which gives minimum error. It is shown that the minimum error can always be accomplished as long as the ratio between the mass of the pendulum and that of the cart satisfies a certain constancy, regardless the type of material we use for the pendulum.
Co-Authors A. KUSNANTO A. S. PERMADI D. NATALIA F. HANUM Farida Hanum J. JAHARUDDIN L. HAKIM N. ALIATININGTYAS N. FAJRI P. SIANTURI R. NURBAYAN S. SAKIRMAN S. SAMSURIZAL