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Redemtus Heru Tjahjana
Department Of Mathematics, Diponegoro University Semarang, Indonesia

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Modeling CD4+ T cells and CTL response in HIV-1 infection with antiretroviral therapy Sutimin, Sutimin; Sunarsih, Sunarsih; Tjahjana, R. Heru
Communication in Biomathematical Sciences Vol 1, No 2 (2018)
Publisher : Indonesian Bio-Mathematical Society

#### Abstract

The majority of an immune system infected by HIV (Human Immunodeficiency Virus) is CD4+ T cells. The HIV-1 transmission through cell to cell of CD4+ T cells supports the productive infection. On the other hand, infected CD4+ T cells stimulate cytotoxic T-lymphocytes cells to control HIV-1 infection. We develop and analyze a mathematical model incorporating the infection process through cell to cell contact of CD4+ T cells, CTL compartment and the combination of RTI and PI treatments. By means of the alternative reproduction ratio, it is analyzed the stability criteria and the existence of endemic equilibrium. Numerical simulations are presented to study the implication of the combination of RTI and PI therapy. The results indicate that RTI drug shows more significant effect in reducing HIV-1 infection compared to PI drug.
APLIKASI SISTEM MULTI AGEN PADA PENGENDALIAN TIGA KAPAL SEKALIGUS Tjahjana, R. Heru
MATEMATIKA Vol 14, No 2 (2011): JURNAL MATEMATIKA
Publisher : MATEMATIKA

#### Abstract

This paper presented a problem controlling the three ships as the application of multi-agent system. The multi-agent system model which used in this exposition is linear multi-agent system Â and the ship modelÂ  which used in this paper is linear ship model from Hocking. The Control design completion for each ship used the optimal control design strategy by utilizing Pontryagin Maximum Principle. This principle leads to the classical problem of optimum control Â that treatment using the steepest descent method. Â
STRATEGI DASAR PENGENDALIAN MULTI ROBOT APUNG DAN MANFAATNYA Tjahjana, Redemtus Heru
MATEMATIKA Vol 17, No 1 (2014): Jurnal Matematika
Publisher : MATEMATIKA

#### Abstract

This paper describes floating multi-robot control strategies. Exposure starts from inspiration and the use of floating multi-robot in daily life, especially in the industrial world. Furthermore, with the model of multi-robot and functional model that describe the state of the cost to be met the floating robots, floating multi-robot control designed with optimal control strategy. The design of optimal control is done through the Pontryagin Maximum Principle, brings the model to a system of equations consisting of state equations and costate equations. In the system of states equations, each having initial and final condition, in the costate equations system has no requirements at all. The next problem is converted to the initial value problem and search for the approximate initial condition equation of state auxiliary systems which has no requirements using a modified method of steepest descent. Thus, the control of multi-robot successfully performed and the simulation results presented on the results and discussion.
KEKONVERGENAN BARISAN FUNGSI TERINTEGRAL HENSTOCK-DUNFORD PADA [a,b] ., Solikhin; Zaki, Solichin; Tjahjana, Redemtus Heru
MATEMATIKA Vol 19, No 1 (2016): Jurnal Matematika
Publisher : MATEMATIKA

#### Abstract

Artikel ini membahas tentang kekonvergenan barisan fungsi yang terintegral Henstock-Dunford pada [a,b]. Dalam hal ini dikaji syarat cukup agar limit barisan nilai integral suatu fungsi terintegral Henstock-Dunford sama dengan limit barisan fungsinya. Diperoleh bahwaÂ  untuk menjamin fungsi Â terintegral Henstock-Dunford dan limit barisannya sama dengan nilai fungsinya maka barisan fungsi yang terintegral Henstock-Dunford harus konvergen seragam atau barisan fungsi yang terintegral Henstock-Dunford harus konvergen lemah dan monoton lemah serta limitnya ada, atau barisan fungsinya konvergen lemah dan terbatas.
MATRIKS HANKEL Tjahjana, R. Heru
MATEMATIKA Vol 4, No 2 (2001): JURNAL MATEMATIKA
Publisher : MATEMATIKA

#### Abstract

InÂ  this paper,Â  we talkÂ  about HankelÂ  Operator andÂ  Hankel Matrix. Operator Hg:F[z]Â®z-1F[[z-1]] defined byÂ  Hg(f)=p_(gf) is called the Hankel Operator. Hankel Operator can be represented by a Hankel matrix.
PERANCANGAN KONTROL SISTEM INTEGRATOR MULTI AGEN DENGAN FORMASI SEGITIGA tjahjana, remedetus heru
MATEMATIKA Vol 13, No 1 (2010): JURNAL MATEMATIKA
Publisher : MATEMATIKA

#### Abstract

In this paper, a model of swarm movement in triangular formation is considered. The flocking of geese happening in nature motivates this model. The modelÂ  is described by several integrator systems. The movement of the swarm formation is required to preserve a triangle formation from one particular position to the other position. The triangular formation above is translated to a functional cost that must be minimized.Â  This functional cost consists of an error function, repellant term and energy put to control each agent. The theoremÂ  of swarm movement in a triangular formation and some simulation results are presented in the end of the paper.Â  Â
PENENTUAN TRAJEKTORI KERETA DUBIN MELALUI KONTROL OPTIMUM Tjahjana, Redemtus Heru
MATEMATIKA Vol 15, No 1 (2012): JURNAL MATEMATIKA
Publisher : MATEMATIKA

#### Abstract

This paper addressed the control of a Dubinâ€™s vehicle. The Dubinâ€™s vehicle control design, using the Pontryagin Maximum Principle. The application of this principle, bring the matter to the Hamiltonian system with some partial equations excess conditions, while others do not have any conditions. The difference approach, which usedÂ  in this paper to design of the control. This paper solve the problem by transforming the problem into the initial values problem, by finding the best approach to obtain the initial condition equations for some equations that do not have any conditions.
ANALISIS KESTABILAN MODEL DINAMIK ALIRAN FLUIDA DUA FASE PADA SUMUR PANAS BUMI Utomo, Robertus Heri Soelistyo; ., Widowati; Tjahjana, Redemtus Heru; Niswah, L
MATEMATIKA Vol 17, No 1 (2014): Jurnal Matematika
Publisher : MATEMATIKA

#### Abstract

In this paper is discussed about the analysis of the stability of fluid flow dynamical model of two phases on the geothermal wells. The form of the model is non-linear differential equation. To analyze the local stability around the equilibrium point, first, the non linear models of is linearized around the equilibrium point using Taylor series. Further, from linearized model, we find a Jacobian matrix, where all of the real eigen values of the Jacobian matrix are zeros. So that the behviour of the dynamical system obtained around the equilibrium point is stable. Â
MODEL SISTEM MULTI AGEN LINEAR DENGAN FORMASI SEGITIGA Tjahjana, Redemtus Heru
MATEMATIKA Vol 13, No 3 (2010): JURNAL MATEMATIKA
Publisher : MATEMATIKA

#### Abstract

In this paper, a linear model of multi agent movement in equilateral triangle formation is considered. The agents have initial and final state in triangular formation. Along the motion, all agents can not move far away and collide. The agents are steered from initial position to final position in fixed time. For this goal, optimal control with Pontryagin Maximum PrincipleÂ  is applied and the classic difficulty in the optimal control problem is appear. To solve the classic difficulty above, the steepest descent method is used.
MODEL PERTUMBUHAN LOGISTIK DENGAN KONTROL OPTIMAL PENYEBARAN DEMAM BERDARAH DENGUE ., Kartono; ., Widowati; Utomo, Robertus Heri Soelistyo; Tjahjana, Redemtus Heru
MATEMATIKA Vol 18, No 1 (2015): Jurnal Matematika
Publisher : MATEMATIKA

#### Abstract

Controlling of spread of dengue fever was sought by the government together with the people by, among others, campaigning â€œ3M controllingâ€ and eradicating of the vector population using insecticide and threating the infected people. The aim of this research is constructing the optimal control dynamic model by applying several strategies to control the spread of dengue fever. In this paper, the optimal control is constructed by using host logistic growth population model approach and then it is solved by using maximum Pontryagin principle. The results show that in the equilibrium condition, the effect of the control variable u1 (â€œ3M campaigningâ€ and eradicating of the mosquito by using insecticide) is strongly affected by the rate of the direct contact between host population and the infected and susceptible vector whereas the control variable u2 is strongly affected by the number of the infected host population