Aljabar maks-plus tersimetri merupakan perluasan dari aljabar maks-plus. Karena matriks atas alja... more Aljabar maks-plus tersimetri merupakan perluasan dari aljabar maks-plus. Karena matriks atas aljabar maks-plus tersimetri dapat didefinisikan determinan maka persamaan karakteristiknya dapat diformulasikan sebagai sistem persamaan polinomial multivariabel aljabar maks-plus. Diperlukan suatu langkah menentukan nilai eigen dengan menggunakan alat yang disebut Masalah Linear Komplementer Diperluas (Extended Linear Complementarity Problem atau ELCP). Dalam tulisan ini, dipaparkan penggunaan ELCP dalam menentukan nilai eigen matriks atas aljabar maks-plus tersimetri. Penggunaan ELCP dilakukan dengan langkah-langkah yaitu mengubah persamaan karakteristik yang diperoleh dari suatu matriks ke bentuk sistem kesetimbangan linear. Selanjutnya, akar persamaan karakteristik yang diperoleh merupakan penyelesaian dari sistem kesetimbangan linear yang merupakan nilai eigen dari matriks tersebut. Akibatnya, diperoleh representasi nilai eigen matriks atas aljabar maks-plus tersimetri dengan ELCP.
The set together with the operation maximum (max) denoted as and addition (+) denoted as is ca... more The set together with the operation maximum (max) denoted as and addition (+) denoted as is called max-plus algebra. Max-plus algebra may be used to apply algebraically a few programs of Discrete Event Systems (DES), certainly one of the examples in the production system. In this study, the application of max-plus algebra in a serial manufacturing machine with a storage unit is discussed. The results of this are the generalization system max-plus-linear equations on a production system that is, in addition, noted the max-plus-linear time-invariant system. From the max-plus-linear time-invariant system, it can be obtained the equation which is then used to determine the beginning time of a production system so the manufacturing machine work periodically. The eigenvector and eigenvalue of the matrix are then used to find the beginning time and the period time of the manufacturing machine. Furthermore, the time when the product leaves the manufacturing machine with the time while ...
This paper aims to model and determine the service cycle completion time of noncyclic fork-join q... more This paper aims to model and determine the service cycle completion time of noncyclic fork-join queueing networks with infinite buffer capacity, using max-plus algebra. The finding show that the dynamics of the noncyclic fork-join queuing networks with infinite buffer capacity can be modeled into a matrix equation over max-plus algebra. We can also show that the service cycle completion time of queuing networks is a max-plus eigenvalues of the matrix in the equation.slklsklslsllsllllllllllllllllllllll
JP journal of algebra, number theory and applications, 2016
Suppose that R is the set of real numbers and { } ε = ε U R R with . −∞ = ε Max-plus algebra is t... more Suppose that R is the set of real numbers and { } ε = ε U R R with . −∞ = ε Max-plus algebra is the set ε R that is equipped with two operations, maximum and addition. Matrices over max-plus algebra Siswanto, Ari Suparwanto and M. Andy Rudhito 64 are matrices whose elements belong to . ε R The set ( ) = ε R I [ ] { } { } ε ≤ < ε ∈ = U x x x x x x x , , , R with [ ] ε ε = ε , which is equipped with maximum and addition operations is known as interval max-plus algebra. Matrices over interval max-plus algebra are matrices whose elements belong to ( ). ε R I The research about image set, strongly regular matrix and simple image set in max-plus algebra have been done. In this paper, we investigate image set, strongly regular matrix and simple image set in interval max-plus algebra.
Makalah ini membahas suatu aljabar himpunan semua bilangan kabur (fuzzy number) yang dilengkapi d... more Makalah ini membahas suatu aljabar himpunan semua bilangan kabur (fuzzy number) yang dilengkapi dengan operasi maximum dan penjumlahan. Aljabar ini merupakan perluasan aljabar max-plus melalui aljabar max-plus interval dan Teorema Dekomposisi dalam himpunan kabur. Dapat ditunjukkan operasi maximum dan penjumlahan yang didefinisikan melalui potongan-alfa tertutup dalam himpunan semua bilangan kabur tersebut. Selanjutnya himpunan semua bilangan kabur yang dilengkapi dengan operasi maximum dan penjumlahan tersebut merupakan semiring idempoten komutatif. Kata-kata kunci: semiring , idempoten, aljabar max-plus, bilangan kabur.
Model interaksi fiskal moneter antar negara secara natural merupakan model permainan dinamis line... more Model interaksi fiskal moneter antar negara secara natural merupakan model permainan dinamis linear kuadratis. Pada makalah ini model tersebut yang terdiri dari N negara akan ditinjau sebagai permainan dinamis linear kuadratis sistem deskriptor. Dengan mengambil state deskriptor diperoleh fungsi objektif berbentuk blok diagonal. Rumus non-rekursif penyelesaian permainan dinamis linear kuadratis N pemain akan diturunkan.
This paper investigates safety analysis of reachability of timed automata hybrid systems as an ex... more This paper investigates safety analysis of reachability of timed automata hybrid systems as an extension of safety analysis of linear system. By studying the initial and terminal sets, the safety analysis problems can be represented as geometric optimization problems which can be transformed into a linear programming. Solution of the optimization problem results in time interval of a safe and unsafe condition of linear systems. Safety analysis of linear systems is extended to safety analysis of timed automata hybrid systems which each mode is linear systems. Suppose given polyhedral sets of the initial state at mode i and terminal set mode i+1. The safety analysis is solved by determining the solution of the differential solution at mode i and the solution of the mode i at the discrete occurence. This solution the becomes the initial condition of the next mode i+1 and analysis by using the safety analysis.
Dalam makalah ini dibahas tentang kestabilan sistem switch linear menggunakan fungsi Lyapunov kua... more Dalam makalah ini dibahas tentang kestabilan sistem switch linear menggunakan fungsi Lyapunov kuadratik.
. This article discussed about the properties of closed periodic queuing network series susing m... more . This article discussed about the properties of closed periodic queuing network series susing max-plus algebra. The result showed that the properties of closed periodic dinamic queuing network series can be determined by using the concept of eigen values and eigen vectors of max-plus matrix in the network model. Through the max-plus eigen vector fundamental, can be determined faster early time departure of customers of departure to the next customer periodically, with a large period of max-plus eigenvalue
Waktu aktivitas dalam suatu jaringan kadang tidak dapat diketahui dengan pasti, dan dapat dinyata... more Waktu aktivitas dalam suatu jaringan kadang tidak dapat diketahui dengan pasti, dan dapat dinyatatakan ke dalam suatu bilangan kabur (fuzzy number). Dengan pendekatan aljabar max-plus, dinamika jaringan dapat dimodelkan dan dianalisis melalui sistem persamaan linear iteratif max-plus yang terkait. Artikel ini bertujuan untuk menentukan eksistensi dan ketunggalan penyelesaian sistem persamaan linear iteratif max-plus bilangan kabur. Dapat ditunjukkan bahwa jika matriks persegi bilangan kabur dari sistem adalah semi-definite, maka sistem mempunyai penyelesaian. Penyelesaian sistem dapat ditentukan dengan terlebih dahulu menentukan penyelesaian sistem potongan-alfa-nya, yang berupa sistem persamaan linear iteratif max-plus interval. Dengan didasarkan pada Teorema Dekomposisi pada himpunan kabur, dapat ditentukan fungsi keanggotaan elemen-elemen vektor penyelesaiannya. Lebih lanjut, penyelesaian sistem tunggal jika matriks persegi bilangan kaburnya adalah definit
Let R be the set of real numbers and { }, ε = ε U R R . −∞ = ε Maxplus algebra is the set ε R tha... more Let R be the set of real numbers and { }, ε = ε U R R . −∞ = ε Maxplus algebra is the set ε R that is equipped with two operations maximum and addition. It can be formed matrices in the size of , n m × Siswanto, Ari Suparwanto and M. Andy Rudhito 18 whose elements belong to , ε R called matrix over max-plus algebra. Let ( ) { [ ] } { } ε ≤ < ε ∈ | = = ε U x x x x x x x I , , , R R and { }. , ε ε = ε The set ( )ε R I which is equipped with two operations maximum and addition is called interval max-plus algebra. It can be formed matrices in the size , n m × whose elements belong to ( ) , ε R I called matrices over interval max-plus algebra. Optimizing range norm of the image set of matrix over max-plus algebra has been discussed. In this paper, we discuss optimizing range norm of the image set of matrix over interval max-plus algebra.
Dalam makalah ini akan diperkenalkan definisi dan sifat-sifat semiring pseudo-ternary. Selanjutny... more Dalam makalah ini akan diperkenalkan definisi dan sifat-sifat semiring pseudo-ternary. Selanjutnya, akan diperkenalkan subsemiring pseudo-ternary dan ideal pada semiring pseudo-ternary. Lebih lanjut, ideal-ideal yang terbentuk pada semiring pseudo-ternary akan digunakan untuk membentuk semiring pseudo-ternary faktor. Pseudo- Ternary Semiring Abstract In this paper we introduce the notion of pseudo-ternary semiring. Furthermore, we will introduce pseudo-ternary subsemiring and ideals in pseudo-ternary semiring. Finally, ideals in pseudo-ternary semiring will be used for constructing pseudo-ternary factor semiring. Keywords: Pseudo-ternary semiring, Factor pseudo-ternary semiring.
Let R be a commutative ring with 1. Ring R has a feedback cyclization property if for any reachab... more Let R be a commutative ring with 1. Ring R has a feedback cyclization property if for any reachable system (A
2017 5th International Conference on Instrumentation, Control, and Automation (ICA), 2017
This paper presents a design of light rail vehicles (LRVs) active suspension system control using... more This paper presents a design of light rail vehicles (LRVs) active suspension system control using model predictive control (MPC) scheme with assumption that the preview information of oncoming disturbance is available. The aims of control design are to provide ride comfort and safety. A multibody dynamical model of the tree-car train set is considered. Numerical simulation is performed to verify the performance of the proposed controller. The simulation results show that the deflections of suspension system are in the admissible range and the vertical accelaration of all cars are brought to zero. This implies that the proposed control design provides ride comfort and safety.
BAREKENG: Jurnal Ilmu Matematika dan Terapan, 2021
If the characteristic polynomial of a linear operator is completely factored in scalar field of ... more If the characteristic polynomial of a linear operator is completely factored in scalar field of then Jordan canonical form of can be converted to its rational canonical form of , and vice versa. If the characteristic polynomial of linear operator is not completely factored in the scalar field of ,then the rational canonical form of can still be obtained but not its Jordan canonical form matrix . In this case, the rational canonical form of can be converted to its Jordan canonical form by extending the scalar field of to Splitting Field of minimal polynomial of , thus forming the Jordan canonical form of over Splitting Field of . Conversely, converting the Jordan canonical form of over Splitting Field of to its rational canonical form uses symmetrization on the Jordan decomposition basis of so as to form a cyclic decomposition basis of which is then used to form the rational canonical matrix of
Max-Plus algebra is the set of R U {-~} with R is the set of all real numbersthat are equipped wi... more Max-Plus algebra is the set of R U {-~} with R is the set of all real numbersthat are equipped with maximum operation and addition. Max-Plus algebra is able tomodel several types of Discrete Event System (DES) which are nonlinear in conventional algebra to be linear in Max-Plus algebra, so we can do further analysis of the system. Types of DES will be linear in the form of Max-Plus algebra which only synchronizes without any concurrency such as railway network systems, production systems, traffic lights, etc. This research discusses the application of the linear Max-Plus equation in the train schedules and involves synchronization between trains. The result of this study are obtained DAOP VI Yogyakarta rail network system model in the form of x(k + 1) = A otimes x (k) which is then used to determine the departure period and the time of initial train departure. The departure period is obtained from the eigenvalue (lambda) from the A matrix and the initial departure is obtained from t...
The symmetrized max-plus algebra is an algebraic structure which is a commutative semiring, has a... more The symmetrized max-plus algebra is an algebraic structure which is a commutative semiring, has a zero element = −∞, the identity element e = 0, and an additively idempotent. Motivated by the the previous study as in conventional linear algebra, in this paper will be described the necessary and sufficient condition of linear independent over the symmetrized max-plus algebra. We show that a columns of a matrix over the symmetrized max-plus algebra are linear dependent if and only if the determinat of that matrix is .
This paper aims to discuss the matrix algebra over interval max-plus algebra (interval matrix) an... more This paper aims to discuss the matrix algebra over interval max-plus algebra (interval matrix) and a method tosimplify the computation of the operation of them. This matrix algebra is an extension of matrix algebra over max-plus algebra and can be used to discuss the matrix algebra over fuzzy number max-plus algebra via its alpha-cut.The finding shows that the set of all interval matrices together with the max-plus scalar multiplication operationand max-plus addition is a semimodule. The set of all square matrices over max-plus algebra together with aninterval of max-plus addition operation and max-plus multiplication operation is a semiring idempotent. As reasoningfor the interval matrix operations can be performed through the corresponding matrix interval, because thatsemimodule set of all interval matrices is isomorphic with semimodule the set of corresponding interval matrix,and the semiring set of all square interval matrices is isomorphic with semiring the set of the correspon...
Let ℝ be the set of all real numbers and ℝ = ℝ ⋃ { } whose = − . Maxplus algebra is the set ℝ th... more Let ℝ be the set of all real numbers and ℝ = ℝ ⋃ { } whose = − . Maxplus algebra is the set ℝ that is equipped two operations maximum and addition. It can be formed matrices in the size of × whose elements belong to ℝ , called matrix over max-plus algebra. Optimizing range norm of the image set of matrix over max-plus algebra with prescribed components has been discussed. Interval Max-Plus Algebra is the set (ℝ) = { x = [x, x]|x, x ∈ ℝ, < x ≤ x} ∪ {ε} with ε = [ , ], is equipped with two operations maximum (⊕) and addition (⊗). The set of all matrices in the size of × whose elements belong to (ℝ) , called matrix over interval max-plus algebra. Optimizing range norm of the image set of matrix over interval max-plus algebra has been discussed. In this paper, we will discuss optimizing range norm of the image set of matrix over interval max-plus algebra with prescribed components.
JURNAL SILOGISME : Kajian Ilmu Matematika dan Pembelajarannya, 2019
Aljabar maks-plus merupakan suatu struktur aljabar (ℝ ℰ ,⊕,⊗) yang tidak mempunyai elemen negatif... more Aljabar maks-plus merupakan suatu struktur aljabar (ℝ ℰ ,⊕,⊗) yang tidak mempunyai elemen negatif, yaitu invers terhadap operasi ⊕. Oleh karena itu, dikembangkan suatu struktur yang lebih luas yang disebut aljabar maks-plus tersimetri, dinotasikan dengan (,⊕ ,⊗) dengan dikonstruksi dari kelas ekuivalensi. Dengan adanya struktur ini, maka elemen di dalam aljabar maks-plus tersimetri akan mempunyai elemen negatif. Akibatnya, determinan matriks atas aljabar maks-plus tersimetri dapat didefinisikan. Dalam tulisan ini akan dikembangkan karakterisasi determinan matriks atas aljabar maks-plus tersimetri, khususnya di dalam hubungannya dengan adjoint. Hasil utama yang diperoleh yaitu untuk suatu matriks atas aljabar maks-plus tersimetri, hasilkali determinan matriks dan matriks identitas berelasi setimbang dengan hasilkali matriks dan adjoinnya
Aljabar maks-plus tersimetri merupakan perluasan dari aljabar maks-plus. Karena matriks atas alja... more Aljabar maks-plus tersimetri merupakan perluasan dari aljabar maks-plus. Karena matriks atas aljabar maks-plus tersimetri dapat didefinisikan determinan maka persamaan karakteristiknya dapat diformulasikan sebagai sistem persamaan polinomial multivariabel aljabar maks-plus. Diperlukan suatu langkah menentukan nilai eigen dengan menggunakan alat yang disebut Masalah Linear Komplementer Diperluas (Extended Linear Complementarity Problem atau ELCP). Dalam tulisan ini, dipaparkan penggunaan ELCP dalam menentukan nilai eigen matriks atas aljabar maks-plus tersimetri. Penggunaan ELCP dilakukan dengan langkah-langkah yaitu mengubah persamaan karakteristik yang diperoleh dari suatu matriks ke bentuk sistem kesetimbangan linear. Selanjutnya, akar persamaan karakteristik yang diperoleh merupakan penyelesaian dari sistem kesetimbangan linear yang merupakan nilai eigen dari matriks tersebut. Akibatnya, diperoleh representasi nilai eigen matriks atas aljabar maks-plus tersimetri dengan ELCP.
The set together with the operation maximum (max) denoted as and addition (+) denoted as is ca... more The set together with the operation maximum (max) denoted as and addition (+) denoted as is called max-plus algebra. Max-plus algebra may be used to apply algebraically a few programs of Discrete Event Systems (DES), certainly one of the examples in the production system. In this study, the application of max-plus algebra in a serial manufacturing machine with a storage unit is discussed. The results of this are the generalization system max-plus-linear equations on a production system that is, in addition, noted the max-plus-linear time-invariant system. From the max-plus-linear time-invariant system, it can be obtained the equation which is then used to determine the beginning time of a production system so the manufacturing machine work periodically. The eigenvector and eigenvalue of the matrix are then used to find the beginning time and the period time of the manufacturing machine. Furthermore, the time when the product leaves the manufacturing machine with the time while ...
This paper aims to model and determine the service cycle completion time of noncyclic fork-join q... more This paper aims to model and determine the service cycle completion time of noncyclic fork-join queueing networks with infinite buffer capacity, using max-plus algebra. The finding show that the dynamics of the noncyclic fork-join queuing networks with infinite buffer capacity can be modeled into a matrix equation over max-plus algebra. We can also show that the service cycle completion time of queuing networks is a max-plus eigenvalues of the matrix in the equation.slklsklslsllsllllllllllllllllllllll
JP journal of algebra, number theory and applications, 2016
Suppose that R is the set of real numbers and { } ε = ε U R R with . −∞ = ε Max-plus algebra is t... more Suppose that R is the set of real numbers and { } ε = ε U R R with . −∞ = ε Max-plus algebra is the set ε R that is equipped with two operations, maximum and addition. Matrices over max-plus algebra Siswanto, Ari Suparwanto and M. Andy Rudhito 64 are matrices whose elements belong to . ε R The set ( ) = ε R I [ ] { } { } ε ≤ < ε ∈ = U x x x x x x x , , , R with [ ] ε ε = ε , which is equipped with maximum and addition operations is known as interval max-plus algebra. Matrices over interval max-plus algebra are matrices whose elements belong to ( ). ε R I The research about image set, strongly regular matrix and simple image set in max-plus algebra have been done. In this paper, we investigate image set, strongly regular matrix and simple image set in interval max-plus algebra.
Makalah ini membahas suatu aljabar himpunan semua bilangan kabur (fuzzy number) yang dilengkapi d... more Makalah ini membahas suatu aljabar himpunan semua bilangan kabur (fuzzy number) yang dilengkapi dengan operasi maximum dan penjumlahan. Aljabar ini merupakan perluasan aljabar max-plus melalui aljabar max-plus interval dan Teorema Dekomposisi dalam himpunan kabur. Dapat ditunjukkan operasi maximum dan penjumlahan yang didefinisikan melalui potongan-alfa tertutup dalam himpunan semua bilangan kabur tersebut. Selanjutnya himpunan semua bilangan kabur yang dilengkapi dengan operasi maximum dan penjumlahan tersebut merupakan semiring idempoten komutatif. Kata-kata kunci: semiring , idempoten, aljabar max-plus, bilangan kabur.
Model interaksi fiskal moneter antar negara secara natural merupakan model permainan dinamis line... more Model interaksi fiskal moneter antar negara secara natural merupakan model permainan dinamis linear kuadratis. Pada makalah ini model tersebut yang terdiri dari N negara akan ditinjau sebagai permainan dinamis linear kuadratis sistem deskriptor. Dengan mengambil state deskriptor diperoleh fungsi objektif berbentuk blok diagonal. Rumus non-rekursif penyelesaian permainan dinamis linear kuadratis N pemain akan diturunkan.
This paper investigates safety analysis of reachability of timed automata hybrid systems as an ex... more This paper investigates safety analysis of reachability of timed automata hybrid systems as an extension of safety analysis of linear system. By studying the initial and terminal sets, the safety analysis problems can be represented as geometric optimization problems which can be transformed into a linear programming. Solution of the optimization problem results in time interval of a safe and unsafe condition of linear systems. Safety analysis of linear systems is extended to safety analysis of timed automata hybrid systems which each mode is linear systems. Suppose given polyhedral sets of the initial state at mode i and terminal set mode i+1. The safety analysis is solved by determining the solution of the differential solution at mode i and the solution of the mode i at the discrete occurence. This solution the becomes the initial condition of the next mode i+1 and analysis by using the safety analysis.
Dalam makalah ini dibahas tentang kestabilan sistem switch linear menggunakan fungsi Lyapunov kua... more Dalam makalah ini dibahas tentang kestabilan sistem switch linear menggunakan fungsi Lyapunov kuadratik.
. This article discussed about the properties of closed periodic queuing network series susing m... more . This article discussed about the properties of closed periodic queuing network series susing max-plus algebra. The result showed that the properties of closed periodic dinamic queuing network series can be determined by using the concept of eigen values and eigen vectors of max-plus matrix in the network model. Through the max-plus eigen vector fundamental, can be determined faster early time departure of customers of departure to the next customer periodically, with a large period of max-plus eigenvalue
Waktu aktivitas dalam suatu jaringan kadang tidak dapat diketahui dengan pasti, dan dapat dinyata... more Waktu aktivitas dalam suatu jaringan kadang tidak dapat diketahui dengan pasti, dan dapat dinyatatakan ke dalam suatu bilangan kabur (fuzzy number). Dengan pendekatan aljabar max-plus, dinamika jaringan dapat dimodelkan dan dianalisis melalui sistem persamaan linear iteratif max-plus yang terkait. Artikel ini bertujuan untuk menentukan eksistensi dan ketunggalan penyelesaian sistem persamaan linear iteratif max-plus bilangan kabur. Dapat ditunjukkan bahwa jika matriks persegi bilangan kabur dari sistem adalah semi-definite, maka sistem mempunyai penyelesaian. Penyelesaian sistem dapat ditentukan dengan terlebih dahulu menentukan penyelesaian sistem potongan-alfa-nya, yang berupa sistem persamaan linear iteratif max-plus interval. Dengan didasarkan pada Teorema Dekomposisi pada himpunan kabur, dapat ditentukan fungsi keanggotaan elemen-elemen vektor penyelesaiannya. Lebih lanjut, penyelesaian sistem tunggal jika matriks persegi bilangan kaburnya adalah definit
Let R be the set of real numbers and { }, ε = ε U R R . −∞ = ε Maxplus algebra is the set ε R tha... more Let R be the set of real numbers and { }, ε = ε U R R . −∞ = ε Maxplus algebra is the set ε R that is equipped with two operations maximum and addition. It can be formed matrices in the size of , n m × Siswanto, Ari Suparwanto and M. Andy Rudhito 18 whose elements belong to , ε R called matrix over max-plus algebra. Let ( ) { [ ] } { } ε ≤ < ε ∈ | = = ε U x x x x x x x I , , , R R and { }. , ε ε = ε The set ( )ε R I which is equipped with two operations maximum and addition is called interval max-plus algebra. It can be formed matrices in the size , n m × whose elements belong to ( ) , ε R I called matrices over interval max-plus algebra. Optimizing range norm of the image set of matrix over max-plus algebra has been discussed. In this paper, we discuss optimizing range norm of the image set of matrix over interval max-plus algebra.
Dalam makalah ini akan diperkenalkan definisi dan sifat-sifat semiring pseudo-ternary. Selanjutny... more Dalam makalah ini akan diperkenalkan definisi dan sifat-sifat semiring pseudo-ternary. Selanjutnya, akan diperkenalkan subsemiring pseudo-ternary dan ideal pada semiring pseudo-ternary. Lebih lanjut, ideal-ideal yang terbentuk pada semiring pseudo-ternary akan digunakan untuk membentuk semiring pseudo-ternary faktor. Pseudo- Ternary Semiring Abstract In this paper we introduce the notion of pseudo-ternary semiring. Furthermore, we will introduce pseudo-ternary subsemiring and ideals in pseudo-ternary semiring. Finally, ideals in pseudo-ternary semiring will be used for constructing pseudo-ternary factor semiring. Keywords: Pseudo-ternary semiring, Factor pseudo-ternary semiring.
Let R be a commutative ring with 1. Ring R has a feedback cyclization property if for any reachab... more Let R be a commutative ring with 1. Ring R has a feedback cyclization property if for any reachable system (A
2017 5th International Conference on Instrumentation, Control, and Automation (ICA), 2017
This paper presents a design of light rail vehicles (LRVs) active suspension system control using... more This paper presents a design of light rail vehicles (LRVs) active suspension system control using model predictive control (MPC) scheme with assumption that the preview information of oncoming disturbance is available. The aims of control design are to provide ride comfort and safety. A multibody dynamical model of the tree-car train set is considered. Numerical simulation is performed to verify the performance of the proposed controller. The simulation results show that the deflections of suspension system are in the admissible range and the vertical accelaration of all cars are brought to zero. This implies that the proposed control design provides ride comfort and safety.
BAREKENG: Jurnal Ilmu Matematika dan Terapan, 2021
If the characteristic polynomial of a linear operator is completely factored in scalar field of ... more If the characteristic polynomial of a linear operator is completely factored in scalar field of then Jordan canonical form of can be converted to its rational canonical form of , and vice versa. If the characteristic polynomial of linear operator is not completely factored in the scalar field of ,then the rational canonical form of can still be obtained but not its Jordan canonical form matrix . In this case, the rational canonical form of can be converted to its Jordan canonical form by extending the scalar field of to Splitting Field of minimal polynomial of , thus forming the Jordan canonical form of over Splitting Field of . Conversely, converting the Jordan canonical form of over Splitting Field of to its rational canonical form uses symmetrization on the Jordan decomposition basis of so as to form a cyclic decomposition basis of which is then used to form the rational canonical matrix of
Max-Plus algebra is the set of R U {-~} with R is the set of all real numbersthat are equipped wi... more Max-Plus algebra is the set of R U {-~} with R is the set of all real numbersthat are equipped with maximum operation and addition. Max-Plus algebra is able tomodel several types of Discrete Event System (DES) which are nonlinear in conventional algebra to be linear in Max-Plus algebra, so we can do further analysis of the system. Types of DES will be linear in the form of Max-Plus algebra which only synchronizes without any concurrency such as railway network systems, production systems, traffic lights, etc. This research discusses the application of the linear Max-Plus equation in the train schedules and involves synchronization between trains. The result of this study are obtained DAOP VI Yogyakarta rail network system model in the form of x(k + 1) = A otimes x (k) which is then used to determine the departure period and the time of initial train departure. The departure period is obtained from the eigenvalue (lambda) from the A matrix and the initial departure is obtained from t...
The symmetrized max-plus algebra is an algebraic structure which is a commutative semiring, has a... more The symmetrized max-plus algebra is an algebraic structure which is a commutative semiring, has a zero element = −∞, the identity element e = 0, and an additively idempotent. Motivated by the the previous study as in conventional linear algebra, in this paper will be described the necessary and sufficient condition of linear independent over the symmetrized max-plus algebra. We show that a columns of a matrix over the symmetrized max-plus algebra are linear dependent if and only if the determinat of that matrix is .
This paper aims to discuss the matrix algebra over interval max-plus algebra (interval matrix) an... more This paper aims to discuss the matrix algebra over interval max-plus algebra (interval matrix) and a method tosimplify the computation of the operation of them. This matrix algebra is an extension of matrix algebra over max-plus algebra and can be used to discuss the matrix algebra over fuzzy number max-plus algebra via its alpha-cut.The finding shows that the set of all interval matrices together with the max-plus scalar multiplication operationand max-plus addition is a semimodule. The set of all square matrices over max-plus algebra together with aninterval of max-plus addition operation and max-plus multiplication operation is a semiring idempotent. As reasoningfor the interval matrix operations can be performed through the corresponding matrix interval, because thatsemimodule set of all interval matrices is isomorphic with semimodule the set of corresponding interval matrix,and the semiring set of all square interval matrices is isomorphic with semiring the set of the correspon...
Let ℝ be the set of all real numbers and ℝ = ℝ ⋃ { } whose = − . Maxplus algebra is the set ℝ th... more Let ℝ be the set of all real numbers and ℝ = ℝ ⋃ { } whose = − . Maxplus algebra is the set ℝ that is equipped two operations maximum and addition. It can be formed matrices in the size of × whose elements belong to ℝ , called matrix over max-plus algebra. Optimizing range norm of the image set of matrix over max-plus algebra with prescribed components has been discussed. Interval Max-Plus Algebra is the set (ℝ) = { x = [x, x]|x, x ∈ ℝ, < x ≤ x} ∪ {ε} with ε = [ , ], is equipped with two operations maximum (⊕) and addition (⊗). The set of all matrices in the size of × whose elements belong to (ℝ) , called matrix over interval max-plus algebra. Optimizing range norm of the image set of matrix over interval max-plus algebra has been discussed. In this paper, we will discuss optimizing range norm of the image set of matrix over interval max-plus algebra with prescribed components.
JURNAL SILOGISME : Kajian Ilmu Matematika dan Pembelajarannya, 2019
Aljabar maks-plus merupakan suatu struktur aljabar (ℝ ℰ ,⊕,⊗) yang tidak mempunyai elemen negatif... more Aljabar maks-plus merupakan suatu struktur aljabar (ℝ ℰ ,⊕,⊗) yang tidak mempunyai elemen negatif, yaitu invers terhadap operasi ⊕. Oleh karena itu, dikembangkan suatu struktur yang lebih luas yang disebut aljabar maks-plus tersimetri, dinotasikan dengan (,⊕ ,⊗) dengan dikonstruksi dari kelas ekuivalensi. Dengan adanya struktur ini, maka elemen di dalam aljabar maks-plus tersimetri akan mempunyai elemen negatif. Akibatnya, determinan matriks atas aljabar maks-plus tersimetri dapat didefinisikan. Dalam tulisan ini akan dikembangkan karakterisasi determinan matriks atas aljabar maks-plus tersimetri, khususnya di dalam hubungannya dengan adjoint. Hasil utama yang diperoleh yaitu untuk suatu matriks atas aljabar maks-plus tersimetri, hasilkali determinan matriks dan matriks identitas berelasi setimbang dengan hasilkali matriks dan adjoinnya
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