Sistem linear max-plus waktu-invariant.

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SISTEM LINEAR MAX-PLUS WAKTU-INVARIANT

Oleh M. Andy Rudhitol)

Di bawah bimbingan: Dr. Lina Aryati, M.S 2)

Dr. Ari Suparwanto, M.Si 3)

INTISAR1

Dalam tesis ini dibahas sistem linear max-plus waktu-invariant yang meliputi analisis input-output dan sifat periodik sistem linear max-plus waktu-invariant.

Aljabar max-plus, dengan maximum da.n penjumlahan sebagai operasi dasarnya, digunakan sebagai konsep dasar sistem linear max-plus waktu-invariant. Jika diberikan barisan input pada sistem linear max-plus waktu-invariant, maka daPat ditentukan barisan output yang bersesuaian dengan barisan input. Masalah input paling lambat pada sistem linear max-plus waktu-invariant diselesaikan dengan menggunakan subpenyelesaian terbesar sistem persamaan linear max-plus yang bersesuaian dengan input-output sistem. Penyelesaian masalah minimisasi simpangan maksimum output pada sistem linear max-plus waktu-invariant merupakan jumlahan subpenyelesaian terbesar sistem persamaan linear max-plus yang bersesuaian dengan input-output sistem dan setengah simpangan maksimal antara barisan output yang diinginkan dengan barisan output sesungguhnya. Sistem linear max-plus waktu-invariant autonomous periodik dengan periode sebesar nilai eigen max-plus matriks yang inembentuk keadaan sistem.

Diberikan ilustrasi dan contoh penerapan dalam sistem produksi sederhana dan sistem jaringan kereta sederhana. Disusun siinulasi input-output sistem linear max-plus waktu-invariant dengan program Matlab.

Kata-kata kunci : Aljabar Max-Plus, Sistem Linear Max-Plus Waktu-Invariant.

1) FKIP USD, Yogyakarta.

FMIPA UGM, Yogyakarta. FMIPA UGM, Yogyakarta.

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TIME-INVARIANT MAX-PLUS LINEAR SYSTEMS

By M. Andy Rudbitol)

Under supervision: Dr. Lina Aryati, M.S 2)

Dr. Ari Suparwanto, M.Si 3)

ABSTRACT

In this thesis we discuss time-invariant max-plus linear systems that cover input-output analysis and periodic property of time-invariant max-plus linear systems.

Max-plus algebra, with maximum and addition as basic operations, is used as basic concept of time-invariant plus linear systems. If the input sequence of time-invariant max-plus linear systems are given, then the output sequence that corresponds to the input sequence can be calculated. The latest input problem on time-invariant max-plus linear systems is solved by using the greatest subsolution of the max-plus systems of linear equation that corresponds to the input-output of systems. The solution of output maximal deviation minimization problem is addition of greatest subsolution of the max-plus systems of linear equation that corresponds to the input-output of systems and a half of maximal deviation between the desired and the actual output sequence. The autonomous time-invariant max-plus linear systems is periodic. The period is equal the max-max-plus eigenvalue of matrix that form state of the systems.

Ilustration and example of application on simple production system and simple railway system are given. Input-output simulation of time-invariant max-plus linear systems are written with Matlab _program.

Keywords : Max-Plus Algebra, Time-Invariant Max-Plus Linear Systems.

)) FKIP USD, Yogyakarta.

FMIPA UGM, Yogyakarta. FMIPA UGM, Yogyakarta.

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