Rekayasa Sistem Kontrol Optimal Berdasarkan Kriteria Indeks Performansi Kuadratik Menggunakan Matrix Laboratory


  • Fiktor Sihombing Universitas HKBP Nommensen
  • Marhiras Sitanggang Universitas HKBP Nommensen
  • Zody Chrisna Setiawan Sitompul Universitas HKBP Nommensen
  • Martin Luter Simanjuntak Universitas HKBP Nommensen



State-space,, Controllability,, Weighting matrices,, Riccati equation,, Optimal control vector,, Quadratic performance index.


The concept of control system optimization comprises a selection of a performance index and design which yields the optimal control system within limits imposed by physical constraints. In solving problems of  optimal control systems, we may have the goal of finding  a rule for the determining the present control decision, subject to certain constraints which will minimize some measure of a deviation from ideal behavior. Such a measure is usually provided by a criterion of optimization or performance index. The quantities appearing in control system optimization problems are state variables, control variables, system parameters and the conditions for complete state controllability. The problem in the optimal control system based on quadratic performance index is determine the matrix K of the optimal control vector so as to minimize the performance index.

where the weighting matrices S and Q are positive definite or positive semidefinite Hermitian matrices and R is appositive definite Hermitian matrix.


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