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All Journal Mandalika Mathematics and Educations Journal
Budi Rudianto
Andalas University
Mathematics

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Eksistensi dan Keunikan dalam Pengendalian LQ Berhorison Tak Terbatas Melalui Analisis Riccati Berbasis Sontag Budi Rudianto; Muhafzan Muhafzan; Mahdhivan Syafwan; Syafrizal Sy
Mandalika Mathematics and Educations Journal Vol 8 No 1 (2026): Edisi Maret
Publisher : FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jm.v8i1.10782

Abstract

This paper examines the existence and uniqueness of solutions to Linear Quadratic (LQ) optimal control problems with infinite time horizons in time-varying dynamic systems. By extending Sontag's Theorem to semi-infinite intervals, the properties of The Riccati Differential Equation’s solutions are analyzed under assumptions of essential boundedness and boundedness of the system matrix and cost weights. It is proven that the Riccati matrix solution P(t) exists globally, remains positive definite, and converges to the steady-state limit P∞. The uniqueness of the optimal control–state pair (x,u) is obtained through P(t)-based co-state analysis. Simulations on satellite attitude control systems demonstrate convergence and robustness towards periodic disturbances, supporting applications in adaptive control, robust estimation, and time-varying filtering.
Co-Authors Muhafzan Muhafzan Syafrizal Sy Syafwan, Mahdhivan