KERANGKA KERJA DIFFERENSIAL RICCATI UNTUK ROBUST KALMAN FILTERING PADA KETIDAKPASTIAN INTERVAL SEMI-TAK HINGGA
Abstract
Penelitian ini mengusulkan pendekatan baru untuk merancang Penyaringan Kalman yang Kuat (Robust Kalman Filtering, RKF) pada sistem waktu kontinu yang menghadapi ketidakpastian parametris pada model dinamis, disertai gangguan eksternal dan noise pengukuran yang berlaku pada interval waktu semi-tak hingga. Pada pendekatan ini, digunakan teori H_\infty untuk mengurangi pengaruh gangguan dan noise terhadap akurasi estimasi. Persamaan diferensial Riccati dirumuskan sebagai dasar perancangan filter, di mana gain filter diturunkan dari solusi Riccati yang memenuhi syarat kestabilan asimtotik. Hasil utama menunjukkan bahwa solusi tersebut eksis, terbatas dan stabil, serta mampu menjaga kestabilan kesalahan estimasi meskipun terdapat ketidakpastian model. Studi kasus numerik pada sistem termal dua zona memperlihatkan bahwa filter yang diusulkan lebih tangguh, karena mampu meredam osilasi kesalahan, mempertahankan konvergensi yang lebih cepat, dan menjaga akurasi estimasi pada kondisi ketidakpastian parameter dan noise non-Gaussian dibandingkan Kalman Filter klasik. Kontribusi utama penelitian ini terletak pada integrasi pendekatan H_\infty dengan kerangka diferensial Riccati dalam domain waktu kontinu pada interval semi-tak hingga, yang memperluas konsep estimasi robust yang belum banyak dikaji sebelumnya. Keterbatasan dari studi ini adalah model masih linear dan jenis ketidakpastian yang terbatas. Pemilihan model linear dilakukan untuk memungkinkan analisis stabilitas dan eksistensi solusi yang rigor dalam kerangka semi-tak hingga, yang menjadi prasyarat penting untuk pengembangan ke sistem nonlinier. Penelitian lanjutan dapat mengembangkan pendekatan ini untuk sistem nonlinier atau berbasis adaptif.
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DOI: https://doi.org/10.15548/map.v7i2.12351
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