Radyal Tabanlı Fonksiyon Ağları ile Dışbükeyliği Koruyan Azaltılmış Karmaşıklıklı Model Öngörülü Kontrol

Öz

Bu çalışmada, durum, kontrol ve çıkış değişkenleri üzerindeki kısıtlar altında çalışan sistemler için Model Öngörülü Kontrol (MPC) yöntemi incelenmiş ve hesaplama yükünü önemli ölçüde azaltan yeni bir formülasyon önerilmiştir. MPC çerçevesinde, kontrol sinyalinin gösterimi için güçlü fonksiyon yaklaşım kabiliyetiyle bilinen Radyal Tabanlı Fonksiyon Ağları (RBFN) kullanılarak yenilikçi bir yaklaşım sunulmaktadır. Geleneksel MPC’de kontrol sinyali, zamana göre ayrık vektör elemanları biçiminde optimize edilirken, önerilen yöntemde kontrol yörüngesi, RBFN ağırlıkları aracılığıyla kompakt bir biçimde kodlanmaktadır. Bu yeniden parametrelendirme, optimizasyon değişkenlerinin sayısını önemli ölçüde azaltmakta ve MPC’nin çözmesi gereken kısıtlı ikinci dereceden optimizasyon problemlerinin hesaplama yükünü düşürmektedir. Kuramsal analiz, standart kontrol uzayından RBFN ağırlık uzayına yapılan dönüşümün, maliyet fonksiyonunun dışbükeyliğini ve pozitif tanımlılığını koruduğunu; dolayısıyla çözümün kararlılığını ve tekilliğini garanti ettiğini göstermektedir. Yöntemin etkinliğini değerlendirmek amacıyla, önerilen MPC–RBFN yaklaşımı bir uçak modelinin boylamsal kontrol problemine uygulanmıştır. Benzetim sonuçları, önerilen denetleyicinin klasik MPC ile benzer izleme başarımı sağlarken hesaplama süresinde belirgin bir iyileşme elde ettiğini göstermiş, böylece yöntemin gerçek zamanlı ve gömülü kontrol uygulamaları için uygunluğunu ortaya koymuştur.

Anahtar Kelimeler

• Kısıtlamalı Optimizasyon
• Model Öngörülü Kontrol
• Radyal-Tabanlı Fonksiyon Ağları

Convexity-Preserving Reduced-Complexity Model Predictive Control via Radial Basis Function Networks

Öz

In this study, we investigate Model Predictive Control (MPC) for systems operating under state, control, and output constraints, and propose an enhanced formulation that significantly reduces computational demand. Within the MPC framework, we introduce a novel representation of the control signal based on Radial Basis Function Networks (RBFNs)—well known for their strong function approximation capabilities. Instead of optimizing over a conventional vector of discrete control inputs, the proposed approach encodes the control trajectory using a compact set of RBFN weights. This reformulation substantially decreases the number of optimization variables, thereby reducing the computational burden associated with solving constrained quadratic programs in MPC. The theoretical analysis demonstrates that the transformation from the standard control space to the RBFN weight space preserves convexity and positive definiteness of the original cost function, ensuring stability and uniqueness of the optimal solution. To evaluate the practical benefits of this approach, the MPC–RBFN method is applied to the longitudinal control of an aircraft model. Simulation results confirm that the proposed controller achieves comparable tracking performance to conventional MPC while providing a marked improvement in computational efficiency, highlighting its suitability for real-time and embedded control applications.

Anahtar Kelimeler

• Constrained Optimization
• Model Predictive Control
• Radial-Basis Function Network

Kaynakça

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