On the Properties of the Set of Trajectories of the Control System with Integrable Trajectories and Limited Control Resources

Öz

In this paper the control system given by Urysohn type integral equation with integral constraint on the control functions is studied. The admissible control functions are chosen from the closed ball of the space L_p (E;R^m ) (p>1) centered at the origin with radius r. The trajectory of the system is defined as a multivariable integrable function which satisfies the system’s equation almost everywhere. An upper evaluation for diameter of the set of trajectories is obtained and it is proved that the set of trajectories is Lipschitz continuous with respect to r.

Anahtar Kelimeler

• Hausdorff distance
• integral constraint
• control system
• Urysohn integral equation
• set of trajectories.

İntegrallenebilir Yörüngeleri ve Kontrol Kaynakları Kısıtlı olan Kontrol Sistemin Yörüngeler Kümesinin Özellikleri Üzerine

Öz

Bu çalışmada, davranışı Urysohn tür integral denklem ile verilen ve kontrol fonksiyonları üzerinde integral kısıt olan kontrol sistem incelenmektedir. Mümkün kontrol fonksiyonlar L_p (E;R^m ) (p>1) uzayının merkezi orijinde olan r yarıçaplı kapalı yuvarından seçilmektedir. Sistemin yörüngesi verilen denklemi hemen hemen her yerde sağlayan çok değişkenli integrallenebilir fonksiyon olarak tanımlanmaktadır. Yörüngeler kümesinin çapı için bir üst sınır elde edilmiş, yörüngeler kümesinin r ‘ye göre Lipschitz sürekli olduğu kanıtlanmıştır.

Anahtar Kelimeler

• Hausdorff uzaklığı
• integral kısıt
• kontrol sistem
• Urysohn integral denklemi
• yörüngeler kümesi

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