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Predictor control for wave PDE / nonlinear ODE cascaded system with boundary value-dependent propagation speed

Xiushan Cai, Yuhang Lin, Junfeng Zhang, Cong Lin (2022)

Kybernetika

This paper investigates predictor control for wave partial differential equation (PDE) and nonlinear ordinary differential equation (ODE) cascaded system with boundary value-dependent propagation speed. A predictor control is designed first. A two-step backstepping transformation and a new time variable are employed to derive a target system whose stability is established using Lyapunov arguments. The equivalence between stability of the target and the original system is provided using the invertibility...

Properties of set-valued stochastic integrals

Jerzy Motyl, Joachim Syga (2006)

Discussiones Mathematicae Probability and Statistics

We introduce set-valued stochastic integrals driven by a square-integrable martingale and by a semimartingale. We investigate properties of both integrals.

Protector control: Extension to a class of nonlinear distributed systems

Youssef Qaraai, Abdes Samed Bernoussi (2010)

International Journal of Applied Mathematics and Computer Science

We present an extension of the protector control scheme introduced for the linear case in a previous work to a class of nonlinear systems. The systems considered are assumed to have a finite propagation velocity while the initial state is subject to a spreading disturbance. We characterize such a control first by using the remediability approach to the resulting nonlinear delay system, and then by coupling families of transformations and the delay approach. To illustrate this work, we provide a...

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