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arXiv · 2311.02473

Designing controllers with predefined convergence-time bound using bounded time-varying gains

Rodrigo Aldana-López·Richard Seeber·Hernan Haimovich·David Gómez-Gutiérrez
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Abstract

Recently, there has been a great deal of attention in a class of controllers based on time-varying gains, called prescribed-time controllers, that steer the system's state to the origin in the desired time, a priori set by the user, regardless of the initial condition. Furthermore, such a class of controllers has been shown to maintain a prescribed-time convergence in the presence of disturbances even if the disturbance bound is unknown. However, such properties require a time-varying gain that becomes singular at the terminal time, which limits its application to scenarios under quantization or measurement noise. This chapter presents a methodology to design a broader class of controllers, called predefined-time controllers, with a prescribed convergence-time bound. Our approach allows designing robust predefined-time controllers based on time-varying gains while maintaining uniformly bounded time-varying gains. We analyze the condition for uniform Lyapunov stability under the proposed time-varying controllers.

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Rodrigo Aldana-López, Richard Seeber, Hernan Haimovich, David Gómez-Gutiérrez. 2023-11-04. Designing controllers with predefined convergence-time bound using bounded time-varying gains. https://doi.org/10.1007/978-3-031-37089-2_3

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