Resumo

JIMENEZ-RODRIGUEZ, Esteban; SANCHEZ-TORRES, Juan Diego  e  LOUKIANOV, Alexander G.. Optimal Predefined-Time Stabilization for a Class of Linear Systems. EAC [online]. 2017, vol.38, n.1, pp.90-101. ISSN 1815-5928.

This paper addresses the problem of optimal predefined-time stability. Predefined-time stable systems are a class of fixed-time stable dynamical systems for which a bound of the settling-time function can be defined a priori as an explicit parameter of the system. Sufficient conditions for a controller to solve the optimal predefined-time stabilization problem for a given nonlinear system are provided. Furthermore, for nonlinear affine systems and a specific performance index, a family of inverse optimal predefined-time stabilizing controllers is derived. This class of controllers is applied to the inverse predefined-time optimization of the sliding manifold reaching phase in linear systems, jointly with the idea of integral sliding mode control to ensure robustness. Finally, as a study case, the developed methods are applied to an uncertain satellite system, and numerical simulations are carried out to show their behavior.

Palavras-chave : Hamilton-Jacobi-Bellman Equation; Lyapunov Functions; Optimal Control; Predefined-Time Stability.

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