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A specified-time control framework for control-affine systems and rigid bodies: a time-rescaling approach. (English) Zbl 1418.93205
Summary: This paper addresses the specified-time control problem for control-affine systems and rigid bodies, wherein the specified-time duration can be designed in advance according to the task requirements. By using the time-rescaling approach, a novel framework to solve the specified-time control problem is proposed, and the original systems are converted to the transformation systems based on which the specified-time control laws for both control-affine systems and rigid bodies are studied. Compared with the existing approaches, our proposed specified-time control laws can be derived from the known stabilization control laws. To our best knowledge, it is the first time that transformation system-based specified-time control framework for control-affine system and rigid body dynamics is proposed. To further improve the convergence performance of specified-time control, a finite-time attitude synchronization control law for rigid bodies on rotation matrices is proposed, and thereby, the finite-time-based specified-time control law is designed eventually. In the end, numerical simulations and SimMechanics experiments are provided to illustrate effectiveness of the theoretical results.

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93B17 Transformations
93C05 Linear systems in control theory
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