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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.

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