A specified-time control framework for control-affine systems and rigid bodies: a time-rescaling approach.

*(English)*Zbl 1418.93205Summary: 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 |