27.01.2025 16:15 Konrad Reichel:
Trajectory-wise Time Rescaling in Controllability and Optimal Control TheoryMI 03.06.011 (Boltzmannstr. 3, 85748 Garching)

Similar to ODEs, time-continuous control systems have trajectory-wise time rescaled solutions when a state-dependent scalar field is multiplied with the vector field of the control system and the time variable of the vector field is rescaled appropriately. In my talk, I will give an introduction about control systems, controllability and optimal control. I will explain how known results about controllability like the Kalman criterion can be extended by a suitable choice of the control function in combination with trajectory-wise time rescaling. This strategy has its limits with regard to Chow's theorem1 for affine nonlinear control systems. Finally, I will present how optimal control problems with a fixed time domain change under trajectory-wise time rescaling and that the new optimizer and the new adjoint solution of the necessary conditions from Pontryagin's maximum principle² are time-rescaled versions of the original optimizer and adjoint solution.

[1] D. Cheng, X. Hu, and T. Shen. Analysis and Design of Nonlinear Control Systems. Springer Berlin, Heidelberg, 2011. Theorem 3.5 [2] R. Vinter. Optimal Control. Birkhäuser Boston, MA, 2010. Theorem 8.7.1