Interplay of MPC and the Viability Kernel.
Franz Rußwurm, Willem Esterhuizen, Karl Worthmann, Stefan Streif · arXiv (Cornell University) · 2021
In this paper we consider the problem of steering a state and input constrained differential drive robot to a desired position and orientation using model-predictive control (MPC). The viability kernel of the system is determined using the theory of barriers. Moreover, local asymptotic stability of the origin under the MPC closed-loop solution without stabilizing conditions is shown. We then present numerical experiments to examine the dependency of the required prediction horizon length in MPC near the origin, as well as at parts of the kernel's boundary. It is found that the horizon increases as initial conditions approach the boundary and, in particular, non-differentiable parts of the boundary.