Continuous Approximations of Projected Dynamical Systems via Control Barrier Functions
CoRR(2024)
Abstract
Projected Dynamical Systems (PDSs) form a class of discontinuous constrained
dynamical systems, and have been used widely to solve optimization problems and
variational inequalities. Recently, they have also gained significant attention
for control purposes, such as high-performance integrators, saturated control
and feedback optimization. In this work, we establish that locally Lipschitz
continuous dynamics, involving Control Barrier Functions (CBFs), namely
CBF-based dynamics, approximate PDSs. Specifically, we prove that trajectories
of CBF-based dynamics uniformly converge to trajectories of PDSs, as a
CBF-parameter is taken to infinity. Towards this, we also prove that CBF-based
dynamics are perturbations of PDSs, with quantitative bounds on the
perturbation. Our results pave the way to implement discontinuous PDS-based
controllers in a continuous fashion, employing CBFs. Moreover, they can be
employed to numerically simulate PDSs, overcoming disadvantages of existing
discretization schemes, such as computing projections to possibly non-convex
sets. Finally, this bridge between CBFs and PDSs may yield other potential
benefits, including novel insights on stability.
MoreTranslated text
AI Read Science
Must-Reading Tree
Example
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined