Scalable Safety-Preserving Robust Control Synthesis for Continuous-Time Linear Systems
Abstract
We present a scalable set-valued safety-preserving controller for constrained continuous-time linear time-invariant (LTI) systems subject to additive, unknown but bounded disturbance or uncertainty. The approach relies upon a conservative approximation of the discriminating kernel using robust maximal reachable sets---an extension of our earlier work on computation of the viability kernel for high-dimensional systems. Based on ellipsoidal techniques for reachability, a piecewise ellipsoidal algorithm with polynomial complexity is described that under-approximates the discriminating kernel under LTI dynamics. This precomputed piecewise ellipsoidal set is then used online to synthesize a permissive state-feedback safety-preserving controller. The controller is modeled as a hybrid automaton and can be formulated such that under certain conditions the resulting control signal is continuous across its transitions. We show the performance of the controller on a twelve-dimensional flight envelope protection problem for a quadrotor with actuation saturation and unknown wind disturbances.
Keywords
Cite
@article{arxiv.1312.3399,
title = {Scalable Safety-Preserving Robust Control Synthesis for Continuous-Time Linear Systems},
author = {Shahab Kaynama and Ian M. Mitchell and Meeko Oishi and Guy A. Dumont},
journal= {arXiv preprint arXiv:1312.3399},
year = {2013}
}