Scalable Safety-Preserving Robust Control Synthesis for Continuous-Time Linear Systems

Shahab Kaynama; Ian M. Mitchell; Meeko Oishi; Guy A. Dumont

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arXiv · 1312.3399

Scalable Safety-Preserving Robust Control Synthesis for Continuous-Time Linear Systems

Shahab Kaynama·Ian M. Mitchell·Meeko Oishi·Guy A. Dumont

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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.

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BibTeX RIS

Shahab Kaynama, Ian M. Mitchell, Meeko Oishi, Guy A. Dumont. 2013-12-12. Scalable Safety-Preserving Robust Control Synthesis for Continuous-Time Linear Systems. https://arxiv.org/abs/1312.3399

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