[2203.03865] A Second-Order Reachable Sets Computation Scheme via a Cauchy-Type Variational Hamilton-Jacobi-Isaacs Equation
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Electrical Engineering and Systems Science > Systems and Control

arXiv:2203.03865 (eess)
[Submitted on 8 Mar 2022 (v1), last revised 22 Jun 2022 (this version, v2)]

Title:A Second-Order Reachable Sets Computation Scheme via a Cauchy-Type Variational Hamilton-Jacobi-Isaacs Equation

Authors:Lekan Molu, Ian Abraham, Sylvia Herbert
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Abstract:Motivated by the scalability limitations of Eulerian methods for variational Hamilton-Jacobi-Isaacs (HJI) formulations that provide a least restrictive controller in problems that involve state or input constraints under a worst-possible disturbance, we introduce a second-order, successive sweep algorithm for computing the zero sublevel sets of a popular reachability value functional. Under sufficient HJI partial differential equation regularity and continuity assumption throughout the state space, we show that with state feedback control under the worst-possible disturbance, we can compute the state set that are reachable within a prescribed verification time bound.
Comments: 6 pages
Subjects: Systems and Control (eess.SY)
Cite as: arXiv:2203.03865 [eess.SY]
  (or arXiv:2203.03865v2 [eess.SY] for this version)
  https://doi.org/10.48550/arXiv.2203.03865

Submission history

From: Olalekan Ogunmolu [view email]
[v1] Tue, 8 Mar 2022 06:03:39 UTC (160 KB)
[v2] Wed, 22 Jun 2022 11:50:06 UTC (160 KB)
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