Reach-Avoid Analysis for Delay Differential Equations

Bai, Xue; Bai, Ye; Zhan, Naijun; Liu, Wenyou; Li, Jiao

doi:10.1109/cdc45484.2021.9683555

Cited by 1 publication

(2 citation statements)

References 37 publications

(89 reference statements)

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“…In this work we extend the aforementioned exponential and asymptotic control guidance-barrier functions for deterministic systems to stochastic systems for synthesizing reach-avoid controllers such that the system enters a target set eventually while staying inside a specified safe set before the first target hitting time in probability. Among these two extensions, the asymptotic control guidance-barrier function is constructed based on guidance-barrier functions in [37], which was developed to inner-approximating reach-avoid sets for stochastic systems.…”

Section: Related Workmentioning

confidence: 99%

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Reach-avoid Controllers Synthesis for Safety Critical Systems

Bai¹

2023

Preprint

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In this paper we propose sufficient conditions to synthesizing reach-avoid controllers for deterministic systems modelled by ordinary differential equations and stochastic systems modeled by stochastic differential equations based on the notion of control guidance-barrier functions. We begin with considering deterministic systems. Given an open safe set, a target set and a nominal controller, we attempt to synthesize a reach-avoid controller, which modifies the nominal controller in a minimal way enforcing the reach-avoid objective, i.e., the system will enter the target set eventually while staying inside the safe set before the first target hitting time. Three control guidance-barrier functions are developed and three corresponding conditions for synthesizing reach-avoid controllers are constructed, which get progressively weaker and thus facilitate the optimal controller design. The first and second ones are termed exponential and asymptotic control guidance-barrier functions, which guarantee that every trajectory starting from the safe set will enter the target set respectively at an exponential rate and in an asymptotic way. However, it is observed that these two control guidancebarrier functions have one condition in common of enforcing invariance of its every positive sublevel set until the system enters the target set, which is strict and thus limits the space of admissible controllers. Consequently, a lax control guidancebarrier function is further developed such that only the safe set set is an invariance before the system enters the target set, expanding the space of admissible control inputs. Then, we extend the methodologies for deterministic systems to stochastic systems, which synthesize reach-avoid controllers in the probabilistic setting. Finally, several numerical examples demonstrate the performance of proposed methods.

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Section: Related Workmentioning

confidence: 99%

“…The conclusion can be assured by following arguments in Theorem 5 with small modifications. Assume that x 0 ∈ C. According to Lemma 1 in [37],…”

Section: The Proof Of Propositionmentioning

confidence: 99%