Auditor Product and Controller Synthesis for Nondeterministic Transition Systems With Practical LTL Specifications

Zibaeenejad, M. H.; Liu, Jun

doi:10.1109/tac.2019.2953452

Cited by 5 publications

(5 citation statements)

References 24 publications

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“…By the definition of T, if [t] = F [i], any x t ∈ A l ν [i] for S 0 can trigger the transition in A ϕ to F [j] within l steps. By (20),…”

Section: B Robustly Complete Control Synthesismentioning

confidence: 97%

“…Consider arbitrary t ∈ N and arbitrary ν ∈ {1, • • • , N Z }. We first discuss two situations based on (20) and the definition of T δ in ( 12):…”

Section: B Robustly Complete Control Synthesismentioning

confidence: 99%

“…While the restriction to DBA specifications can significantly reduce the complexity, a promising finite abstraction of nonlinear dynamics is usually huge in size, and control synthesis on a product system would still be intractable because the number of states is the multiplication of the sizes of both the abstraction and the DBA. In [20], the authors investigated how to incrementally take product between an abstraction and multiple DBAs. While this can potentially reduce the overall product system size, it does not directly provides a reduction in the size of the specification.…”

Section: Introduction a Background And Motivationmentioning

confidence: 99%

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A Specification-Guided Framework for Temporal Logic Control of Nonlinear Systems

Li,

Sun,

Liu

2021

Preprint

Self Cite

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This paper proposes a specification-guided framework for control of nonlinear systems with linear temporal logic (LTL) specifications. In contrast with well-known abstractionbased methods, the proposed framework directly characterizes the winning set, i.e., the set of initial conditions from which a given LTL formula can be realized, over the continuous state space of the system via a monotonic operator. Following this characterization, an algorithm is proposed to practically approximate the operator via an adaptive interval subdivision scheme, which yields a finite-memory control strategy. We show that the proposed algorithm is sound for full LTL specifications, and robustly complete for specifications recognizable by deterministic B üchi automata (DBA), the latter in the sense that control strategies can be found whenever the given specification can be satisfied with additional bounded disturbances. Without having to compute and store the abstraction and the resulting product system with the DBA, the proposed method is more memory efficient, which is demonstrated by complexity analysis and performance tests. A pre-processing stage is also devised to reduce computational cost via a decomposition of the specification. We show that the proposed method can effectively solve real-world control problems such as jet engine compressor control and motion planning for manipulators and mobile robots.

show abstract

“…By the definition of T, if [t] = F [i], any x t ∈ A l ν [i] for S 0 can trigger the transition in A ϕ to F [j] within l steps. By (20),…”

Section: B Robustly Complete Control Synthesismentioning

confidence: 97%

“…Consider arbitrary t ∈ N and arbitrary ν ∈ {1, • • • , N Z }. We first discuss two situations based on (20) and the definition of T δ in ( 12):…”

Section: B Robustly Complete Control Synthesismentioning

confidence: 99%

Section: Introduction a Background And Motivationmentioning

confidence: 99%

See 1 more Smart Citation

A Specification-Guided Framework for Temporal Logic Control of Nonlinear Systems

Li,

Sun,

Liu

2021

Preprint

Self Cite

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show abstract

“….19) in which ε x and ε u are computed based on γ = ε as in Lemma 4.3, with ε as in (A. 18). Accordingly, one can verify .20) by leveraging Lemma 4.…”

Section: Appendix a Proof Of Statementsmentioning

confidence: 99%

“…[14][15][16]), by leveraging a counterexample-guided abstraction refinement framework [17], or by applying a specification-guided framework (see e.g. [18][19][20]). However, these results require either specific properties of the systems (e.g., dissipativity, mixed-monotonicity, etc.…”

Section: Introductionmentioning

confidence: 99%

Formal Synthesis of Controllers for Uncertain Linear Systems against $ω$-Regular Properties: A Set-based Approach

Zhong¹,

Caccamo²

2021

Preprint

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In this paper, we present how to synthesize controllers to enforce ω-regular properties over linear control systems affected by bounded disturbances. In particular, these controllers are synthesized based on socalled hybrid controlled invariant (HCI) sets. To compute these sets, we first construct a product system using the linear control system and the deterministic Rabin automata (DRA) modeling the negation of the desired property. Then, we compute the maximal HCI set over the state set of the product system by leveraging a set-based approach. To ensure termination of the computation of the HCI sets within a finite number of iterations, we also propose two iterative schemes to compute approximations of the maximal HCI set. Finally, we show the effectiveness of our approach on two case studies.

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A Specification-Guided Framework for Temporal Logic Control of Nonlinear Systems

Sun

2023

IEEE Trans. Automat. Contr.

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Auditor Product and Controller Synthesis for Nondeterministic Transition Systems With Practical LTL Specifications

Cited by 5 publications

References 24 publications

A Specification-Guided Framework for Temporal Logic Control of Nonlinear Systems

A Specification-Guided Framework for Temporal Logic Control of Nonlinear Systems

Formal Synthesis of Controllers for Uncertain Linear Systems against $ω$-Regular Properties: A Set-based Approach

A Specification-Guided Framework for Temporal Logic Control of Nonlinear Systems

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