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Automated and Sound Synthesis of Lyapunov Functions with SMT Solvers
[chapter]
2020
Lecture Notes in Computer Science
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In this paper we employ SMT solvers to soundly synthesise Lyapunov functions that assert the stability of a given dynamical model. ...
soundness proof for the generated Lyapunov functions and their domains of validity. ...
Conclusions and Future Work In this work, we have studied the problem of automated and sound synthesis of Lyapunov functions. ...
doi:10.1007/978-3-030-45190-5_6
fatcat:o4cwzmdekvgcdjw2h4m3yksbvi
Automated and Formal Synthesis of Neural Barrier Certificates for Dynamical Models
[article]
2020
arXiv
pre-print
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We introduce an automated, formal, counterexample-based approach to synthesise Barrier Certificates (BC) for the safety verification of continuous and hybrid dynamical models. ...
We compare the approach against state-of-the-art techniques, over polynomial and non-polynomial dynamical models: the outcomes show that we can synthesise sound BCs up to two orders of magnitude faster ...
and sound Lyapunov function synthesis: in [26] Lyapunov functions are soundly found within parametric templates, by constructing a system of linear inequality constraints over unknown coefficients ...
arXiv:2007.03251v2
fatcat:voq7prf6fzhslodibxnt3httqq
Automated and Formal Synthesis of Neural Barrier Certificates for Dynamical Models
[chapter]
2021
Lecture Notes in Computer Science
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AbstractWe introduce an automated, formal, counterexample-based approach to synthesise Barrier Certificates (BC) for the safety verification of continuous and hybrid dynamical models. ...
We compare the approach against state-of-the-art techniques, over polynomial and non-polynomial dynamical models: the outcomes show that we can synthesise sound BCs up to two orders of magnitude faster ...
and sound Lyapunov function synthesis: in [27] Lyapunov functions are soundly found within parametric templates, by constructing a system of linear inequality constraints over unknown coefficients ...
doi:10.1007/978-3-030-72016-2_20
fatcat:bpbllc6omzedhowy3gvwextkjq
Formal Synthesis of Lyapunov Neural Networks
[article]
2020
arXiv
pre-print
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We propose an automatic and formally sound method for synthesising Lyapunov functions for the asymptotic stability of autonomous non-linear systems. ...
Traditional methods are either analytical and require manual effort or are numerical but lack of formal soundness. ...
In particular, we present a novel method for the automated and formal synthesis of Lyapunov functions. Lyapunov functions are formal certificates for the asymptotic stability of ODEs. ...
arXiv:2003.08910v2
fatcat:7a7mzu3t2nckpkbauhgyq67knm
Synthesis of Lyapunov Functions using Formal Verification
[article]
2021
arXiv
pre-print
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Recent employments of SMT solvers within the Lyapunov function synthesis provided effective tools for automated construction of Lyapunov functions alongside with sound computer-assisted certificates. ...
In the present work, we extend the SMT-based synthesis approach for wider classes of continuous and discrete-time systems. ...
Counterexample based synthesis of a Lyapunov function.
Fig. 2 . 2 Fig. 2. Algorithm counterexample based synthesis of a Lyapunov function. ...
arXiv:2112.01835v1
fatcat:y4erhzxp55cndhodhvl6nudx7q
Formal controller synthesis for hybrid systems using genetic programming
[article]
2020
arXiv
pre-print
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These candidate Lyapunov-like functions are used to formally verify the control specification, and their correctness is proven using a Satisfiability Modulo Theories solver. ...
This paper proposes a framework for automatic formal controller synthesis for general hybrid systems with a subset of safety and reachability specifications. ...
The proposed method differs from previous work on GP for Lyapunov function synthesis in e.g. [48, 49] and/or controller synthesis in e.g. ...
arXiv:2003.14322v2
fatcat:swoofpfrcrbddd2vxacyfgo3ua
Counterexample- and Simulation-Guided Floating-Point Loop Invariant Synthesis
[chapter]
2020
Lecture Notes in Computer Science
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AbstractWe present an automated procedure for synthesizing sound inductive invariants for floating-point numerical loops. ...
Such invariants are a prerequisite for reasoning about the safety and roundoff errors of floating-point programs. ...
Since such an automated method does not exist for nonlinear functions, SMT-AI is limited to linear loops. ...
doi:10.1007/978-3-030-65474-0_8
fatcat:g62rmena2ranrmrobp6jmwqhde
Verification of Cyber-Physical Systems (Dagstuhl Seminar 14122)
2014
Dagstuhl Reports
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This report documents the program and the outcomes of Dagstuhl Seminar 14122 "Verification of Cyber-Physical Systems". ...
Cyber-physical systems refer to a new genre of engineered systems consisting of a tight coupling between computation, communication and physical entities. ...
and nonlinear SMT solvers. ...
doi:10.4230/dagrep.4.3.85
dblp:journals/dagstuhl-reports/MajumdarMP14
fatcat:qm5epthwvbgf5mk74me42qcpei
Combining Induction, Deduction, and Structure for Verification and Synthesis
2015
Proceedings of the IEEE
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We present a formalization of such an integration, show how it can tackle hard problems in verification and synthesis, and outline directions for future work. ...
Chief amongst these are environment modeling, incompleteness in specifications, and the hardness of underlying decision problems. ...
Acknowledgments This article is a result of ideas synthesized and verified (!) over many years in collaboration with several students and colleagues. ...
doi:10.1109/jproc.2015.2471838
fatcat:cfj3tcy3njg3debcuxzqjye2ii
Automated Synthesis of Safe Digital Controllers for Sampled-Data Stochastic Nonlinear Systems
[article]
2019
arXiv
pre-print
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We present a new method for the automated synthesis of digital controllers with formal safety guarantees for systems with nonlinear dynamics, noisy output measurements, and stochastic disturbances. ...
In the subsequent verification step, we use a validated solver based on SMT (Satisfiability Modulo Theories) to compute a numerically and statistically valid confidence interval for the safety probability ...
CONCLUSIONSThe synthesis of digital controllers for cyber-physical systems with nonlinear and stochastic dynamics is a challenging problem, and for such systems, no automated methods currently exist for ...
arXiv:1901.03315v1
fatcat:ecahc2u6wjfondsyqxblf3pat4
Numerically-Robust Inductive Proof Rules for Continuous Dynamical Systems
[chapter]
2019
Lecture Notes in Computer Science
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These induction rules robustify standard notions of Lyapunov functions and barrier certificates so that they can tolerate small numerical errors. ...
In this way, numerically-driven decision procedures can establish a sound and relative-complete proof system for unbounded properties of very general nonlinear systems. ...
In this way, we can rely on various numerically-driven SMT solvers to establish a sound and relative-complete proof systems for unbounded stability and safety properties of highly nonlinear dynamical systems ...
doi:10.1007/978-3-030-25543-5_9
fatcat:33dacwjf7jgonlcsjxdezghrbi
Fast and Guaranteed Safe Controller Synthesis for Nonlinear Vehicle Models
[chapter]
2020
Lecture Notes in Computer Science
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We address the problem of synthesizing a controller for nonlinear systems with reach-avoid requirements. ...
We show that FACTEST can find controllers for four vehicle models (3-6 dimensional state space and 2-4 dimensional input space) across eight scenarios (with up to 22 obstacles), all with running time at ...
SMT solvers (see Sect. 6 for empirical results). ...
doi:10.1007/978-3-030-53288-8_31
fatcat:oqr7zo5iz5dxda6rc64qkpygey
Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions
[article]
2021
arXiv
pre-print
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We take inspiration from robust convex optimization and Lyapunov theory to define robust control Lyapunov barrier functions that generalize despite model uncertainty. ...
We demonstrate our approach in simulation on problems including car trajectory tracking, nonlinear control with obstacle avoidance, satellite rendezvous with safety constraints, and flight control with ...
article solely reflects the opinions and conclusions of its authors and not any NASA entity, DSTA Singapore, or the Singapore Government. ...
arXiv:2109.06697v2
fatcat:3nfpe2ijqffmrfsptm233lhlhi
Automated formal synthesis of provably safe digital controllers for continuous plants
2019
Acta Informatica
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We present a sound and automated approach to synthesizing safe, digital controllers for physical plants represented as time-invariant models. ...
The synthesis precisely accounts for the effects of finite-precision arithmetic introduced by the controller. ...
To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. ...
doi:10.1007/s00236-019-00359-1
pmid:32189718
pmcid:PMC7056743
fatcat:eepm6zg2cvb3tlkz7w4r3ppmxe
Automated Synthesis of Safe Digital Controllers for Sampled-Data Stochastic Nonlinear Systems
2020
IEEE Access
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Yet another issue is the lack of automated synthesis techniques with provable guarantees, especially for properties beyond stability (e.g., safety) for nonlinear stochastic systems. ...
of the system with a nonvalidated ordinary differential equation (ODE) solver. ...
.: Automated Synthesis of Safe Digital Controllers for Sampled-Data Stochastic Nonlinear Systems whereQ 1 := G T 1 Q 1 G 1 ,Q 2 := (1 + µ) 2 Q 2 , and κ := T T −1 ĥ 1 (τ ) 2 +ĥ 2 (τ ) 2 + 1, withĥ 1 (τ ...
doi:10.1109/access.2020.3028476
fatcat:pimzbg7gwrasljigrfk3y6w5tq
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