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Automated and Sound Synthesis of Lyapunov Functions with SMT Solvers [chapter]

Daniele Ahmed, Andrea Peruffo, Alessandro Abate
2020 Lecture Notes in Computer Science  
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]

Andrea Peruffo, Daniele Ahmed, Alessandro Abate
2020 arXiv   pre-print
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]

Andrea Peruffo, Daniele Ahmed, Alessandro Abate
2021 Lecture Notes in Computer Science  
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]

Alessandro Abate, Daniele Ahmed, Mirco Giacobbe, Andrea Peruffo
2020 arXiv   pre-print
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]

Lukas Munser, Grigory Devadze, Stefan Streif
2021 arXiv   pre-print
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]

Cees F. Verdier, Manuel Mazo Jr
2020 arXiv   pre-print
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]

Anastasiia Izycheva, Eva Darulova, Helmut Seidl
2020 Lecture Notes in Computer Science  
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)

Rupak Majumdar, Richard M. Murray, Pavithra Prabhakar, Marc Herbstritt
2014 Dagstuhl Reports  
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

Sanjit A. Seshia
2015 Proceedings of the IEEE  
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]

Fedor Shmarov and Sadegh Soudjani and Nicola Paoletti and Ezio Bartocci and Shan Lin and Scott A. Smolka and Paolo Zuliani
2019 arXiv   pre-print
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]

Sicun Gao, James Kapinski, Jyotirmoy Deshmukh, Nima Roohi, Armando Solar-Lezama, Nikos Arechiga, Soonho Kong
2019 Lecture Notes in Computer Science  
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]

Chuchu Fan, Kristina Miller, Sayan Mitra
2020 Lecture Notes in Computer Science  
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]

Charles Dawson, Zengyi Qin, Sicun Gao, Chuchu Fan
2021 arXiv   pre-print
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

Alessandro Abate, Iury Bessa, Lucas Cordeiro, Cristina David, Pascal Kesseli, Daniel Kroening, Elizabeth Polgreen
2019 Acta Informatica  
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

Fedor Shmarov, Sadegh Soudjani, Nicola Paoletti, Ezio Bartocci, Shan Lin, Scott A. Smolka, Paolo Zuliani.
2020 IEEE Access  
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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