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A scalable algebraic method to infer quadratic invariants of switched systems

Xavier Allamigeon, Stéphane Gaubert, Eric Goubault, Sylvie Putot, Nikolas Stott
2015 2015 International Conference on Embedded Software (EMSOFT)  
We finally develop a fast non-linear power-type algorithm, which allows one to determine sound quadratic invariants on switched systems in a tractable way, by solving fixed point problems over the space  ...  We present a new numerical abstract domain based on ellipsoids designed for the formal verification of switched linear systems.  ...  -THALES -FX -DGA -DASSAULT AVIATION -DCNS Research -ENSTA ParisTech -Télécom ParisTech -Fondation Paris-Tech -FDO ENSTA and by the PGMO programme of EDF and FMJH.  ... 
doi:10.1109/emsoft.2015.7318262 dblp:conf/emsoft/AllamigeonGGPS15 fatcat:6ro5ttp3anbmvhcd5zzohilsce

A Scalable Algebraic Method to Infer Quadratic Invariants of Switched Systems

Xavier Allamigeon, Stéphane Gaubert, Nikolas Stott, Éric Goubault, Sylvie Putot
2016 ACM Transactions on Embedded Computing Systems  
We finally develop a fast non-linear power-type algorithm, which allows one to determine sound quadratic invariants on switched systems in a tractable way, by solving fixed point problems over the space  ...  We present a new numerical abstract domain based on ellipsoids designed for the formal verification of switched linear systems.  ...  -THALES -FX -DGA -DASSAULT AVIATION -DCNS Research -ENSTA ParisTech -Télécom ParisTech -Fondation Paris-Tech -FDO ENSTA and by the PGMO programme of EDF and FMJH.  ... 
doi:10.1145/2932187 fatcat:zesxfsxgpbesbkspnnfjmhdg4y

Synthesizing Switching Controllers for Hybrid Systems by Generating Invariants [chapter]

Hengjun Zhao, Naijun Zhan, Deepak Kapur
2013 Lecture Notes in Computer Science  
We extend a template-based approach for synthesizing switching controllers for semi-algebraic hybrid systems, in which all expressions are polynomials.  ...  Our synthesis method is relatively complete with regard to a given family of predefined templates.  ...  Jiang Liu for his great contribution to our previous joint work on invariant generation. We also thank Dr. Matthias Horbach, Mr.  ... 
doi:10.1007/978-3-642-39698-4_22 fatcat:na6ge7pjandallod5rdqksmyd4

Synthesizing Switching Controllers for Hybrid Systems by Continuous Invariant Generation [article]

Deepak Kapur, Naijun Zhan, Hengjun Zhao
2013 arXiv   pre-print
We extend a template-based approach for synthesizing switching controllers for semi-algebraic hybrid systems, in which all expressions are polynomials.  ...  Our synthesis method is relatively complete with regard to a given family of predefined templates.  ...  Jiang Liu for his contribution to our previous joint work on invariant generation. We also thank Dr. Matthias Horbach and Mr. ThanhVu Nguyen for their valuable comments on our old drafts.  ... 
arXiv:1304.0825v1 fatcat:ygwraqcmbvbwbdlekx2anqcfni

Guest Editorial for Special Issue of ESWEEK 2015

Petru Eles, Rolf Ernst
2016 ACM Transactions on Embedded Computing Systems  
The authors of the eight papers nominated as Best Paper Candidates for the three ESWEEK conferences have been invited to submit extended versions of their work to this special issue.  ...  of the Internet of Things with a strong impact on technology and market development.  ...  The authors of "A Scalable Algebraic Method to Infer Quadratic Invariants of Switched Systems" propose a new technique for efficient abstract interpretation-based verification of switched linear systems  ... 
doi:10.1145/2968218 fatcat:was6e46scvcbfmlbdirffmdwdu

Stability Domains for Quadratic-Bilinear Reduced-Order Models [article]

Boris Kramer
2021 arXiv   pre-print
We propose a computational approach to estimate the stability domain of quadratic-bilinear reduced-order models (ROMs), which are low-dimensional approximations of large-scale dynamical systems.  ...  We do not assume a specific ROM method, so a particular appeal is that the approach is applicable to quadratic-bilinear models obtained via data-driven approaches, where ROM stability properties cannot  ...  For linear time-invariant systems, the LQG-balancing framework finds a coordinate transformation (and subsequent reduction) so that the LQG solutions to the algebraic Riccati equations of the ROM are equal  ... 
arXiv:2009.02769v2 fatcat:uvt5t7gx6jebrdekzwu7cau6o4

Verification and synthesis using real quantifier elimination

Thomas Sturm, Ashish Tiwari
2011 Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11  
We present the application of real quantifier elimination to formal verification and synthesis of continuous and switched dynamical systems.  ...  Through a series of case studies, we show how first-order formulas over the reals arise when formally analyzing models of complex control systems.  ...  Acknowledgments We would like to thank Andreas Weber for encouraging and supporting the first author in visiting SRI.  ... 
doi:10.1145/1993886.1993935 dblp:conf/issac/SturmT11 fatcat:jeyfoaeqcncznflip2fzymnzl4

2018 Index IEEE Transactions on Automatic Control Vol. 63

2018 IEEE Transactions on Automatic Control  
., +, TAC Sept. 2018 2867-2882 Convergence of numerical methods A Distributed Observer for a Time-Invariant Linear System.  ...  Benallegue, A., +, TAC Nov. 2018 3986-3993 Inference mechanisms Decentralized Supervisory Control of Discrete Event Systems: An Arbores- cent Architecture to Realize Inference-Based Control.  ... 
doi:10.1109/tac.2019.2896796 fatcat:bwmqasulnzbwhin5hv4547ypfe

A dynamic systems approach to fermions and their relation to spins

Zoltán Zimborás, Robert Zeier, Michael Keyl, Thomas Schulte-Herbrüggen
2014 EPJ Quantum Technology  
We determine the respective dynamic system Lie algebras to express reachable sets of pure (and mixed) states by explicit orbit manifolds.  ...  Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory.  ...  It paves the way for optimal-control methods to be applied to fermionic systems and leads to a plethora of new results presented here.  ... 
doi:10.1140/epjqt11 fatcat:opcnsrawi5dkbomuyheayybwmu

The Daikon system for dynamic detection of likely invariants

Michael D. Ernst, Jeff H. Perkins, Philip J. Guo, Stephen McCamant, Carlos Pacheco, Matthew S. Tschantz, Chen Xiao
2007 Science of Computer Programming  
Invariants can be useful in program understanding and a host of other applications.  ...  Daikon is an implementation of dynamic detection of likely invariants; that is, the Daikon invariant detector reports likely program invariants.  ...  Note that while Daikon is the name of the entire system, it is also used to refer specifically to the inference engine.  ... 
doi:10.1016/j.scico.2007.01.015 fatcat:v4ciuqlcazeolf6mdrfxoozqiy

A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates

Stephen Prajna, Ali Jadbabaie, George J. Pappas
2007 IEEE Transactions on Automatic Control  
Some examples are provided to illustrate the use of the method.  ...  In the worst-case setting, a function of state termed barrier certificate is used to certify that all trajectories of the system starting from a given initial set do not enter an unsafe region.  ...  Hence, we expect our method to be more scalable than many other existing methods.  ... 
doi:10.1109/tac.2007.902736 fatcat:idwocxaltbhrfjyfgm2hszykjm

SOS-Convex Lyapunov Functions and Stability of Difference Inclusions [article]

Amir Ali Ahmadi, Raphael M. Jungers
2018 arXiv   pre-print
In the case of switched nonlinear systems, we prove that existence of a common non-convex Lyapunov function does not imply stability, but existence of a common convex Lyapunov function does.  ...  We then provide a semidefinite programming-based procedure for computing a full-dimensional subset of the region of attraction of equilibrium points of switched polynomial systems, under the condition  ...  The authors are thankful to Alexandre Megretski for insightful discussions around convex Lyapunov functions.  ... 
arXiv:1803.02070v1 fatcat:kmmqoqyvljf63phxggfdbcu73e

Formal Modelling, Analysis and Verification of Hybrid Systems [chapter]

Naijun Zhan, Shuling Wang, Hengjun Zhao
2013 Lecture Notes in Computer Science  
In addition, based on our invariant generation approach, we consider how to synthesize a switching logic for a considered hybrid system by reduction to constraint solving, to meet a given safety, liveness  ...  For deductive verification of hybrid systems, a complete approach to generating polynomial invariants for polynomial hybrid systems is proposed; meanwhile, a theorem prover for HHL that can provide tool  ...  Jiang Liu is one of the major contributors to the work on invariant generation and stability analysis of hybrid systems; the part on (optimal) controller synthesis of hybrid systems is joint work with  ... 
doi:10.1007/978-3-642-39721-9_5 fatcat:vcw3zr5b5vhi7izotaf5pbmige

7 Data-driven methods for reduced-order modeling [chapter]

2020 Snapshot-Based Methods and Algorithms  
These methods aim to discover and exploit a relatively small subset of the full highdimensional state space where low-dimensional models can be used to describe the evolution of the system.  ...  These methods can be used in a nonintrusive, equation-free manner for improved computational performance on parametric PDE systems.  ...  Moreover, the technique can be integrated with randomized linear algebra decomposition methods to achieve further enhancements in computational speed and scalability.  ... 
doi:10.1515/9783110671490-007 fatcat:wc6wctzwnfcnznb4scr6s5lyou

Large Scale Model Predictive Control with Neural Networks and Primal Active Sets [article]

Steven W. Chen, Tianyu Wang, Nikolay Atanasov, Vijay Kumar, Manfred Morari
2021 arXiv   pre-print
Our method achieves a 2x reduction in online inference time compared to the best method in a benchmark suite of different solver and initialization strategies.  ...  The neural network is trained with a primal-dual loss function, aiming to generate control sequences that are primal feasible and meet a desired level of suboptimality.  ...  We are grateful to Elizabeth Wong for answering our many questions about SQOPT and providing guidance on initialization and accurate timing.  ... 
arXiv:1910.10835v2 fatcat:x4z2r3p75bdadh4jv7xdqoldjy
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