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Simulation-Based Reachability Analysis for High-Index Large Linear Differential Algebraic Equations [article]

Hoang-Dung Tran, Weiming Xiang, Nathaniel Hamilton, Taylor T. Johnson
2018 arXiv   pre-print
Reachability analysis for DAE systems is more complex than ODE systems, especially for high-index DAEs because they contain both a differential part (i.e., ODE) and algebraic constraints (AC).  ...  In this paper, we extend the recent scalable simulation-based reachability analysis in combination with decoupling techniques for a class of high-index large linear DAEs.  ...  Conclusion and Future Work We have studied a simulation-based reachability analysis for high-index, linear DAE systems.  ... 
arXiv:1804.03227v1 fatcat:bmuno4ddfrhllm2qiq5uvsquqq

Transient stability analysis by reachable set computation

M. Althoff, M. Cvetkovic, M. Ilic
2012 2012 3rd IEEE PES Innovative Smart Grid Technologies Europe (ISGT Europe)  
The procedure uses reachability analysis to compute the complete set of possible transient responses starting from a set of initial states, subject to a dynamics specified by differential-algebraic equations  ...  The method is constructive and fully automatic, two properties that are often hard to achieve with direct Lyapunov methods when the differential-algebraic equations are not simplified.  ...  The presented approach is versatile since it can handle any nonlinear differential-algebraic equations with index-1 property.  ... 
doi:10.1109/isgteurope.2012.6465673 dblp:conf/isgteurope/AlthoffCI12 fatcat:pu2sxxgb4nfy3odjtmypoun7be

Verification of Analog and Mixed-Signal Circuits Using Hybrid System Techniques [chapter]

Thao Dang, Alexandre Donzé, Oded Maler
2004 Lecture Notes in Computer Science  
First, we extend our algorithm for approximating sets of reachable sets for dense-time continuous systems to deal with differential algebraic equations (DAEs) and apply it to a biquad low-pass filter.  ...  algebraic equations.  ...  We thank Lars Hedrich for his help in modeling the biquad filter and for providing us with a lot of information about various techniques used for validating analog circuits.  ... 
doi:10.1007/978-3-540-30494-4_3 fatcat:k7p4dwhrxvaa5f72td7yh6rhgm

Continuous-Time Enclosures for Uncertain Implicit Differential Equations

Jai Rayjaguru, Mario E. Villanueva, Boris Houska, Benoit Chachuat
2015 IFAC-PapersOnLine  
Even though many systems in engineering are best modeled as implicit differential equations (IDEs) and differential algebraic equations (DAEs), methods for the construction of enclosures for these are  ...  This approach builds on novel high-order inclusion techniques for the solution set of algebraic equations and state-of-the-art techniques for bounding the solution of nonlinear ODEs.  ...  Eng. at ICL for the DTA. MV thanks CONACYT for doctoral scholarship.  ... 
doi:10.1016/j.ifacol.2015.08.163 fatcat:wn6bfceqpfcxtoekktsd2hk2n4

Formal and Compositional Analysis of Power Systems Using Reachable Sets

Matthias Althoff
2014 IEEE Transactions on Power Systems  
Index Terms-Reachability analysis, stability analysis, compositional analysis, power systems, transient stability analysis, uncertain energy production, differential-algebraic equations, formal verification  ...  Contrary to previous work, the presented approach does not require model simplifications when the system is described by semiexplicit, nonlinear, index-1 differential-algebraic equations.  ...  In [25] , [26] , reachability analysis is performed for a single-machine-infinite-bus system modeled by ordinary differential equations with only 2 state variables.  ... 
doi:10.1109/tpwrs.2014.2306731 fatcat:utcawqvpergfzkknqsz2qi2ra4

Dynamic Polytopic Template Approach to Robust Transient Stability Assessment [article]

Dongchan Lee, Konstantin Turitsyn
2017 arXiv   pre-print
This paper proposes a reachability analysis approach that computes bounds of the possible trajectories from uncertain initial conditions.  ...  The problem is solved with linear programming relaxation based on outer-approximations of nonlinear functions, which is scalable for large scale systems.  ...  variables for the differential equation and algebraic equations, respectively.  ... 
arXiv:1705.01189v1 fatcat:adkkszm5kzcphnjthnmmzusb6u

Computational Methods for Identification and Modelling of Complex Biological Systems

Alejandro F. Villaverde, Carlo Cosentino, Attila Gábor, Gábor Szederkényi
2019 Complexity  
The candidate models are given in the form of parameterized polynomial ordinary differential equations.  ...  of view ("Reachability Analysis of Low-Order Discrete State Reaction Networks Obeying Conservation Laws").  ...  The candidate models are given in the form of parameterized polynomial ordinary differential equations.  ... 
doi:10.1155/2019/4951650 fatcat:nadlh6m7ozhrpgyvprb7vefz3m

Review on Set-Theoretic Methods for Safety Verification and Control of Power System [article]

Yichen Zhang and Yan Li and Kevin Tomsovic and Seddik Djouadi and Meng Yue
2020 arXiv   pre-print
Set operation-based methods are more computationally efficient, while passivity-based methods provide semi-analytical expression of reachable sets, which can be readily employed for control.  ...  For instance, [63] computes reachable sets of nonlinear differential-algebraic systems under uncertain initial states and inputs.  ...  partial derivative matrix of differential equations with respect to state variables, f y = ∂f /∂y is the partial derivative matrix of differential equations with respect to the algebraic variables, g x  ... 
arXiv:2001.00080v2 fatcat:eoego43gsbbo5awzl2tin4e6qq

Symbolic-Numeric Methods for Problem Solving in CPS (Dagstuhl Seminar 16491)

Sergiy Bogomolov, Martin Fränzle, Kyoko Makino, Nacim Ramdani, Marc Herbstritt
2017 Dagstuhl Reports  
Reflecting the fundamental role numeric and mixed symbolic-numeric arguments play in the analysis, decision making, and control of cyber-physical processes, this seminar promoted crossfertilization between  ...  relevant to problem solving in cyber-physical domains: verification of numerical reactive systems such as embedded floating-point programs and hybrid systems, including novel means of error-propagation analysis  ...  high-index DAEs.  ... 
doi:10.4230/dagrep.6.12.1 dblp:journals/dagstuhl-reports/BogomolovFMR16 fatcat:sydj4slvefa7boehai7gpnfupm

Page 4471 of Mathematical Reviews Vol. , Issue 87h [page]

1987 Mathematical Reviews  
Numerical analysis of selected semilinear differential equations (Dresden, 1984), 94-104, Math. Res., 21, Akademie- Verlag, Berlin, 1984. To (numerically) integrate systems of ODEs, H. H.  ...  Math. 38 (1981/82), no. 2, 193-208; MR 82m:65065] for the integration of initial value problems in ordinary differential equations.  ... 

Efficient algorithm for computing large scale systems of differential algebraic equations [article]

Xiaolin Qin, Juan Tang, Yong Feng, Bernhard Bachmann, Peter Fritzson
2015 arXiv   pre-print
In many mathematical models of physical phenomenons and engineering fields, such as electrical circuits or mechanical multibody systems, which generate the differential algebraic equations (DAEs) systems  ...  In general, the feature of DAEs is a sparse large scale system of fully nonlinear and high index.  ...  We also give some results for large scale systems of differential algebraic equations via numerical simulation experiments.  ... 
arXiv:1506.03963v1 fatcat:j3n7vrsum5amna5o3pxn2e2rhu

Dynamic Security Analysis of Power Systems by a Sampling-Based Algorithm

Qiang Wu, T. John Koo, Yoshihiko Susuki
2018 ACM Transactions on Cyber-Physical Systems  
In this paper, we use the hybrid automaton model to describe the dynamics of a power system and mainly deal with the index-1 differential-algebraic equation models regarding the continuous dynamics in  ...  The analysis problem is formulated as a reachability problem of the associated hybrid model.  ...  The continuous-time dynamics of power systems are normally governed by a nonlinear Differential-Algebraic Equation (DAE), since the swing of rotors in generators is represented by nonlinear differential  ... 
doi:10.1145/3208093 fatcat:teiwam3rxjfrpocvy5p5kg7gom

A Successive Linear Programming Approach for Initialization and Reinitialization after Discontinuities of Differential-Algebraic Equations

Vipin Gopal, Lorenz T. Biegler
1998 SIAM Journal on Scientific Computing  
Determination of consistent initial conditions is an important aspect of the solution of differential algebraic equations (DAEs).  ...  In this paper, we present a Successive Linear Programming (SLP) approach for the solution of the DAB derivative array equations for the initialization problem.  ...  Campbell for his valuable comments and for suggesting the example in Sections 3.2 and 3.3.  ... 
doi:10.1137/s1064827596307725 fatcat:om3lwxtejzcwhbajmvl2vlxqja

Analog and Mixed-Signal Verification Using Satisfiability Solver on Discretized Models

Henry Selvaraj, Nikita Ramesh Wanjale
2017 2017 25th International Conference on Systems Engineering (ICSEng)  
The iii verification problem is first defined using the state space equations for the given circuit and applying Satisfiability Modulo Theories (SMT) solver to determine a region that encloses complete  ...  In this thesis, we present a technique for analog and mixed-signal verification targeting DC verification using Berkeley Short-channel Igfet Models (BSIM) for approximation.  ...  Obtaining DAE System Equation (1) depicts description of a nonlinear analog system in terms of a differential algebraic equation (DAE).  ... 
doi:10.1109/icseng.2017.10 dblp:conf/icseng/SelvarajW17 fatcat:xql7w557o5ckvo3qerk4siqvqi

A systems engineering approach to collaborative coordination of UAS in the NAS with safety guarantees

Jacob Moschler, Yuchen R. Zhou, John S. Baras, Jungwoo Joh
2014 2014 Integrated Communications, Navigation and Surveillance Conference (ICNS) Conference Proceedings  
We develop new fundamental methodologies for high performance and provably safe autonomous and collaborative control and operation of autonomous unmanned aerial systems (UAS) in the national airspace (  ...  We develop on-line control laws that allow for multiple UAS agents to reconfigure to different formations with proofs of safety and convergence while navigating in integrated airspace with piloted air  ...  Thanks also to Daniel Mellinger, Matthew Turpin, Kmel Robotics and Vijay Kumar's GRASP Laboratory at the University of Pennsylvania for helpful discussions of quadrotor dynamical models.  ... 
doi:10.1109/icnsurv.2014.6820021 fatcat:2ukouen5nff7xp72o36mqwo4i4
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