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Reachability analysis of linear hybrid systems via block decomposition [article]

Sergiy Bogomolov, Marcelo Forets, Goran Frehse, Kostiantyn Potomkin, Christian Schilling
2020 arXiv   pre-print
Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems.  ...  Reachability analysis works by iteratively applying continuous and discrete post operators to compute states reachable according to continuous and discrete dynamics, respectively.  ...  Reachability analysis of linear hybrid systems We now discuss a standard reachability algorithm for hybrid systems.  ... 
arXiv:1905.02458v3 fatcat:yvcr72wkabg5vbhmkjqvsfq2mm

Constructing verification models of nonlinear Simulink systems via syntactic hybridization

Nikolaos Kekatos, Marcelo Forets, Goran Frehse
2017 2017 IEEE 56th Annual Conference on Decision and Control (CDC)  
The focus is on set-based reachability analysis and on control systems that are described by hybrid dynamics and nonlinear components.  ...  If only a small subset of the partitions is reachable, the bottleneck of having excessively large PWA models can be avoided by composing the model on-the-fly during the reachability analysis.  ...  The focus is on set-based reachability analysis and on control systems that are described by hybrid dynamics and nonlinear components.  ... 
doi:10.1109/cdc.2017.8263907 dblp:conf/cdc/KekatosFF17 fatcat:3mjjeu6y5vdftifdm2zuw6c6mm

Complexity reduction through a Schur-based decomposition for reachability analysis of linear time-invariant systems

Shahab Kaynama, Meeko Oishi
2011 International Journal of Control  
We present a method for complexity reduction in reachability analysis and controller synthesis via a Schur-based decomposition for LTI systems.  ...  The decomposition yields either decoupled or weakly-coupled subsystems, each of lower dimension than the original system.  ...  INTRODUCTION Reachability analysis is key for verification and controller synthesis of continuous and hybrid dynamical systems, yet a major obstacle in employing reachability analysis is the "curse of  ... 
doi:10.1080/00207179.2010.543703 fatcat:mmze3joyjrecvpsdgzmpgfts3i

Schur-based decomposition for reachability analysis of linear time-invariant systems

Shahab Kaynama, Meeko Oishi
2009 Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference  
We present a method for complexity reduction in reachability analysis and controller synthesis via a Schur-based decomposition for LTI systems.  ...  The decomposition yields either decoupled or weakly-coupled subsystems, each of lower dimension than the original system.  ...  INTRODUCTION Reachability analysis is key for verification and controller synthesis of continuous and hybrid dynamical systems, yet a major obstacle in employing reachability analysis is the "curse of  ... 
doi:10.1109/cdc.2009.5400336 dblp:conf/cdc/KaynamaO09 fatcat:dp75ojwlfjg23bg2oxbwg3ze7y

Reach Set Approximation through Decomposition with Low-dimensional Sets and High-dimensional Matrices [article]

Sergiy Bogomolov, Marcelo Forets, Goran Frehse, Andreas Podelski, Christian Schilling, Frédéric Viry
2018 arXiv   pre-print
Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety.  ...  While modern linear algebra packages are efficient for matrices with tens of thousands of dimensions, set-based image computations are limited to a few hundred.  ...  The analysis scales to systems with tens of thousands of variables, which are out of scope of state-of-the-art tools for dense-time reachability.  ... 
arXiv:1801.09526v1 fatcat:3vf22wugefcbpojbanzqacljui

Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances [article]

Somil Bansal, Mo Chen, Sylvia Herbert, Claire J. Tomlin
2017 arXiv   pre-print
Hamilton-Jacobi (HJ) reachability analysis is an important formal verification method for guaranteeing performance and safety properties of dynamical systems; it has been applied to many small-scale systems  ...  In addition, we review some of the current work in high-dimensional HJ reachability to show how the dimensionality challenge can be alleviated via various general theoretical and application-specific insights  ...  System Decomposition Techniques for Linear Time-Invariant Systems In the linear time-invariant case, many non-HJ-based computation techniques have been developed for approximating reachable sets.  ... 
arXiv:1709.07523v1 fatcat:rsmzcy5dk5cl7n74cwwulgqhj4

A Simple Time Scale Decomposition Technique for Stochastic Process Algebras

J. Hillston
1995 Computer journal  
Our technique is illustrated by an example based on a closed network of queues with nite capacity in which blocking may occur.  ...  Many modern computer and communication systems result in large, complex performance models.  ...  It is not very di cult to apply decomposition of the state space after a complete reachability analysis has been applied.  ... 
doi:10.1093/comjnl/38.7.566 fatcat:s4kltebflvcz3hz447g6azidti

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

Sergiy Bogomolov, Martin Fränzle, Kyoko Makino, Nacim Ramdani, Marc Herbstritt
2017 Dagstuhl Reports  
the following research areas relevant to problem solving in cyber-physical domains: verification of numerical reactive systems such as embedded floating-point programs and hybrid systems, including novel  ...  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  ...  Flowpipe-construction-based reachability analysis is one prominent approach, which over-approximates the set of reachable states of a hybrid system by a union of state sets, each of them being represented  ... 
doi:10.4230/dagrep.6.12.1 dblp:journals/dagstuhl-reports/BogomolovFMR16 fatcat:sydj4slvefa7boehai7gpnfupm

A piecewise ellipsoidal reachable set estimation method for continuous bimodal piecewise affine systems [article]

Thuan Le Quang, Nam Phan Thanh, Simone Baldi
2021 arXiv   pre-print
Although bimodal piecewise affine systems can be seen as a special class of affine hybrid systems, reachability methods developed for affine hybrid systems might be inappropriately complex for bimodal  ...  Finally, linear matrix characterizations of the estimate of the reachable set are derived.  ...  Acknowledgments The research of the first two authors were supported by  ... 
arXiv:2106.06776v1 fatcat:qewtw3vfsjgdbhrx7rcqvu2a4q

Reachability and Control Synthesis for Piecewise-Affine Hybrid Systems on Simplices

L.C.G.J.M. Habets, P.J. Collins, J.H. Van Schuppen
2006 IEEE Transactions on Automatic Control  
In this paper, we consider the synthesis of control laws for piecewise-affine hybrid systems on simplices.  ...  Index Terms-Discrete-event system (DES), exit facet, piecewiseaffine hybrid systems, reachability, simplex, stability.  ...  The authors plan to implement the algorithms to allow the synthesis of control laws for realistically-sized piecewise-affine hybrid systems of practical interest.  ... 
doi:10.1109/tac.2006.876952 fatcat:yyo2l2n42vh5lk4brcq4c6swru

Unbounded-Time Analysis of Guarded LTI Systems with Inputs by Abstract Acceleration [chapter]

Dario Cattaruzza, Alessandro Abate, Peter Schrammel, Daniel Kroening
2015 Lecture Notes in Computer Science  
To tackle this general problem, we use abstract acceleration, a method for unboundedtime polyhedral reachability analysis for linear systems.  ...  Linear Time Invariant (LTI) systems are ubiquitous in software systems and control applications.  ...  We formalise the description of such a system both via a linear loop and via hybrid dynamics.  ... 
doi:10.1007/978-3-662-48288-9_18 fatcat:yphi3muwobclznwsqprerzt5py

Table of contents

2021 IEEE Control Systems Letters  
Shor 469 Synchronization Analysis of Networks of Linear Parabolic Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ...  Herzallah 577 Five-Full-Block Structured Singular Values of Real Matrices Equal Their Upper Bounds . . . . . . . . . . O.  ... 
doi:10.1109/lcsys.2020.3008985 fatcat:f7cfogr3ajdslk7gmrv7chcvku

Morse Graphs: Topological Tools for Analyzing the Global Dynamics of Robot Controllers [article]

Ewerton R. Vieira, Edgar Granados, Aravind Sivaramakrishnan, Marcio Gameiro, Konstantin Mischaikow, Kostas E. Bekris
2022 arXiv   pre-print
This allows to use the Morse graph to identify how to synthesize controllers to form improved hybrid solutions or how to identify the physical limitations of a robotic system.  ...  Understanding the global dynamics of a robot controller, such as identifying attractors and their regions of attraction (RoA), is important for safe deployment and synthesizing more effective hybrid controllers  ...  Reachability analysis [4] is also relevant as it computes the backward reachable tube of a dynamical system and can recover the maximal RoA without imposing shape restrictions.  ... 
arXiv:2202.08383v1 fatcat:gzvaatqla5de3kab3oeajrmpli

Model checking sequential software programs via mixed symbolic analysis

Zijiang Yang, Chao Wang, Aarti Gupta, Franjo Ivanvčić
2009 ACM Transactions on Design Automation of Electronic Systems  
Experiments on real-world C programs show that the new symbolic search algorithms can achieve several orders-of-magnitude improvements over existing methods based on bit-level (Boolean) reasoning.  ...  Our algorithms perform word-level reasoning by using a combination of decision procedures in Boolean and integer and real domains, and use novel symbolic search strategies optimized specifically for sequential  ...  Linear constraint representations and polyhedral analysis have also been used in the verification of real-time and hybrid systems [Henzinger et al. 1995; Asarin et al. 2000 ].  ... 
doi:10.1145/1455229.1455239 fatcat:jgxnkajci5c2njql4ihysrlq2q

Languages and Tools for Hybrid Systems Design

Luca P. Carloni, Roberto Passerone, Alessandro Pinto, Alberto L. Angiovanni-Vincentelli
2006 Foundations and Trends® in Electronic Design Automation  
Formal definition of hybrid systems 11 considering classes of discrete dynamical systems underlying each state.  ...  The design is therefore subject to extensive mathematical analysis and simulation.  ...  Hybrid and Embedded Software Systems), which receives funding from the National Science Foundation (NSF award number CCF-0424422).  ... 
doi:10.1561/1000000001 fatcat:e27dfodqcranhememam757wdj4
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