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Reachability analysis of linear hybrid systems via block decomposition
[article]
2020
arXiv
pre-print
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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
2017
2017 IEEE 56th Annual Conference on Decision and Control (CDC)
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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
2011
International Journal of Control
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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
2009
Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference
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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]
2018
arXiv
pre-print
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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]
2017
arXiv
pre-print
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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
1995
Computer journal
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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)
2017
Dagstuhl Reports
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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]
2021
arXiv
pre-print
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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
2006
IEEE Transactions on Automatic Control
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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]
2015
Lecture Notes in Computer Science
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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
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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]
2022
arXiv
pre-print
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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
2009
ACM Transactions on Design Automation of Electronic Systems
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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
2006
Foundations and Trends® in Electronic Design Automation
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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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