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Consistent Approximations of the Zeno Behaviour in Affine-Type Switched Dynamic Systems
2016
Abstract and Applied Analysis
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This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. ...
We propose two useful approximative approaches to the Zeno dynamics, namely, an analytic technique and a variational description of this phenomenon. ...
The aim of our contribution is to give a constructive characterization of the Zeno executions in a specific case of affine switched systems. ...
doi:10.1155/2016/2091526
fatcat:d3q3mia2lrdtzhew5hbtibzgdm
Counter-Example Guided Synthesis of Control Lyapunov Functions for Switched Systems
[article]
2015
arXiv
pre-print
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First, we introduce a class of control Lyapunov functions (CLFs) for switched systems along with a switching strategy that yields a closed loop system with a guaranteed minimum dwell time in each switching ...
We also evaluate our approach on a number of interesting benchmarks, and compare the performance of the new approach with our previous work that uses off-the-shelf nonlinear constraint solvers instead ...
All opinions expressed are those of the authors and not necessarily of the NSF. ...
arXiv:1509.03688v2
fatcat:lcrzk2suxndedasogxv72orb2u
Current Challenges in the Verification of Hybrid Systems
[chapter]
2015
Lecture Notes in Computer Science
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for the verification of hybrid systems. ...
Latest developments brought interesting theoretical results and powerful tools for the reachability analysis of hybrid systems. ...
Examples for chattering Zeno behaviours can be found in switching systems, where the state space is divided into grids, each grid having its own dynamics, modelled by an own location. ...
doi:10.1007/978-3-319-25141-7_2
fatcat:zvdce2gma5hwfnpeid64dstaki
Hybridization methods for the analysis of nonlinear systems
2007
Acta Informatica
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The main idea of our hybridization approach is to apply the hybrid systems methodology as a systematic approximation method. ...
More concretely, we partition the state space of a complex system into regions that only intersect on their boundaries, and then approximate its dynamics in each region by a simpler one. ...
Acknowledgments We would like to thank our colleagues at the laboratories Verimag and LMC in Grenoble for their collaboration and encouragement. ...
doi:10.1007/s00236-006-0035-7
fatcat:v3b3xvpkhvdsbatmx6oovwbwh4
Augmented finite transition systems as abstractions for control synthesis
2017
Discrete event dynamic systems
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This work is motivated by the problem of synthesizing switching protocols for continuous switched systems described by differential or difference equations, in a way that guarantees that the resulting ...
in accordance with the underlying continuous dynamics. ...
Acknowledgments The authors would like to thank Pavithra Prabhakar, Fei Sun, Eric M. Wolff and Richard M. Murray for useful discussions at the early stages of this work. ...
doi:10.1007/s10626-017-0243-z
fatcat:ip7rzwvkmndhpi6ibognrveqti
Reachability analysis of a biodiesel production system using stochastic hybrid systems
2007
2007 Mediterranean Conference on Control & Automation
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The verification method employs dynamic programming based on a discretization of the state space and therefore suffers from the curse of dimensionality. ...
Our analysis can potentially provide useful insights into the complicated dynamics of the chemicals and assist in focusing experiments and tuning the production system for efficiency. ...
Hybrid systems have been used for modeling biological-based systems in order to capture the complicated dynamics using well-defined abstractions. ...
doi:10.1109/med.2007.4433779
fatcat:kfypa2seabgpxacleuep5pt3zm
Controlled synchronization of mechanical systems with a unilateral constraint**M. Baumann is supported by the Swiss National Science Foundation through the project 'Synchronization of Dynamical Systems with Impulsive Motion' (SNF 200021-144307). J.J.B. Biemond received support as FWO Pegasus Marie Curie Fellow, from FWO G071711N and the Optimization in Engineering Center (OPTEC) of KU Leuven
2016
IFAC-PapersOnLine
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We present a (coupling) control law which ensures global synchronization, also in the presence of grazing trajectories and accumulation points (Zeno behavior). ...
We present a (coupling) control law which ensures global synchronization, also in the presence of grazing trajectories and accumulation points (Zeno behavior). ...
The presented Lyapunov function is constructed using an approximation of the distance function. ...
doi:10.1016/j.ifacol.2016.10.188
fatcat:2zzd25iuazddbkhazk3dz6qrmy
From non-zenoness verification to termination
2015
2015 ACM/IEEE International Conference on Formal Methods and Models for Codesign (MEMOCODE)
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We investigate the problem of verifying the absence of zeno executions in a hybrid system. A zeno execution is one in which there are infinitely many discrete transitions in a finite time interval. ...
We illustrate the feasibility of our approach by applying it on hybrid system examples. ...
The work of Pierre Ganty was funded partially by the EU project FP7-ICT-610686 POLCA and by the Madrid Regional Government CM project S2013/ICE-2731 (N-Greens). ...
doi:10.1109/memcod.2015.7340490
dblp:conf/memocode/GantyGLP15
fatcat:gnuzdlc2zvdl5fueoghajy5viq
Adaptive Output Tracking Control of Piecewise Affine Systems With Prescribed Performance
2021
IEEE Transactions on Systems, Man & Cybernetics. Systems
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Based on these common Lyapunov functions, the stability of the closed-loop system under arbitrary switching is established. ...
In this article, we investigate the adaptive output tracking control for multiinput-multioutput piecewise affine systems with prescribed performance. ...
A similar concept to construct the common Lyapunov function can be found in the adaptive control for switched systems in Brunovsky form [36] , where an error metric is constructed based on the tracking ...
doi:10.1109/tsmc.2021.3122982
fatcat:xhtwbwm6ijejphodktzdk62q7u
Peak Estimation of Hybrid Systems with Convex Optimization
[article]
2023
arXiv
pre-print
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This LP may in turn be approximated by a convergent sequence of upper bounds attained from solutions of Linear Matrix Inequalities (LMIs) using the Moment-Sum-of-Squares hierarchy. ...
The peak estimation problem is extended to problems with uncertainty and safety settings, such as measuring the distance of closest approach between points along hybrid system trajectories and unsafe sets ...
The work in [8] treated the peak estimation problem as an infinite-dimensional LP in measures, and proposed approximations solved based on successively refined finite-dimensional gridded LPs. ...
arXiv:2303.11490v1
fatcat:y4rsjez3fnhehdc5axa3cyu5iy
HYSDEL—A Tool for Generating Computational Hybrid Models for Analysis and Synthesis Problems
2004
IEEE Transactions on Control Systems Technology
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We introduce the class of discrete hybrid automata (DHA) and show its relation with several other existing model paradigms: piecewise affine systems, mixed logical dynamical systems, (extended) linear ...
This paper presents a computational framework for modeling hybrid systems in discrete-time. ...
Jost, for helping in the implementation of HYSDEL, and Ms. F. Porro for drawing some of the figures reported in this paper. ...
doi:10.1109/tcst.2004.824309
fatcat:6p3eljy5tvhsxoqybwbpbbhpra
A Semi-Continuous PWA Model Based Optimal Control Method for Nonlinear Systems
2020
Processes
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To alleviate the mode mismatch of multiple model methods for nonlinear systems when completely discrete dynamical equations are adopted, a semi-continuous piecewise affine (SCPWA) model based optimal control ...
Firstly, a SCPWA model is constructed where modes evolve in continuous time and continuous states evolve in discrete time. ...
Acknowledgments: We thank the associate editor and anonymous reviewers for their careful reading of the paper and very constructive comments that led to a substantially improved paper. ...
doi:10.3390/pr8020170
fatcat:r2w2nghrvre6db2jeeaq47qfqy
Tutorial introduction to the modelling and control of hybrid systems
2007
International journal of Modeling, identification and control
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He has been involved in the management of many research projects especially with large international participation. ...
This arises in some of the most critical operating regions where systems are under start-up, shutdown or are undergoing major planned changes. ...
The switching costs can prevent the system from taking Zeno execution 1 since infinite mode changes in infinite time would mean infinite cost. ...
doi:10.1504/ijmic.2007.016409
fatcat:roqnctp3qzacddraucqsjg3cfu
Languages and Tools for Hybrid Systems Design
2006
Foundations and Trends® in Electronic Design Automation
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The mapping S provides the association between the continuous time definition of the dynamical system in terms of differential equations and the discrete behavior in terms of states. ...
The mapping R provides the initial conditions for the dynamical system upon entering a state. The transition and dynamical structure of a hybrid system determines a set of executions. ...
This work has been supported in part by the Columbus Project of the European Community, the GSRC (MARCO Award#: 2003-DT-660), the Artist 2 and HYCON Networks of Excellence, and by CHESS (the Center for ...
doi:10.1561/1000000001
fatcat:e27dfodqcranhememam757wdj4
Hybrid Dynamical Systems: An Introduction to Control and Verification
2014
Foundations and Trends® in Systems and Control
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Acknowledgements We highly appreciate the constructive and helpful comments from four anonymous reviewers. ...
The financial supports of NSF-CNS-1239222 and NSF-CAREER-1253488 for this work are greatly acknowledged. ...
Based on these approximations, we introduce new atomic propositions,π i , and construct a new version of the specification φ, calledφ. ...
doi:10.1561/2600000001
fatcat:kxr4yc3rjzet7kwzz7pcm6a2ri
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