On the complexity of bounded time and precision reachability for piecewise affine systems

被引：1
|
作者：
Bazille, Hugo [3 ,4 ]
Bournez, Olivier [1 ]
Gomaa, Walid [2 ,5 ]
Pouly, Amaury [1 ]
机构：
[1] Ecole Polytech, LIX, F-91128 Palaiseau, France
[2] Egypt Japan Univ Sci & Technol, CSE, Alexandria, Egypt
[3] ENS Cachan Bretagne, Rennes, France
[4] Univ Rennes 1, Rennes, France
[5] Alexandria Univ, Fac Engn, Alexandria, Egypt
来源：
THEORETICAL COMPUTER SCIENCE | 2018年 / 735卷
关键词：
Complexity; Reachability; Piecewise affine; DYNAMICAL-SYSTEMS;
D O I：
10.1016/j.tcs.2016.09.021
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Reachability for piecewise affine systems is known to be undecidable, starting from dimension 2. In this paper we investigate the exact complexity of several decidable variants of reachability and control questions for piecewise affine systems. We show in particular that the region-to-region bounded time versions leads to NP-complete or co-NP-complete problems, starting from dimension 2. We also prove that a bounded precision version leads to PSPACE-complete problems. (C) 2016 Elsevier B.V. All rights
引用
收藏
页码：132 / 146
页数：15
相关论文
共 50 条
  • [1] On the Complexity of Reachability and Mortality for Bounded Piecewise Affine Maps
    Tveretina, Olga
    REACHABILITY PROBLEMS, RP 2024, 2024, 15050 : 141 - 153
  • [2] Robust bounded feasibility verification of piecewise affine systems via reachability computations
    Desimini, Riccardo
    Prandini, Maria
    IFAC PAPERSONLINE, 2019, 52 (16): : 78 - 83
  • [3] Reachability analysis of continuous-time piecewise affine systems
    Hamadeh, Abdullah
    Goncalves, Jorge
    AUTOMATICA, 2008, 44 (12) : 3189 - 3194
  • [4] State estimation for piecewise affine, discrete time systems with bounded disturbances
    Rakovic, SV
    Mayne, DQ
    2004 43RD IEEE CONFERENCE ON DECISION AND CONTROL (CDC), VOLS 1-5, 2004, : 3557 - 3562
  • [5] Robust low complexity predictive control of constrained piecewise affine systems with bounded disturbances
    Fu Chen
    Dong-Lian Qi
    International Journal of Control, Automation and Systems, 2010, 8 : 439 - 444
  • [6] Robust Low Complexity Predictive Control of Constrained Piecewise Affine Systems with Bounded Disturbances
    Chen, Fu
    Qi, Dong-Lian
    INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS, 2010, 8 (02) : 439 - 444
  • [7] Control of Discrete-Time Piecewise Affine Probabilistic Systems using Reachability Analysis
    Asselborn, Leonhard
    Stursberg, Olaf
    2016 IEEE CONFERENCE ON COMPUTER AIDED CONTROL SYSTEM DESIGN (CACSD), 2016, : 661 - 666
  • [8] Reachability algorithm for biological piecewise-affine hybrid systems
    Aswani, Anil
    Tomlin, Claire
    HYBRID SYSTEMS: COMPUTATION AND CONTROL, PROCEEDINGS, 2007, 4416 : 633 - +
  • [9] Reachability Analysis for Nonlinear Systems by Guaranteed Piecewise Affine Approximation
    Nasri, Othman
    Gueguen, Herve
    Lefebvre, Marie-Anne
    18TH MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION, 2010, : 1218 - 1223
  • [10] THE COMPLEXITY OF REACHABILITY IN AFFINE VECTOR ADDITION SYSTEMS WITH STATES
    Blondin, Michael
    Raskin, Mikhail
    LOGICAL METHODS IN COMPUTER SCIENCE, 2021, 17 (03) : 3:1 - 3:31
12345