Finite-step approximately bi-similar symbolic model for switched systems

被引：0
作者：
Liu, Yongzhuang [1 ]
Song, Yang [2 ,3 ]
Lin, Hai [4 ]
机构：
[1] Shanghai Univ, Sch Mechatron Engn & Automat, Dept Automat, Shanghai 200444, Peoples R China
[2] Shanghai Univ, Sch Mechatron Engn & Automat, Dept Elect Engn, Shanghai 200444, Peoples R China
[3] Shanghai Key Lab Power Stn Automat Technol, Shanghai 200444, Peoples R China
[4] Univ Notre Dame, Dept Elect Engn, Notre Dame, IN 46556 USA
来源：
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS | 2024年 / 361卷 / 10期
基金：
上海市自然科学基金;
关键词：
Switched system; Symbolic model; Finite-time uniform incremental stability; Finite-step approximate bi-simulation; TIME STABILITY; DISCRETE; CONTROLLERS;
D O I：
10.1016/j.jfranklin.2024.106943
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Obtaining an approximately bi-similar symbolic model for a continuous-state system is a crucial step in symbolic control. Symbolic control aims to design switching logic to achieve temporal logic specifications. Most existing approaches to approximate bi-simulation are developed over infinite time horizons. However, many control tasks are set within finite periods in practical scenarios. Hence, it makes sense to consider the behavior of trajectories within finite-time horizons. Therefore, this paper introduces two new notions: finite-time uniform incremental stability (FUI-stability) and finite-step approximate bi-simulation. Furthermore, a FUI-stability condition for switched system is derived using the multiple incremental Lyapunovlike functions technique. A symbolic model is constructed for switched system by the state space grid technique. Subsequently, a sufficient condition for finite-step approximate bi-simulation between the finite-time uniformly incrementally stable (FUI-stable) switched system and the constructed symbolic model is derived. Finally, the obtained results are illustrated by two numerical examples.
引用
收藏
页数：11
相关论文
共 44 条
[1]  
Amato F., 2014, Finite-Time Stability and Control
[2]   Forward completeness, unboundedness observability, and their Lyapunov characterizations [J].
Angeli, D ;
Sontag, ED .
SYSTEMS & CONTROL LETTERS, 1999, 38 (4-5) :209-217
[3]   A Lyapunov approach to incremental stability properties [J].
Angeli, D .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2002, 47 (03) :410-421
[4]   Games for synthesis of controllers with partial observation [J].
Arnold, A ;
Vincent, A ;
Walukiewicz, I .
THEORETICAL COMPUTER SCIENCE, 2003, 303 (01) :7-34
[5]   Analysis of Stochastic Switched Systems With Application to Networked Control Under Jamming Attacks [J].
Cetinkaya, Ahmet ;
Ishii, Hideaki ;
Hayakawa, Tomohisa .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2019, 64 (05) :2013-2028
[6]   Formal Methods for Control of Traffic Flow AUTOMATED CONTROL SYNTHESIS FROM FINITE-STATE TRANSITION MODELS [J].
Coogan, Samuel ;
Arcak, Murat ;
Belta, Calin .
IEEE CONTROL SYSTEMS MAGAZINE, 2017, 37 (02) :109-128
[7]   Finite-Time Consensus Tracking Neural Network FTC of Multi-Agent Systems [J].
Dong, Guowei ;
Li, Hongyi ;
Ma, Hui ;
Lu, Renquan .
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2021, 32 (02) :653-662
[8]   Approximation metrics for discrete and continuous systems [J].
Girard, Antoine ;
Pappas, George J. .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2007, 52 (05) :782-798
[9]   Safety synthesis for incrementally stable switched systems using discretization-free multi-resolution abstractions [J].
Girard, Antoine ;
Gossler, Gregor .
ACTA INFORMATICA, 2020, 57 (1-2) :245-269
[10]   Approximately Bisimilar Symbolic Models for Incrementally Stable Switched Systems [J].
Girard, Antoine ;
Pola, Giordano ;
Tabuada, Paulo .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2010, 55 (01) :116-126
12345