Robustness analysis of nonlinear observers for the slow variables of singularly perturbed systems

被引:9
作者
Cuevas, Luis [1 ]
Nesic, Dragan [1 ]
Manzie, Chris [1 ]
机构
[1] Univ Melbourne, Dept Elect & Elect Engn, Parkville, Vic 3010, Australia
基金
澳大利亚研究理事会;
关键词
input-to-state stability; <mml; math altimg="urn; x-wiley; rnc; media; rnc5100; rnc5100-math-0001" display="inline" overflow="scroll"><mml; mrow><mml; msub><mml; mi>Script capital L</mml; mi></mml; mn>2</mml; mn></mml; mrow></mml; msub></mml; math>stability; observer design; semiglobal practical asymptotical stability; singularly perturbed systems; DESIGN;
D O I
10.1002/rnc.5100
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
Estimation of unmeasured variables is a crucial objective in a broad range of applications. However, the estimation process turns into a challenging problem when the underlying model is nonlinear and even more so when additionally it exhibits multiple time scales. The existing results on estimation for systems with two time scales apply to a limited class of nonlinear plants and observers. We focus on analyzing nonlinear observers designed for the slow state variables of nonlinear singularly perturbed systems. Moreover, we consider the presence of bounded measurement noise in the system. We generalize current results by considering broader classes of plants and estimators to cover reduced-order, full-order, and higher-order observers. First, we show that the singularly perturbed system has bounded solutions under an appropriate set of assumptions on the corresponding boundary layer and reduced systems. We then exploit this property to prove that, under reasonable assumptions, the error dynamics of the observer designed for the reduced system are semiglobally input-to-state practically stable when the observer is implemented on the original plant. We also concludeScript capital L2stability results when the measurement noise belongs to Script capital L2 boolean AND Script capital L infinity. In the absence of measurement noise, we state results on semiglobal practical asymptotical stability for the error dynamics. We illustrate the generality of our main results through three classes of systems with corresponding observers and one numerical example.
引用
收藏
页码:5628 / 5656
页数:29
相关论文
共 34 条
  • [1] [Anonymous], 2013, Electron. J. Differential Equations
  • [2] Arcak M., 2000, THESIS
  • [3] A High-Gain Nonlinear Observer With Limited Gain Power
    Astolfi, Daniele
    Marconi, Lorenzo
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2015, 60 (11) : 3059 - 3064
  • [4] Besancon G, 2007, LECT NOTES CONTR INF, V363, P1
  • [5] BRUNO AD, 1994, NATO ADV SCI INST SE, V331, P43
  • [6] Cheng CA, 2010, C IND ELECT APPL, P556
  • [7] A robust circle criterion observer with application to neural mass models
    Chong, Michelle
    Postoyan, Romain
    Nesic, Dragan
    Kuhlmann, Levin
    Varsavsky, Andrea
    [J]. AUTOMATICA, 2012, 48 (11) : 2986 - 2989
  • [8] Singular perturbations and input-to-state stability
    Christofides, PD
    Teel, AR
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1996, 41 (11) : 1645 - 1650
  • [9] Cuevas L, 2018, 2018 AUSTRALIAN & NEW ZEALAND CONTROL CONFERENCE (ANZCC), P352, DOI 10.1109/ANZCC.2018.8606545
  • [10] Cuevas L, 2018, 2018 AUSTRALIAN & NEW ZEALAND CONTROL CONFERENCE (ANZCC), P297, DOI 10.1109/ANZCC.2018.8606595