Data-based controllability analysis for generalised linear discrete-time system

ABSTRACT In this paper, we aim to propose a data-based method to testify whether the system is a normal linear system or a generalised linear system and then analyse its controllability via the measured state data and the control input satisfying certain condition. For this purpose, we first describe a linear discrete-time system in a general form and derive a necessary and sufficient condition for the equivalent condition of complete controllability with a normal linear discrete time system. Second, we check whether the system is normal or singular, and then construct the controllability matrices only based on the input and measured state data. Third, the controllability of the corresponding system is investigated thoroughly based on available data without identifying system parameters. Finally, a numerical example and a stock price example are used to show the effectiveness and feasibility of the proposed data-based method.

[1]  Johan A. K. Suykens,et al.  LS-SVM approximate solution to linear time varying descriptor systems , 2012, Autom..

[2]  Xin-zhuang Dong.  Admissibility analysis of linear singular systems via a delta operator method , 2014, Int. J. Syst. Sci..

[3]  G. Duan.  Analysis and Design of Descriptor Linear Systems , 2010 .

[4]  Yang Liu,et al.  Controllability of probabilistic Boolean control networks based on transition probability matrices , 2015, Autom..

[5]  Abhijit Gosavi,et al.  Reinforcement learning for long-run average cost , 2004, Eur. J. Oper. Res..

[6]  Huaguang Zhang,et al.  Nearly data-based optimal control for linear discrete model-free systems with delays via reinforcement learning , 2016, Int. J. Syst. Sci..

[7]  Hao Xu,et al.  Optimal regulation of uncertain dynamic systems using adaptive dynamic programming , 2014, J. Control. Decis..

[8]  莊哲男.  Applied System Identification , 1994 .

[9]  Yang Liu,et al.  Controllability of Boolean control networks with impulsive effects and forbidden states , 2014 .

[10]  Victor Sreeram,et al.  Model reduction of singular systems , 2001, Int. J. Syst. Sci..

[11]  Franco Blanchini.  Computation of the transfer function for singular systems , 1990 .

[12]  Yang Liu,et al.  Controllability for a Class of Linear Time-Varying Impulsive Systems With Time Delay in Control Input , 2011, IEEE Transactions on Automatic Control.

[13]  Hao Zhang,et al.  Multirate parallel distributed compensation of a cluster in wireless sensor and actor networks , 2016, Int. J. Syst. Sci..

[14]  Dirk Söffker,et al.  A data-driven quadratic stability condition and its application for stabilizing unknown nonlinear systems , 2014 .

[15]  Derong Liu,et al.  Data-Based Controllability and Observability Analysis of Linear Discrete-Time Systems , 2011, IEEE Transactions on Neural Networks.

[16]  Yang Liu,et al.  Data-based controllability analysis of discrete-time linear time-delay systems , 2014, Int. J. Syst. Sci..

[17]  Nicholas P. Karampetakis,et al.  Reachability and controllability of discrete time descriptor systems , 2012, CCCA12.

[18]  Weida Zhou,et al.  Identification and Control of Discrete-Time Nonlinear Systems Using Affine Support Vector Machines , 2009, Int. J. Artif. Intell. Tools.

[19]  Qi Chao,et al.  Review on Data-based Decision Making Methodologies , 2009 .

[20]  Jianquan Lu,et al.  Some necessary and sufficient conditions for the output controllability of temporal Boolean control networks , 2014 .

[21]  Jing Lu,et al.  Least squares based iterative identification for a class of multirate systems , 2010, Autom..

[22]  Yuanqing Li,et al.  Bifurcation on stability of singular systems with delay , 1999, Int. J. Syst. Sci..

[23]  Joe Zhu,et al.  DEA models for supply chain efficiency evaluation , 2006, Ann. Oper. Res..

[24]  Bidyadhar Subudhi,et al.  Nonlinear system identification using memetic differential evolution trained neural networks , 2011, Neurocomputing.