On robust control invariance and robust set stabilization of mix-valued logical control networks
Jianjun Wang
School of Science and Technology, University of Camerino, Camerino, Italy
School of Mathematical Science, Liaocheng University, Liaocheng, People's Republic of China
Search for more papers by this authorCorresponding Author
Shihua Fu
School of Mathematical Science, Liaocheng University, Liaocheng, People's Republic of China
Correspondence Shihua Fu, School of Mathematical Science, Liaocheng University, Liaocheng 252026, People's Republic of China.
Email: [email protected]
Renato De Leone, School of Science and Technology, University of Camerino, Camerino 62032, Italy.
Email: [email protected]
Search for more papers by this authorCorresponding Author
Renato De Leone
School of Science and Technology, University of Camerino, Camerino, Italy
Correspondence Shihua Fu, School of Mathematical Science, Liaocheng University, Liaocheng 252026, People's Republic of China.
Email: [email protected]
Renato De Leone, School of Science and Technology, University of Camerino, Camerino 62032, Italy.
Email: [email protected]
Search for more papers by this authorJianwei Xia
School of Mathematical Science, Liaocheng University, Liaocheng, People's Republic of China
Search for more papers by this authorLishan Qiao
School of Mathematical Science, Liaocheng University, Liaocheng, People's Republic of China
Search for more papers by this authorJianjun Wang
School of Science and Technology, University of Camerino, Camerino, Italy
School of Mathematical Science, Liaocheng University, Liaocheng, People's Republic of China
Search for more papers by this authorCorresponding Author
Shihua Fu
School of Mathematical Science, Liaocheng University, Liaocheng, People's Republic of China
Correspondence Shihua Fu, School of Mathematical Science, Liaocheng University, Liaocheng 252026, People's Republic of China.
Email: [email protected]
Renato De Leone, School of Science and Technology, University of Camerino, Camerino 62032, Italy.
Email: [email protected]
Search for more papers by this authorCorresponding Author
Renato De Leone
School of Science and Technology, University of Camerino, Camerino, Italy
Correspondence Shihua Fu, School of Mathematical Science, Liaocheng University, Liaocheng 252026, People's Republic of China.
Email: [email protected]
Renato De Leone, School of Science and Technology, University of Camerino, Camerino 62032, Italy.
Email: [email protected]
Search for more papers by this authorJianwei Xia
School of Mathematical Science, Liaocheng University, Liaocheng, People's Republic of China
Search for more papers by this authorLishan Qiao
School of Mathematical Science, Liaocheng University, Liaocheng, People's Republic of China
Search for more papers by this authorFunding information: National Natural Science Foundation of China, Grant/Award Numbers: 61803240; 62103716; Natural Science Foundation of Shandong Province, Grant/Award Number: ZR2019BF023
Abstract
This article investigates the robust control invariance and robust set stabilization problems based on a semi-tensor product method for a class of mix-valued logical control networks (MVLCNs) with disturbances. First, a calculation method for the largest robust control invariant subset contained in a given set is proposed. Second, based on the robust control invariant subset, the robust set stabilization of MVLCNs is discussed, and new results are presented. Furthermore, the design algorithm of time-optimal state feedback stabilizers via antecedence solution technique is derived. The study of an illustrative example shows the effectiveness of the obtained new results.
CONFLICT OF INTEREST
There is no conflict of interests for this article.
Open Research
DATA AVAILABILITY STATEMENT
Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.
REFERENCES
- 1Kauffman S. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol. 1969; 22(3): 437-467.
- 2Schechter E. Classical and Nonclassical Logics. Princeton University Press; 2005.
10.1515/9780691220147 Google Scholar
- 3Cheng D, Zhao Y, Mu Y. Strategy optimization with its application to dynamic games. Proceedings of the 49th IEEE Conference on Decision and Control; 2010:5822-5827; Atlanta, GA.
- 4Bushnell M, Agrawal V. Essentials of Electronic Testing for Digital Memory and Mixed-Signal VLSI Circuit. Springer Science & Business Media; 2000.
- 5Zhao Y, Li Z, Cheng D. Optimal control of logical control networks. IEEE Trans Automat Contr. 2011; 56(8): 1766-1776.
- 6Jia G, Meng M, Feng J. Function perturbation of mix-valued logical networks with impacts on limit sets. Neurocomputing. 2016; 207: 428-436.
- 7Akutsu T, Miyano S, Kuhara S. Inferring qualitative relations in genetic networks and metabolic pathways. Bioinformatics. 2000; 16(8): 727-734.
- 8Huang S, Ingber I. Shape-dependent control of cell growth, differentiation, and apoptosis: switching between attractors in cell regulatory networks. Exp Cell Res. 2000; 261(1): 91-103.
- 9Cheng D, Qi H, Li Z. Analysis and Control of Boolean Networks: A Semi-Tensor Product Approach. Springer; 2011.
- 10Cheng D, Qi H. Controllability and observability of Boolean control networks. Automatica. 2009; 45: 1659-1667.
- 11Chen B, Yang X, Liu Y, Qiu J. Controllability and stabilization of Boolean control networks by the auxiliary function of flipping. Int J Robust Nonlinear Control. 2020; 30(14): 5529-5541.
- 12Guo Y, Wang P, Gui W, Yang C. Set stability and set stabilization of Boolean control networks based on invariant subsets. Automatica. 2015; 61: 106-112.
- 13Lu X, Li H, Wang C, Zhang X. Stability analysis of positive switched impulsive systems with delay on time scales. Int J Robust Nonlinear Control. 2020; 30(16): 6879-6890.
- 14Lu J, Sun L, Liu Y, Ho D, Cao J. Stabilization of Boolean control networks under aperiodic sampled-data control. SIAM J Control Optim. 2018; 56(6): 4385-4404.
- 15Wang S, Li H, Li Y, Sun W. Event-triggered control for disturbance decoupling problem of mix-valued logical networks. J Franklin Inst. 2020; 357(2): 796-809.
- 16Zhang L, Feng J, Feng X, Yao J. Further results on disturbance decoupling of mix-valued logical networks. IEEE Trans Automat Contr. 2014; 59(6): 1630-1634.
- 17Fu S, Zhao J, Wang J. Input-output decoupling control design for switched Boolean control networks. J Frankl Inst. 2018; 355(17): 8576-8596.
- 18Wang J, De Leone R, Fu S, Xia J. Input-output decoupling for mix-valued logical control networks via the semi-tensor product method. Int J Control. 2021; 94(9): 2419-2427.
- 19Zhang X, Wang Y, Cheng D. Output tracking of Boolean control networks. IEEE Trans Automat Contr. 2020; 65(6): 2730-2735.
- 20Li H, Wang Y, Guo P. State feedback based output tracking control of probabilistic Boolean networks. Inf Sci. 2016; 349: 1-11.
- 21Li H, Yang X, Wang S. Robustness for stability and stabilization of Boolean networks with stochastic function perturbations. IEEE Trans Automat Contr. 2020; 66(3): 1231-1237.
- 22Pan J, Meng M. Optimal one-bit perturbation in Boolean networks based on cascading aggregation. Front Inf Technol Electron Eng. 2020; 21(2): 294-303.
- 23Lu J, Li B, Zhong J. A novel synthesis method for reliable feedback shift registers via Boolean networks. Sci China Inf Sci. 2021; 64(5):152207.
- 24Guo P, Zhang H, Alsaadi FE, Tasawar H. Semi-tensor product method to a class of event-triggered control for finite evolutionary networked games. IET Control Theory Appl. 2017; 11(13): 2140-2145.
- 25 Fu S, Pan Y, Feng J, Zhao J. Strategy optimisation for coupled evolutionary public good games with threshold. Int J Control. 2020. doi:10.1080/00207179.2020.1803411
- 26Li H, Zhao G, Meng M, Feng J. A survey on applications of semi-tensor product method in engineering. Sci China Inf Sci. 2018; 61(01): 28-44.
- 27Ren F, Cao J. Asymptotic and robust stability of genetic regulatory networks with time-varying delays. Neurocomputing. 2008; 71: 834-842.
- 28Li H, Wang Y. Robust stability and stabilisation of Boolean networks with disturbance inputs. Int J Syst Sci. 2017; 48(4): 750-756.
- 29Li H, Xie L, Wang Y. On robust control invariance of Boolean control networks. Automatica. 2016; 68: 392-396.
- 30Li Y, Li H, Sun W. Event-triggered control for robust set stabilization of logical control networks. Automatica. 2018; 95: 556-560.
- 31Li B, Lou J, Liu Y, Wang Z. Robust invariant set analysis of Boolean networks. Complexity. 2019; 2019: 1-8.
- 32Qi H, Qiao Y. Dynamics and control of singular Boolean networks. Asian J Control. 2019; 21(6): 2604-2613.
- 33Ledley R. Digital computational methods in symbolic logic, with examples in biochemistry. Proc Natl Acad Sci. 1955; 41(7): 498-511.
- 34 Jia Y, Cheng D, Feng J. State feedback stabilization of generic logic systems via Ledley antecedence solution. Math Methods Appl Sci. 2021. doi:10.1002/mma.7554
- 35Wang Y, Guo P. Optimal control of singular Boolean control networks via Ledley solution method. J Franklin Inst. 2021; 358(12): 6161-6173.
