SCIENTIA SINICA Informationis, Volume 49 , Issue 11 : 1488-1501(2019) https://doi.org/10.1360/N112018-00048

## Control of asynchronous sequential machine with adversarial input based on the semi-tensor product of matrices

• AcceptedDec 27, 2018
• PublishedNov 14, 2019
Share
Rating

### References

[1] Kohavi Z. Switching and Finite Automata Theory. McGraw-Hill, 1978. Google Scholar

[2] Emad N, Shahzadeh-Fazeli S A, Dongarra J. An asynchronous algorithm on the NetSolve global computing system. Future Generation Comput Syst, 2006, 22: 279-290 CrossRef Google Scholar

[3] Nishimura N. Efficient asynchronous simulation of a class of synchronous parallel algorithms. Journal of Computer and System Sciences, 1995, 50: 598--113. Google Scholar

[4] Alba E, Troya J M. Analyzing synchronous and asynchronous parallel distributed genetic algorithms. Future Generation Comput Syst, 2001, 17: 451-465 CrossRef Google Scholar

[5] Hammer J. On some control problems in molecular biology. In: Proceedings of the 33rd Conference on Decisiion and Control. New York: IEEE, 1995. 4098--4103. Google Scholar

[6] Murphy T E. On the Control of Asynchronous Sequential Machines With Races. Dissertation for Ph.D. Degree. Gainesville: University of Florida, 1996. Google Scholar

[7] Geng X J, Hammer J. Input/output control of asynchronous sequential machines. IEEE Trans Automat Contr, 2005, 50: 1956-1970 CrossRef Google Scholar

[8] Yang J M. Corrective Control of Input/Output Asynchronous Sequential Machines with Adversarial Inputs. IEEE Trans Automat Contr, 2010, 55: 755-761 CrossRef Google Scholar

[9] Yang J M, Hammer J. State feedback control of asynchronous sequential machines with adversarial inputs. Int J Contr, 2008, 81: 1910-1929 CrossRef Google Scholar

[10] Yang J M. Corrective control of asynchronous sequential machines in the presence of adversarial input. IET Contr Theor Appl, 2008, 2: 706-716 CrossRef Google Scholar

[11] Yang J M, Hammer J. Counteracting the Effects of Adversarial Inputs on Asynchronous Sequential Machines. IFAC Proc Volumes, 2008, 41: 1432-1437 CrossRef Google Scholar

[12] Cheng D Z, Qi H S, Zhao Y. An Introduction to Semi-Tensor Product of Matrices and its Applications. Singapore: World Science, 2012. Google Scholar

[13] Cheng D Z. Semi-tensor product of matrices and its application to Morgen's problem. Sci China Ser F-Inf Sci, 2001, 44: 195-212 https://doi.org/10.1007/BF02714570. Google Scholar

[14] Liu R J, Lu J Q, Liu Y. Delayed Feedback Control for Stabilization of Boolean Control Networks With State Delay.. IEEE Trans Neural Netw Learning Syst, 2017, : 1-6 CrossRef PubMed Google Scholar

[15] Chen H W, Liang J L, Lu J Q. Partial Synchronization of Interconnected Boolean Networks.. IEEE Trans Cybern, 2017, 47: 258-266 CrossRef PubMed Google Scholar

[16] Liu Y, Chen H W, Lu J Q. Controllability of probabilistic Boolean control networks based on transition probability matrices. Automatica, 2015, 52: 340-345 CrossRef Google Scholar

[17] Li H T, Wang Y Z, Xie L H. Output tracking control of Boolean control networks via state feedback: Constant reference signal case. Automatica, 2015, 59: 54-59 CrossRef Google Scholar

[18] Han X G, Chen Z Q, Liu Z X. Calculation of Siphons and Minimal Siphons in Petri Nets Based on Semi-Tensor Product of Matrices. IEEE Trans Syst Man Cybern Syst, 2017, 47: 531-536 CrossRef Google Scholar

[19] Han X G, Chen Z Q, Liu Z X, et al. Semi-tensor product of matrices approach to stability and stabilization analysis of bounded Petri net systems. Sci Sin Inform, 2016, 46: 1542--1554. Google Scholar

[20] Zhao J T, Chen Z Q, Liu Z X. Modeling and analysis of colored petri net based on the semi-tensor product of matrices. Sci China Inf Sci, 2018, 61: 010205 CrossRef Google Scholar

[21] Yan Y Y, Chen Z Q, Yue J M. STP Approach to Model Controlled Automata with Application to Reachability Analysis of DEDS. Asian J Contr, 2016, 18: 2027-2036 CrossRef Google Scholar

[22] Xu X R, Hong Y G. Matrix expression and reachability analysis of finite automata. J Contr Theor Appl, 2012, 10: 210-215 CrossRef Google Scholar

[23] Zhang K Z, Zhang L J. Observability of Boolean Control Networks: A Unified Approach Based on Finite Automata. IEEE Trans Automat Contr, 2016, 61: 2733-2738 CrossRef Google Scholar

[24] Xu X R, Hong Y G. Model matching for asynchronous sequential machine via matrix approach. In: Proceedings of the 31st Chinese Control Conference, Hefei, 2012. 4646--4651. Google Scholar

[25] Wang J J, Han X G, Chen Z Q. Model matching of input/output asynchronous sequential machines based on the semi-tensor product of matrices. Future Generation Comput Syst, 2018, 83: 468-475 CrossRef Google Scholar

[26] Wang J J, Han X G, Chen Z Q. Calculating skeleton matrix of asynchronous sequential machines based on the semi-tensor product of matrices. IET Contr Theor Appl, 2017, 11: 2131-2139 CrossRef Google Scholar

[27] Wang B, Feng J E, Meng M. Model matching of switched asynchronous sequential machines via matrix approach. Int J Contr, 2018, 105: 1-11 CrossRef Google Scholar

[28] Wang B, Feng J E, Meng M. Matrix approach to model matching of composite asynchronous sequential machines. IET Contr Theor Appl, 2017, 11: 2122-2130 CrossRef Google Scholar

• Figure 1

The closed-loop system ${\Sigma~_{\left|~C~\right.}}$ with an adversarial input

• Table 1   The stable transition functions and output functions of machine $\Sigma$
 $s$ $(a,\alpha~)$ $(a,\beta~)$ $(b,\alpha~)$ $(b,\beta~)$ $(c,\alpha~)$ $(c,\beta~)$ $(c,\alpha~)$ $(d,\beta~)$ $h$ $X$ ${x_1}$ ${x_2}$ – ${x_4}$ – – – ${x_1}$ – ${x_1}$ ${x_1}$ ${x_2}$ ${x_2}$ ${x_2}$ ${x_4}$ ${x_3}$ ${x_3}$ ${x_2}$ ${x_1}$ – ${x_2}$ ${x_2}$ ${x_3}$ – ${x_2}$ – ${x_3}$ ${x_3}$ – ${x_4}$ ${x_4}$ ${x_3}$ ${x_3}$ ${x_4}$ ${x_2}$ ${x_2}$ ${x_4}$ ${x_3}$ ${x_3}$ – ${x_4}$ ${x_4}$ ${x_4}$ ${x_4}$
• Table 2   The stable transition functions and output functions of machine $\Sigma~'$
 $s'$ $a$ $b$ $c$ $d$ $h'$ $X$ ${{x}_1}$ ${{x}_2}$ ${{x}_4}$ – ${{x}_1}$ ${x_1}$ ${x_1}$ ${{x}_2}$ ${{x}_2}$ ${{x}_3}$ ${{x}_2}$ ${{x}_4}$ ${x_2}$ ${x_2}$ ${{x}_3}$ – ${{x}_3}$ ${{x}_3}$ ${{x}_4}$ ${x_3}$ ${x_3}$ ${{x}_4}$ ${{x}_2}$ ${{x}_4}$ ${{x}_3}$ ${{x}_4}$ ${x_4}$ ${x_4}$

Citations

Altmetric