Max-plus control design for temporal constraints meeting in timed event graphs, IEEE Transactions on Automatic Control, vol.57, issue.2, pp.462-467, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00752347
Synchronisation and Linearity: An Algebra for Discrete Event Systems, 1992. ,
Lattices and Ordered Algebraic Structures, 2005. ,
Control of Cyclically Operated High-Throughput Screening Systems, 10th International Workshop on Discrete Event Systems, pp.177-183, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00857983
Modeling and control of high-throughput screening systems, Control Engineering Practice, vol.20, issue.1, pp.14-23, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00846116
A linear system theoretic view of discrete event processes and its use for performance evaluation in manufacturing, IEEE Trans. on Automatic Control, 1985. ,
Kernels, images and projections in dioids, Proceedings of WODES'96, 1996. ,
Linear projectors in the max-plus algebra, Proceedings of the IEEE-Mediterranean Conference, 1997. ,
Max-plus algebra and system theory : Where we are and where to go now, Annual Reviews in Control, vol.23, pp.207-219, 1999. ,
Linear system theory for discrete-event systems, 23rd IEEE Conf. on Decision and Control, 1984. ,
Model Reference Control for Timed Event Graphs in Dioids, Automatica, vol.37, issue.9, pp.1451-1458, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-00845151
Data processing tool for calculation in dioid, Proceedings of the 5th International Workshop on Discrete Event Systems, 2000. ,
URL : https://hal.archives-ouvertes.fr/hal-00845037
Duality between invariant spaces for max-plus linear discrete event systems, SIAM Journal on Control and Optimization, vol.48, issue.8, pp.5606-5628, 2010. ,
Derivation of the fundamental traffic diagram for two circular roads and a crossing using minplus algebra and petri net modeling, CDC'05, 2005. ,
Observability of place/transition nets, IEEE Trans. on Automatic Control, vol.47, issue.9, pp.1424-1437, 2002. ,
Sur la commande linéaire de systèmesàévénements discrets dans l'algèbre (max,+), 2004. ,
Towards Geometric Control of Max-Plus Linear Systems with Applications to Manufacturing Systems, Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, pp.171-176, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00857469
Max-plus Linear Observer: Application to manufacturing Systems, Proceedings of the 10th International Workshop on Discrete Event Systems, WODES'10, pp.171-176, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00857986
Observer Design for (max,plus) Linear Systems, IEEE Transactions on Automatic Control, vol.55, issue.2, 2010. ,
Max Plus at Work : Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications, 2006. ,
Max-plus (a,b)-invariant spaces and control of timed discrete-event systems, IEEE Transactin on Automatic Control, vol.52, issue.2, pp.229-241, 2007. ,
URL : https://hal.archives-ouvertes.fr/inria-00070485
Optimal control for (max,+)-linear systems in the presence of disturbances, Positive Systems: Theory and Applications, vol.294, pp.47-54, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00859982
Interval Analysis in Dioid : Application to Robust Open Loop Control for Timed Event Graphs, Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference, pp.7744-7749, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00860560
An introduction to observers, IEEE Trans. on Automatic Control, vol.16, issue.6, pp.596-602, 1971. ,
Optimal Closed-Loop Control for Timed Event Graphs in Dioid, IEEE Transactions on Automatic Control, vol.48, issue.12, pp.2284-2287, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00860022
On the Model Reference Control for Max-Plus Linear Systems, Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference, pp.7799-7803, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00860556
An observer for tropical linear event-invariant dynamical systemsl, 53rd IEEE Conference on Decision and Control, 2014. ,
Second Order Theory of Min-linear Systems and its Application to Discrete Event Systems, Proceedings of the 30th CDC, 1991. ,
Just in time control of timed event graphs: update of reference input, presence of uncontrollable input, IEEE Transactions on Automatic Control, vol.45, issue.11, pp.2155-2159, 2000. ,
URL : https://hal.archives-ouvertes.fr/hal-00844944
Max-plus algebra for discrete event systems-some links to structural controllability and structural observability, IEEE International Symposium on Intelligent Control, pp.579-584, 1995. ,
, Observer-based Controllers for (Max-Plus)-Linear Systems
, , 2010.
,
, DRAFT smatrix CA, 2016.
,
,
, A(2,2)=gd(1,4)
, //(g?1,d?4)
, A(2,1)=gd(0,6)
, A(2,0)=gd(0,1)
, A(0,2)=gd(2,0)
, // matrix of inputs
, smatrix As=star(A
, CA=otimes
,
, CAB=otimes
,
,
, CAR=otimes
the disturbance output transfer matrix cout<<" CAR"<<CAR<<endl ,
, CAB
,
, , vol.2
, Lopt noncausal
,
, // the causal projection of the oberver matrix Lopt=Loptcausal
, Lopt causal
, // Below we check the Corollary 2 smatrix Yu
,
,
,
, Yu=otimes
,
,
,
,
, Yw
, DRAFT Yw=otimes, 2016.
, Loptcausal
, CAR
Corollary 2 is satified, the estimated output and the real output are equal cout<< ,
,
,
, // reference model is chosen equal to the system, we want to keep the inp cout<<, Gref "<<Gref<<endl
, CAB
Popt non causal "<<Popt<<endl ,
,
, Popt causal "<<Popt_causal<<endl
, Popt
,
, Popt
, Kopt non causal"<<Kopt<<endl
, // the state feedback controller
,
, // causal projection Kopt=prcaus(Kopt
,
, Fopt "<<Fopt<<endl
, Kopt "<<Kopt<<endl
, From now I try to enlighten that the strategy with oberverbasedcontrol is better // the feedback, I need your help Ying
,
,
,
,
,
,
, Xu
,
,
,
, Xw
, Lopt
,
, Xw
A+LoptC) * )(LoptCA * )R ,