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The optimal control principle and procedure of a tandem cold rolling system for tracking problem have been proposed in this paper for the first time. The state-space description of the tandem cold rolling system for the cold-strip mill of Wuhan Iron and Steel Company is: x_(k+1)=Ax_k+(_k,y_k=Cx_k+η_k The optimum performance index of the system for tracking problem is: J_(min)=minEr[(1/2)sum from k=0 to m e'_kOe_k sum from k=0 to m-1 u'_kRu_k] The authors have deduced the optimal control of the system for tracking problem as follows u_k~*=-S_k(Ay_k+_(k+1)-) the feedback gain matrix S_k is given by S_k=(B'P_(k+1)B-R)~(-1)B'P_(k+1) Pk satisfies the matrix difference equation p_k=P_(k+1)-[(S_k~(-1))'-B']~(-1)R(S_k~(-1)-B)~(-1)+Q with terminal condition P_m=Q. On the above-mentioned principle of optimal control,an optimal control procedure of the tandem cold rolling system has been obtained, and a computer simulation has been performed. The results of the simulation are satisfactory.