分散制御系の可観測性

情報交換が存在しない場合

抄録

This paper gives some necessary and sufficient conditions for a linear decentralized control system with no information exchange between its control stations to be observable.
Consider a system with two control stations, x(k+1)=Ax(k)+B₁u₁(k)+B₂u₂(k), y_i(k)=C_ix(k), (i=1, 2, k=0, 1, 2, …), where u_i is an r_i vector and y_i is an m_i vector. Let the set Z_i(k) of data available to station i at time k be Z_i(k)={y_i(0), …, y_i(k), u_i(0), …, u_i(k-1)}.
Then a necessary and sufficient condition for the system to be observable by station i is that (i) rank C_iB_j=rankB_j, and (ii) A₃₃ is a nilpotent matrix, (i=1, j=2 or i=2, j=1), when the system and the measurement equations of the i-th station are transformed into a canonical form, where A₁₁: r_j×r_j, and {A₂₂, C₂₂}; observable pair (in usual sense).
For the case where m_i=r_j, another necessary and sufficient condition is given, and it is also shown that a necessary condition for the system to be observable by station i is that (i) {A, C_i} is an observable pair (in usual sense), (ii) C_iB_j is non-singular, and (iii) {A, B_j} is a controllable pair.