The Decentralized Control Theory Of Large-Scale Complex Systems And Its Applications

The decentralized control theory of large-scale system was investigated in this paper. From an algebraic approach, the decentralized pole placement problem and robust servomechanism problem were explored; From a geometric approach, the problem of elimination of decentralized fixed modes via time-varying decentralized control was explored. There were fourkinds of contributions which were listed as follows:1.The algebraic aspect of decentralized controlThe decentralized pole placement problem was investigated. Firstly, the algebraic description of fixed modes of general proper system was reproved in the way used by B.D.O.Anderson and D.J.Clements. This new proof simplified those in about the same result.. Secondly, By the rank equality of Xie XuKai and one corollary we developed, the single-channel controllability and observability for general proper system were explored and necessary and sufficient condition was obtained. At last, using the results obtained above, the necessary and sufficient condition for the solvability of the decentralized pole placement was obtained.2.The geometric aspect of decentralized controlThe decentralized controllable subspace and unobservable subspace were defined. We explore in detail the relations of these two concepts with the centralized controllable subspace and unobservable subspace respectively, and found out that the structural properties (such as reachability) played a key role in them. Then by a decomposition method, we proved that every state in the decentralized controllable subspace could be conducted to zero state by time-varying decentralized control, which meant that the decentralized controllable subspace had similar property with centralized controllable subspace. In further study the results obtained in literature about eliminating those unstable decentralized fixed modes via time varying decentralized control was obtained again, which proved that those two subspaces we gave was useful in the study of decentralized control.3. The robust decentralized following controlOn the basis of the principle of inner model, the necessary and sufficient condition for the existence of robust decentralized follower was extended to general proper systems. On the other hand, we had obtained the necessary and sufficient condition for the existence of robust decentralized follower when the external unstable model of every subsystem was different with each other.4. The decentralized control of generalized large-scale systemThe results we developed above were all extended to generalized large-scale system.In addition to the theoretic research, the application of the theory we developed to the control of large-scale flexible space structure was also studied. When the sensors and actuators of the structure were collocated, we analyzed its stabilizability and gave a decentralized PD stabilizing controller; we analyzed its follow ability to step input and give a decentralized P1D controller. Finally, these results were demonstrated in the Purdue model.