On the Stochastic Control of Coupled Linear Systems.
Abstract
The stochastic control of two coupled linear systems with two controllers whose measurements are corrupted by white gaussian noise is considered. Three cases are differentiated: cooperation and centralization, when the information structure consists of identical sets; cooperation and complete decentralization, when each controller has only information about his own system; and cooperation and partial decentralization, when the information sets are in general different. In the cooperative and centralized case, the problem is reduced to an one-controller control problem. By constraining the form of the controls and application of the matrix minimum principle, optimal controls are obtained. The results are the same as those given by the 'Separation Theorem'. Suboptimal controls, good for sufficiently small coupling, are the results of a direct expansion. In the completely decentralized case, an approximate model which gives simple suboptimal controls is proposed by replacing the influence of one system on the other by a white noise. A deterministic optimal control problem for calculating the covariances of these noises is then formulated. For a sufficiently weak coupling, the choice of these covariances is shown to be immaterial. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1970
- Accession Number
- AD0715281
Entities
People
- Chee-yee Chong
Organizations
- Massachusetts Institute of Technology