-I
CONTROLS
I OBSERVATIONS
t CONTROLLER I _-
Figure 6.1.-Classical control theory systems model. tolerance with a limited fuel budget") typically expressed mathematically in a quadratic form computes linear control to correct the system trajectory to meet the stated objective. This type of formulation is known as the LQG (Linear Quadratic Gaussian) formulation and has received wide attention within the control theory community. Clearly, this theory is applicable to navigation and process control problems but will make only a rather minor contribution to the theory of how systems operate as a whole. This is not considered a critical mission technology since it is a fairly well developed and active field. Further, application depends on the notion of a single centralized controller. This is appropriate for micro control applications but inappropriate for macro control of large decentralized systems. Game theory. Systems which employ multiple decision makers have been addressed by game theorists. Much of this work has been defense-related although economics has also provided an applications base. The basic notion of game theory is that there are an arbitrary number of decisionmakers, each of whom has an individual objective function which may be (and likely is) in conflict with the objectives of the other decisionmakers. Each decisionmaker attempts to develop strategies which independently maximize the "payoff" to himself. Much work has been done on the "zero sum game" in which one decisionmaker's gain is another's loss. If one envisions a cooperative, coordinated mission scenario, the current focus of game theory on threat strategies more appropriate to hostile environments seem illsuited to peaceful space activities. A more appropriate meta-model is required for NASA's applications which reflects the necessity for cooperative coordination among the men and machines of the mission. Nonclassical information control theory. The decentralized control problem for large-scale systems with a common (or at least coordinated) objective has received increasing attention in recent years. Initial work on "team theory" (Radner, 1962) has centered on a team which is considered to have as its fundamental problem the coordination of decentralized activities utilizing delayed and imperfect information. The meta-model employed appears to be appropriate for the large-scale space missions considered in this report. Team theorists envision an autonomous ensemble of decisionmakers, each of which senses a local environment ("perfect" information) and can communicate in a delayed fashion with other decisionmakers ("imperfect" information). The ensemble, or team, shares a common objective and attempts to communicate as necessary for collective progress toward that objective to be optimized in some sense. This leads to the notion of an information structure among the members of the team. The team concept has since been adopted within the control theory community and has led to "nonclassical control theory" -control theory which addresses multidecisionmaker types of problems (Ho, 1980; Sandell et al., 1978). Much of this work is supported heavily by the Department of Defense (DOD) and focuses on problems of little direct relevance to NASA. Vigorous support by NASA of work in nonclassical control theory is recommended to develop more appropriate theories for the types of systems which comprise the space missions of the future. For instance, much of the DOD work addresses guidance and control problems, whereas NASA's prime interest would be more appropriately in information systems control. Supporting disciplines include probability and Markov decision processes. These are areas which are required to advance the state of the art in systems theory and control and to apply it effectively to NASA missions. Prior work in these fields tends to focus on performance optimality as an objective. While optimality is a laudable goal, it is not clear that this should override other concerns such as stability and performance predictability. The fomaal tools currently available to evaluate the stability of a large decentralized system are virtually nonexistent. The major recommendation of the study group in this area is that NASA seriously consider the system-wide objectives of its future systems and support a program of basic and applied research the t
