Decentralized optimal control with application to dynamic routing in computer communication networks

This research considers the dynamic routing problem of computer communication networks in the framework of decentralized control theory. The routing dynamics are modeled in terms of a state equation with multiple controllers. Routing, or control of message flow, is formulated as an optimal control problem with multiple decision makers. Each decision maker may have access to different set of information and work cooperatively to optimize a common system performance index. Necessary and sufficient conditions for optimality are derived for a system with a deterministic and a stochastic traffic patterns under a linear information structure and a quadratic performance index. The resultant control strategies are examined with two extreme information cases: (1) complete information where all state information are available to every local controller through measurement or perfect communication, and (2) partial information where there is no communication among controllers. A three node network is used as a numerical example to interpret the results

On Team Decision Problems with Nonclassical Information Structures

In this paper, we consider sequential dynamic team decision problems with nonclassical information structures. First, we address the problem from the point of view of a "manager" who seeks to derive the optimal strategy of the team in a centralized process. We derive structural results that yield an information state for the team which does not depend on the control strategy, and thus it can lead to a dynamic programming decomposition where the optimization problem is over the space of the team's decisions. We, then, derive structural results for each team member that yield an information state which does not depend on their control strategy, and thus it can lead to a dynamic programming decomposition where the optimization problem for each team member is over the space of their decisions. Finally, we show that the control strategy of each team member is the same as the one derived by the manager. We present an illustrative example of a dynamic team with a delayed sharing information structure.Comment: 16 page

Optimal Control of Two-Player Systems with Output Feedback

In this article, we consider a fundamental decentralized optimal control problem, which we call the two-player problem. Two subsystems are interconnected in a nested information pattern, and output feedback controllers must be designed for each subsystem. Several special cases of this architecture have previously been solved, such as the state-feedback case or the case where the dynamics of both systems are decoupled. In this paper, we present a detailed solution to the general case. The structure of the optimal decentralized controller is reminiscent of that of the optimal centralized controller; each player must estimate the state of the system given their available information and apply static control policies to these estimates to compute the optimal controller. The previously solved cases benefit from a separation between estimation and control which allows one to compute the control and estimation gains separately. This feature is not present in general, and some of the gains must be solved for simultaneously. We show that computing the required coupled estimation and control gains amounts to solving a small system of linear equations

Perspectives in modern control theory

Bibliography: leaves 33-36.Prepared under ONR Contract N00014-76-C-0346.by Michael Athans