A class of networked multi-agent control systems: Interference induced games, filtering, Nash equilibria

摘要

We consider a class of networked linear scalar stochastic control systems whereby a large number of controlled agents send their states to a central hub, which in turn sends back noiseless control commands based on its observations, and aimed at minimizing a given quadratic cost. The communication technology is code division multiple access (CDMA), and as a result signals received at the central hub are corrupted by interference. The signals sent by agents are considered proportional to their state, and CDMA based signal processing reduces other agents' interference by a factor of 1/N where N is the number of agents. The existing interference inadvertently creates a game situation whereby the actions of one agent affect its state and thus through interference, the ability of other agents to estimate theirs, in turn influencing their ability to control their state. This leads to highly coupled estimation problems. It also leads to a dual control situation as individual controls both steer the state and affect the estimation potential of that state. The thesis is presented in three main parts.;In the first part, we show that ignoring the interference term and using a separation principle for control provably leads to Nash equilibria asymptotic in N, as long as individual dynamics are stable or "not exceedingly" unstable. In particular, we establish that for certain classes of cost and dynamic parameters, optimal separated control laws obtained by ignoring the interference coupling are asymptotically optimal when the number of agents goes to infinity, thus forming for finite N an epsilon-Nash equilibrium. More generally though, optimal separated control laws may not be asymptotically optimal, and can in fact result in unstable overall behavior. Thus we consider a class of parameterized decentralized control laws whereby the separated Kalman gain is treated as the arbitrary gain of a Luenberger like observer. System stability regions are characterized and the nature of optimal cooperative control policies within the considered class is explored.;The second part is concerned with the extension of the work in the first part past the instability threshold for the previous cooperative Luenberger like observers. It is observed that time invariant linear controls based on the outputs of growing dimension filters appear to always maintain system stability, and intriguing state estimate properties are numerically observed. More specifically, we tackle the case of exact decentralized filtering under a class of time invariant certainty equivalent feedback controllers, and numerically investigate both stabilization ability and performance of such controllers as the state estimate feedback gain varies. While the optimum filters have memory requirements which become infinite over time, the stabilization ability of their finite memory approximation is also tested.