Optimizing controller location in networked control systems with packet drops

In networked control, there is locational freedom in choosing the node at which to locate the controller, so as to mitigate the effects of packet losses in the network. What is the optimal location for the placement of the control logic? Second, what is the optimal control law in that position? The difficulty in answering these two questions is that analysis of optimality in networked control systems subject to random packet drops suffers from Witsenhausen's 'non-classical information pattern'. Thus, the general problem is considered intractable. We make headway on this problem by using a "Long Packet Assumption", LPA, which allows packets to be arbitrarily long. This is not intended for implementation, but only to develop a lower bound on the cost. In particular, under this assumption the optimal controller location can be shown to be collocated with the actuator. For this position, under the LPA, we can also calculate the optimal cost, which is then a lower bound on the optimal cost for the original problem for all locations. Despite the apparent strength of the LPA, we have found that this lower bound is often close to currently realizable upper bounds. This establishes the near optimality of currently implementable controllers in such instances. Using the lower bound on cost we obtain a necessary condition for stabilizability over all controller locations. This condition matches known sufficient conditions for some special cases, thus establishing a necessary and sufficient condition for location optimized stabilizability of networked control systems with packet loss.