Control with Limited Information

Cedric Langbort, UIUC

The design and implementation of controllers for distributed networked systems bring forth a number of new issues related to (i) the absence of a globally known, trusted, model of the plant, (ii) self-interests of individual components/decision makers, which may find it in their own best interest to misreport observations or mis-implement a globally efficient control action, and (iii) the interplay between communication protocols and control systems.

All these effects, which are unique to distributed control scenarios, can loosely be thought of as limiting the information available to different parts of the system (including the control designer), but introduce this information loss in various and complementary ways. In this talk, we consider simple models that address different aspects of control and control design under restricted information.

* First, we study the ``price of silence" in control design, a new metrics inspired by the notion of "price of anarchy" in network games. While the price of anarchy characterizes the loss of performance due to selfish (i.e. Nash equilibrium playing) decision making, the price of silence is aimed at measuring the best achievable closed-loop performance (compared to the optimum) when the various subsystems composing a plant do not share their model's information with each other, i.e. `remain' silent about their subsystems.

* Then, we consider networked control problems in which the observation channel between the plant and the controller is adversarial (in contrast with traditional models where it is assumed to be stochastically, but non-maliciously, dropping, modifying, or delaying packets). Such strategic channels . We study two different types of attacks, -- one occurring solely at the level of the communication protocol, the other at the physical level -- and compute saddle-node solutions for the resulting zero-sum game between controller and jammer.

Different parts of this talk are the result of joint work with J.Ch. Delvenne (UC Louvain), T. Tanaka, A. Gupta and T. Basar (UIUC), and F. Farokhi and K.H. Johansson (KTH Stockholm).