C. Langbort

F. Farokhi, C. Langbort, K. H. Johansson

The design of optimal disturbance accommodation and servomechanism controllers with limited plant model information is considered in this paper. Their closed-loop performance are compared using a performance metric called competitive ratio which is the worst-case ratio of the cost of a given control design strategy to the cost of the optimal control design with full model information. It was recently shown that when it comes to designing optimal centralized or partially structured decentralized state-feedback controllers with limited model information, the best control design strategy in terms of competitive ratio is a static one. This is true even though the optimal structured decentralized state-feedback controller with full model information is dynamic. In this paper, we show that, in contrast, the best limited model information control design strategy for the disturbance accommodation problem gives a dynamic controller. We find an explicit minimizer of the competitive ratio and we show that it is undominated, that is, there is no other control design strategy that performs better for all possible plants while having the same worst-case ratio. This optimal controller can be separated into a static feedback law and a dynamic disturbance observer. For constant disturbances, it is shown that this structure corresponds to proportional-integral control.

F. Farokhi, C. Langbort, K. H. Johansson

The design of optimal dynamic disturbance accommodation controller with limited model information is considered. We adapt the family of limited model information control design strategies, defined earlier by the authors, to handle dynamic controllers. This family of limited model information design strategies construct subcontrollers distributively by accessing only local plant model information. The closed-loop performance of the dynamic controllers that they can produce are studied using a performance metric called the competitive ratio which is the worst case ratio of the cost a control design strategy to the cost of the optimal control design with full model information.

V. Ugrinovskii, C. Langbort

The paper introduces a class of zero-sum games between the adversary and controller as a scenario for a `denial of service' in a networked control system. The communication link is modeled as a set of transmission regimes controlled by a strategic jammer whose intention is to wage an attack on the plant by choosing a most damaging regime-switching strategy. We demonstrate that even in the one-step case, the introduced games admit a saddle-point equilibrium, at which the jammer's optimal policy is to randomize in a region of the plant's state space, thus requiring the controller to undertake a nontrivial response which is different from what one would expect in a standard stochastic control problem over a packet dropping link. The paper derives conditions for the introduced games to have such a saddle-point equilibrium. Furthermore, we show that in more general multi-stage games, these conditions provide `greedy' jamming strategies for the adversary.