Optimal tracking control across erasure communication links in the presence of preview

Consider two identical discrete-time. finite-dimensional. linear and time-invariant systems denoted its the leader and the follower. The leader system is driven by a deterministic control input and by a zero-mean while Gaussian process noise. In this paper. we address the problem of designing a networked control scheme for the follower system. which guarantees that the state of the system tracks the state of the leader system optimally. according to a mean-squared cost We adopt a networked control architecture featuring two erasure links and three design blocks a controller acting on the follower system and two encoders, one at the output of each system. The controller has remote access to noisy measurements of the state of both systems via two erasure links that are used to connect each encoder to the controller We consider erasure links whose erasure events occur according to a Bernoulli process If an erasure occurs. then no uniformation is transmitted: otherwise. a finite vector of teal numbers is conveyed through the link. The purpose of the encoders is to process noisy measurements of the output of each system prior to transmission over the corresponding erasure. link. While the encoder of the follower system has access to current measurements. the encoder of the leader system has access to measurements that are advanced in time by a finite time interval (also denoted as preview) This paper describes a methodology for the design of controller and encoders that tire jointly optimal. with respect to optimal tracking of the leader system by the follower system We also obtain explicit necessary and sufficient conditions for the existence of a scheme that guarantees that the tracking en-or has finite second moment. Copyright (C) 2008 John Wiley & Sons, Ltd.