193 research outputs found
Event-Triggered Estimation of Linear Systems: An Iterative Algorithm and Optimality Properties
This report investigates the optimal design of event-triggered estimation for
first-order linear stochastic systems. The problem is posed as a two-player
team problem with a partially nested information pattern. The two players are
given by an estimator and an event-trigger. The event-trigger has full state
information and decides, whether the estimator shall obtain the current state
information by transmitting it through a resource constrained channel. The
objective is to find an optimal trade-off between the mean squared estimation
error and the expected transmission rate. The proposed iterative algorithm
alternates between optimizing one player while fixing the other player. It is
shown that the solution of the algorithm converges to a linear predictor and a
symmetric threshold policy, if the densities of the initial state and the noise
variables are even and radially decreasing functions. The effectiveness of the
approach is illustrated on a numerical example. In case of a multimodal
distribution of the noise variables a significant performance improvement can
be achieved compared to a separate design that assumes a linear prediction and
a symmetric threshold policy
Value of Information in Feedback Control
In this article, we investigate the impact of information on networked
control systems, and illustrate how to quantify a fundamental property of
stochastic processes that can enrich our understanding about such systems. To
that end, we develop a theoretical framework for the joint design of an event
trigger and a controller in optimal event-triggered control. We cover two
distinct information patterns: perfect information and imperfect information.
In both cases, observations are available at the event trigger instantly, but
are transmitted to the controller sporadically with one-step delay. For each
information pattern, we characterize the optimal triggering policy and optimal
control policy such that the corresponding policy profile represents a Nash
equilibrium. Accordingly, we quantify the value of information
as the variation in the cost-to-go of the system given
an observation at time . Finally, we provide an algorithm for approximation
of the value of information, and synthesize a closed-form suboptimal triggering
policy with a performance guarantee that can readily be implemented
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