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 @math as the variation in the cost-to-go of the system given an observation at time @math . 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.
A special class of event-triggered estimation and event-triggered control is sensor scheduling in which open-loop triggering policies are employed. Sensor scheduling can be traced back to the 1970s. However, recently Trimpe and D'Andrea @cite_25 and Leong @cite_8 adopted sensor scheduling for networked control systems, and obtained open-loop triggering policies in terms of the estimation error covariances. It is also worth mentioning that in a rather different setup from what we consider in this study, Antunes and Heemels @cite_27 considered a networked control system in which the event trigger and controller are both collocated with the sensor, and control inputs are to be transmitted to the process. They proposed an approximation algorithm, and showed that a performance improvement with respect to periodic control can be guaranteed. Our approximation algorithm is inspired by this idea. Nevertheless, herein unlike the above work, the event trigger and controller are distributed.
@cite_27 @cite_25 @cite_8
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Cyber-Physical Systems (CPSs) resulting from the interconnection of computational, communication, and control (cyber) devices with physical processes are wide spreading in our society. In several CPS applications it is crucial to minimize the communication burden, while still providing desirable closed-loop control properties. To this effect, a promising approach is to embrace the recently proposed event-triggered control paradigm, in which the transmission times are chosen based on well-defined events, using state information. However, few general event-triggered control methods guarantee closed-loop improvements over traditional periodic transmission strategies. Here, we provide a new class of event-triggered controllers for linear systems which guarantee better quadratic performance than traditional periodic time-triggered control using the same average transmission rate. In particular, our main results explicitly quantify the obtained performance improvements for quadratic average cost problems. The proposed controllers are inspired by rollout ideas in the context of dynamic programming. An event-based state estimation scenario is considered where a sensor sporadically transmits observations of a scalar linear process to a remote estimator. The remote estimator is a time-varying Kalman filter. The triggering decision is based on the estimation variance: the sensor runs a copy of the remote estimator and transmits a measurement if the associated measurement prediction variance exceeds a tolerable threshold. The resulting variance iteration is a new type of Riccati equation with switching that corresponds to the availability or unavailability of a measurement and depends on the variance at the previous step. We study asymptotic properties of the variance iteration and, in particular, asymptotic convergence to a periodic solution. This paper studies a remote state estimation problem where a sensor, equipped with energy harvesting capabilities, observes a dynamical process and transmits local state estimates over a packet dropping channel to a remote estimator. The objective is to decide, at every discrete time instant, whether the sensor should transmit or not, in order to minimize the expected estimation error covariance at the remote estimator over a finite horizon, subject to constraints on the sensor’s battery energy governed by an energy harvesting process. We establish structural results on the optimal scheduling which show that, for a given battery energy level and a given harvested energy, the optimal policy is a threshold policy on the error covariance. Similarly, for a given error covariance and a given harvested energy, the optimal policy is a threshold policy on the current battery level. An extension to the problem of transmission scheduling and control with an energy harvesting sensor is also considered.