**Networked Control Systems:**

Distributed and Event-Based State Estimation

The Balancing Cube is an example of a networked control system. The rotating modules - each equipped with local actuation, sensing, and computation - share their data over a network to coordinate themselves and stabilize the cube. We use the Balancing Cube as a testbed to develop and test algorithms for control and estimation over networked systems.

A focus of our research is on distributed and event-based state estimation for networked systems where multiple (dynamically coupled) sensor-actuator-agents share data over a broadcast network. We have developed algorithms that estimate the full state of the dynamic system on each agent and, at the same time, adaptively manage the use of the shared network so that data is exchanged between the agents only when required in order to meet a certain estimation performance. Such an event where data is transmitted could be an error passing a threshold level, for example. The key idea of the approach is to use system knowledge, in the form of dynamics models, to allow the agents in the network to make predictions about their peers’ measurements and, this way, avoid some of the communication of sensor data: measurements are only transmitted when the predictions are not good enough. We implemented and verified these methods on the Balancing Cube where we use them for feedback control.

In [1], we present an algorithm for distributed and event-based state estimation where the transmit decision is based on the difference of a sensor measurement and its prediction by a Kalman filter (which uses only the data received over the broadcast network and thus captures the common information of all agents). By this measurement-based triggering rule, sensor update rates can adapt to the need for feedback in real-time. In [3], this approach is extended to a different class of state estimators, which allow for a straightforward performance analysis of the event-based estimator.

In [2], we present an estimation algorithms where the transmit decision is based on the variance of the estimation error (variance-based triggering). The method is amenable to offline analysis and, in [4], we prove for a scalar problem that the resulting transmit schedule is periodic (under certain assumptions), which results in a low-complexity implementation of the transmit decision.

[1] S. Trimpe and R. D'Andrea, An Experimental Demonstration of a Distributed and Event-based State Estimation Algorithm, IFAC World Congress, 2011, pp. 8811–8818.

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[2] S. Trimpe and R. D'Andrea, Reduced Communication State Estimation for Control of an Unstable Networked Control System, 50th IEEE Conference on Decision and Control and European Control Conference, 2011, pp. 2361-2368. (Supplementary material)

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[3] S. Trimpe, Event-Based State Estimation with Switching Static-Gain Observers, 3rd IFAC workshop on Distributed Estimation and Control in Networked Systems, 2012, pp. 91-96.

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[4] S. Trimpe and R. D’Andrea, Event-Based State Estimation with Variance-Based Triggering, 51st IEEE Conference on Decision and Control, 2012, pp. 6583-6590. (Supplementary material)

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