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Start of funding 01.01.2017

Networked Control over Communcation Channels with Large Delays

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Emerging cyber-physical systems (CPS) such as smart industrial production lines, smart energy grids and autonomous vehicles are all characterized by feedback control loops that are closed over a shared communication channel. This poses novel challenges for the control and communication system design to support such networked control systems. We will consider multiple independent feedback control loops where wireless sensors share the resource-limited communication channel for closing the loop between the sensors and the controllers. A medium access control (MAC) mechanism decides which data packets are forwarded over the communication network. It is well known that MAC protocols contribute to high end-to-end latency, whose length depends on the network load. Latency in a closed control loop significantly impairs the performance and may even lead to instability. The objective of this project is to develop a framework for the co-design of the wireless resource management in terms of medium access control and networked control explicitly considering time delay.

Final report:
Emerging cyber-physical systems (CPS) such as smart industrial production lines, smart energy grids and autonomous vehicles are all characterized by feedback control loops that are closed over a shared communication channel. This poses novel challenges for the control and communication system design to support such networked control systems.

We consider a feedback control loop where wireless sensors transmit data over a resourcelimited communication channel. A medium access control (MAC) mechanism decides which data packets are forwarded over the communication network. It is well known that MAC protocols contribute to high end-to-end latency, whose length depends on the network load. Latency in a closed control loop significantly impairs the performance and may even lead to instability.

One of the most common objectives in engineering practice is to extremize the output of a system, for example to maximize the control performance. In contrast to most methods of adaptive control, extremum seeking, also known as self-optimizing control or extremum control, is able to keep the output at its optimum value without knowledge of the underlying input-to-output map.

Within the project, we developed a general scalar stochastic extremum seeking algorithm for systems with (large) constant delay. The goal is to be able to maximize - or minimize - an arbitrarily high derivative of the output of an unknown dynamic map, in the presence of known constant time delays. Employing Newton's Method, our designed system finds the zero-crossing corresponding to the extremum of the objective derivative, while compensating the known delay through predictor-based control. As with other extremum seeking systems, we rely on perturbation-based derivative estimators for the required gradient and Hessian. However, we focus on stochastic perturbations instead of the classic approach with time-deterministic sinusoids. The user-assignability of the convergence rate is guaranteed by our utilization of a differential Riccati equation to estimate the inverse Hessian, as opposed to its dependence on the unknown Hessian with gradient-based algorithms. Moreover, by perturbing stochastically instead of deterministically, we hope to achieve an increase in performance, especially for higher derivative orders. We prove local exponential stability of the mathematically reduced system and demonstrate the effectiveness of our developed scheme through various simulations.

Outcome and Outlook: We derived a controller, that stabilizes an extremum seeking algorithm in presence of constant output delays of a dynamic map using stochastic perturbations.

This project was a milestone in generalization of adaptive algorithms for extremum seeking using stochastic perturbations. In a recent future, we will publish a paper on the above-mentioned topic and will show a complete proof for stochastic perturbation case in term of expectation.