title: Communication Resource Allocation in Wireless Networked Control Systems
Creators: name: Kiekenap, Kilian
Publisher: name: UNSPECIFIED
Year: 2023

description: Today, mobile communication is mainly focused on human communication, like text messaging, video and voice calls, and the transmission of large data volumes for e.g. audio and video streaming applications. Audio and video communication require moderate latencies and low or medium data rates, while the transmissions of large files generally require high data rates, but could also cope with high latencies. In addition to modes with even higher data rates and more devices per single cell compared to previous generations, the current 5G mobile radio standard will allow for more applications from the control domain, since low latencies and guaranteed maximum error rates are required for so-called Wireless Networked Control Systems (WNCS)s. The new 5G standard considers WNCS in its Ultra-Reliable Low Latency Communication (URLLC) scenario, which provides a low-rate communication with minimal latency and improved error correction for this special type of communication with much smaller amounts of data compared to other scenarios. The exact requirements on latency, maximum error probability and data rate are determined by the dynamics of the respective plants. A closed-loop control system consists of three main components, controller, plant and sensor. The controller sends control commands to the plant, based on the estimated plant state. The plant then applies the commands, thus changing its state. The sensor transmits measurements of the plant state back to the controller to close the feedback loop. Wireless transmission can then be used to transmit either sensor values to the controller, transmit control commands from the controller to the actuator at the plant, or even for both. If multiple subsystems are operated on the same wireless communication resources, a multiple access scheme to prevent interference, which considers also the state and demands of the control system, has to be implemented. This can be done either in a centralized fashion, where a central entity allocates the resources to the individual subsystems, or in a decentralized fashion, where the individual subsystems act cooperatively. A crucial element in control theory is the acquisition of as accurate as possible knowledge of the system state by the sensor and the subsequent transmission to the controller to enable it to generate the optimum control input to minimize a cost function, which depends on the respective application. For the transmission over a digital communication channel, the plant state, which can be modeled as a vector of continuous values, is first sensed and has to be translated to digital symbols afterwards. There are two main sources of error in this process. First, the measurements themselves are impaired by the measurement noise. The error resulting from this noise can be reduced, if multiple independent measurements of the same value are taken and combined. Second, the number of available symbols, which can be transmitted in a fixed time frame with a fixed data rate, is limited, so the values have to be quantized. In this thesis, the existence of an optimum in the tradeoff of the number of noisy measurements and the number of available transmit data symbols with an equal number of bits is shown, if the available time or energy is limited and shared by the measurement and the transmission process. Since domains of the continuous state value space are mapped to a single symbol before transmission, information about the system state is lost due to the quantization. Generally, the more distinct symbols are available in the communication link from the sensor to the controller, the smaller is the resulting quantization error. The measure applied to quantify the error is the Bayes risk. To increase the information about the system state carried by each symbol, a scheme of non-equidistant quantization interval bounds, minimizing the quantization error for a given number of transmit data symbols, and a known distribution of possible sensor values is derived. Since the optimization problem for this scheme is computationally demanding, a second scheme purely equalizing the probability of all possible transmit data symbols is implemented. Finally, as a baseline, an equidistant sampling of the sensor value space for a given number of transmit data symbols is compared to the previous two schemes. By applying the three schemes to three different distributions of a scalar sensor value, it can be shown that the information-optimal scheme can save up to 20% of the required bits for the same Bayes risk, when compared to the linear scheme. In most of the cases, the equidistant scheme achieves about half of the reduction of Bayes risk the information based scheme achieves, when compared to the equidistant scheme. If multiple subsystems with individual sensors and plants are competing for wireless communication resources in WNCS, in some situations the resources are insufficient to always transmit sensor readings from all sensors to the central controller. In this case, a subset of sensors has to be selected and the available resources have to be distributed to them to prevent interference between the transmissions. With a centrally scheduled, discrete time system, a central entity can select the sensors to request readings from in each time slot. For the non-selected subsystems, a prediction of the current state has to be made. The control performance depends on minimizing the uncertainty about the current system state, which is modeled as a white Gaussian system noise, where the variance of the noise is a measure for the uncertainty. For this purpose, the optimality of a regular update scheme for linear subsystems with additive white Gaussian noise is shown. After that, the optimum communication resource share for each subsystem for a given number of communication resources is derived. The calculated resource shares for the subsystems from this optimization are then fed to an algorithm to schedule the actual transmissions. This two-step approach allows for an offline calculation of the resource shares, while during runtime only the actual scheduling based on the precalculated shares has to be done. The average uncertainty about the subsystem states is reduced by up to 20% compared to existing scheduling algorithms. Furthermore, the variation over time of the uncertainty about the subsystem states is reduced by up to 60%. Finally, the reduction of the energy consumption of the wireless transmission of control commands to the actuators at the plants is investigated. In control applications, the calculated control inputs sent from the controller to the actuators must be delivered correctly before a system-dependent deadline. These three requirements are competing, so a tradeoff has to be found. Since the data packets containing the commands are small, instead of the well-known Shannon capacity formula for infinite packet length, an adapted formula for short packets is applied to determine the required energy. The adapted formula can then be used to find the optimum number of time-frequency resources for minimal total energy consumption to be allocated for a single transmission. The resulting optimization problem considering the individual deadlines, command packet sizes and channel characteristics of each agent is shown to be convex. The derived optimal distribution of the limited time and bandwidth resources to the individual subsystems for minimal energy consumption is then applied using an Orthogonal Frequency Division Multiplex (OFDM) scheme. Since OFDM does not allow for a continuous, but only for a resource-block based splitting of resources, an algorithm for the allocation of time-frequency blocks from the OFDM scheme is developed and shown to perform close to the theoretical bounds from the continuous solution. Compared to a scheme only balancing the time-frequency resources allocated to each agent, the total required energy to fulfill the error rate and transmission time limits is reduced by up to 50% when applying the proposed scheme.