Optimal Sequence-Based Control of Networked Linear Systems

Digital data networks have been used in control applications for more than 20 years to connect sensors, actuators, and controllers of a control loop. Typically, highly specialized networks are applied, the so called fieldbuses. If sufficiently dimensioned, these networks ensure deterministic data transmission with guaranteed latency. However, the increasing availability, flexibility, and lower costs of general computer networks and wireless networks increased the desire to apply also data networks within a control loop that do not have deterministic transmission characteristics (as, e.g., Ethernet-based LAN, the Internet, WLAN, or Bluetooth). Using this kind of networks not only allows to reduce costs, e.g., by taking advantage of an already installed communication infrastructure, but also to develop new applications. For example, the Internet can be used to bridge long distances within the control loop as, e.g., it occurs in telerobotic applications. In process and factory automation, wireless networks allow to replace costly transmission elements such as slip rings or cable carriers. Also, actuators and sensors can be placed in locations that are hard to access. Moreover, wireless car-to-car communication offers new control perspectives for intelligent highway systems and self-organizing platooning vehicles. However, using non-deterministic data networks within a control loop involves great challenges. In contrast to the specialized fieldbuses, not only time-varying transmission delays can occur but also stochastic data losses as frequently experienced in wireless networks. These network-induced disturbances can massively degrade the control performance and even destabilize the closed-loop system. Therefore, around 15 years ago, research has emerged in the area of Networked Control Systems (NCS) to investigate these problems at the intersection of communication and control. By now, a plethora of methods has been proposed to consider the network effects during the control design. One of these methods is sequence-based control (also referred to as packet-based control or networked predictive control). The analysis, extension, and application of the sequence-based method is the main subject of this work. Sequence-based control uses a property of modern communication networks (such as Ethernet-TCP/IP) that data are sent in form of packets which can transport more information than needed for a single control data transmission. A sequencebased controller uses the available capacity of a data packet and not only sends the current control data but also a sequence of predicted control inputs applicable at future time instants. The predicted control inputs can be applied by the actuator if a subsequent transmission gets delayed or lost. In this way, the network-induced effects can effectively be mitigated. In this work, the newly developed S-LQG (Sequence-Based Linear Quadratic Gaussian) control method is presented. The method combines the idea of the sequencebased control with the LQG approach to stochastic optimal control in order to optimally compensate for network-induced time delays and packet losses. For controller synthesis, the control problem is formulated as an optimization problem that includes a simplified stochastic model of the networks. Using a state augmentation technique, the dynamic programming algorithm can be applied to solve the optimization problem closed-loop optimal in analytic form. In comparison to other optimization-based approaches such as MPC (Model Predictive Control), the S-LQG can be calculated offline. This is a great advantage as it allows the application of the S-LQG also in time critical applications due to the low computation requirements during operation. In addition, the fact that the control law is given in analytic form facilitates the direct analysis of performance and stability of the closed-loop system. Moreover, assuming a time-invariant plant, it is shown that the controller gains converge to a steady-state so that the S-LQG only occupies a small amount of memory. Furthermore, important extensions of the S-LQG are discussed. For example, an event-triggered extension of the proposed approach is presented that can be used in context of band-limited networks to reduce the required bandwidth. Also an optimal tracking controller is derived based on the S-LQG solution that makes optimal use of existing preview information about the reference trajectory. In simulations, the developed approaches show a very good performance compared with state-of-the-art methods. Therefore, the application of the S-LQG method in the field of factory automation has already been initiated in conjunction with an industrial partner. Eidesstattliche Erklärung Hiermit erkläre ich, die vorliegende Dissertation selbstständig angefertigt zu haben. Die verwendeten Quellen sind im Text gekennzeichnet und im Literaturverzeichnis aufgeführt. Karlsruhe, 3. Juni 2014