DECENTRALIZED NETWORKED CONTROL SYSTEMS: CONTROL AND ESTIMATION OVER LOSSY CHANNELS

Traditionally in control design, one assumes that system measurements are fed back, without latency or faults over infinite bandwidth channels, to a centralized location where processing and actuation take place. However, these two assumptions no longer hold in many modern control systems. First, the recent technological advances in wireless communication and the decrease in the cost and size of electronics have promoted the use of shared networks for communication between control system components. Control Systems utilizing networks in their loop are called networked control systems (NCSs), which are termed the "Third Generation of Control Systems", in contrast to its predecessors digital and analog control. However, because of network effects such as time delay, packet losses, and coarse quantization, new control problems in NCSs have been researched actively in the last decade. Second, decentralized control of large-scale systems is having an increasingly important role in real-world problems because of its scalability, robustness and computational efficiency. Applications range from aircraft formations, robotic networks, water transportation networks to power systems, data networks, and process control, to mention just few. However, despite these advantages, decentralized controller design has proven to be a quite challenging and complex task analytically. The work in the literature is abundant when considering only one of the two problems, however, the combined area of decentralized networked control systems (DNCS) is still in its infancy. In this work, we study control and estimation problems associated with DNCSs. To the best of our knowledge, several problem formulations are addressed for the first time here. In the DNCS we are considering, we model the network merely as an erasure communication channel following the Gilbert-Elliot model. Packet-losses can result from dropping by the routers due to congestion, dropping by the receiver due to long delay or corrupted content, or dropping by the transmitter due to the inability to access the network. These losses have adversarial effects that might endanger the stability of the system or cause poor performance. Our approach will be to model the overall system as a discrete-time Markovian xii jump linear system (DMJLS), and study its stability, control, and estimation. When looking at the problems decentralized control and estimation of DMJLSs interconnected with norm-bounded interactions, we consider two performance criteria. The first is achieving optimal H∞ disturbance attenuation level, and the other is guaranteeing a worstcase average quadratic cost. We consider the three canonical problems: state feedback, dynamic output feedback, and filtering. For all of them, we provide necessary and sufficient for the construction of controllers/estimators, that take the form of linear matrix inequalities (LMI) for the first, and the form of rank-constrained LMIs for the other two. Furthermore, we provide controller/estimator synthesis procedures for local mode-dependent controllers, which are more practical. In all the cases, we present simulation examples for the application of the developed theorems for a DNCS with packet-losses, comparisons between packet-holding and packetzeroing are conducted for output feedback, and the effect of the packet-loss probabilities on the performance is investigated. In a later chapter, we study the stability of a recently proposed overlapping distributed estimation scheme with Markovian packet losses, where LMI conditions are derived for several notions of stability. Finally, in order to demonstrate the applicability of the results, we apply decentralized state-feedback H∞ disturbance attenuation to a dynamic routing problem with switching topology in a data network, a scenario which arises for example in mobile ad-hoc networks (MANETs). The previous results are modified to accommodate arbitrary bounded interconnected delays, where LMI synthesis procedures are provided. A simulation example to illustrate the results is also given. The control theoretical tools utilized in the thesis include semi-definite programming, Markovian jump systems, the bounded real lemma, H∞ control, quadratic stability and the S-procedure.