Optimal control of affine connection control systems from the point of view of Lie algebroids

The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems for affine connection control systems (ACCSs) on Lie groups. In this context, the equations for critical trajectories of the problem are geometrically characterized as a Hamiltonian vector field.

On the application of optimal control techniques in lossy fieldbuses

The performance of real-time networks is under continuous improvement as a result of several trends in the digital world. However, these tendencies not only cause improvements, but also exacerbates a series of unideal aspects of real-time networks such as communication latency, jitter of the latency and packet drop rate. This Thesis focuses on the communication errors that appear on such realtime networks, from the point-of-view of automatic control. Specifically, it investigates the effects of packet drops in automatic control over fieldbuses, as well as the architectures and optimal techniques for their compensation. Firstly, a new approach to address the problems that rise in virtue of such packet drops, is proposed. This novel approach is based on the simultaneous transmission of several values in a single message. Such messages can be from sensor to controller, in which case they are comprised of several past sensor readings, or from controller to actuator in which case they are comprised of estimates of several future control values. A series of tests reveal the advantages of this approach. The above-explained approach is then expanded as to accommodate the techniques of contemporary optimal control. However, unlike the aforementioned approach, that deliberately does not send certain messages in order to make a more efficient use of network resources; in the second case, the techniques are used to reduce the effects of packet losses. After these two approaches that are based on data aggregation, it is also studied the optimal control in packet dropping fieldbuses, using generalized actuator output functions. This study ends with the development of a new optimal controller, as well as the function, among the generalized functions that dictate the actuator’s behaviour in the absence of a new control message, that leads to the optimal performance. The Thesis also presents a different line of research, related with the output oscillations that take place as a consequence of the use of classic co-design techniques of networked control. The proposed algorithm has the goal of allowing the execution of such classical co-design algorithms without causing an output oscillation that increases the value of the cost function. Such increases may, under certain circumstances, negate the advantages of the application of the classical co-design techniques. A yet another line of research, investigated algorithms, more efficient than contemporary ones, to generate task execution sequences that guarantee that at least a given number of activated jobs will be executed out of every set composed by a predetermined number of contiguous activations. This algorithm may, in the future, be applied to the generation of message transmission patterns in the above-mentioned techniques for the efficient use of network resources. The proposed task generation algorithm is better than its predecessors in the sense that it is capable of scheduling systems that cannot be scheduled by its predecessor algorithms. The Thesis also presents a mechanism that allows to perform multi-path routing in wireless sensor networks, while ensuring that no value will be counted in duplicate. Thereby, this technique improves the performance of wireless sensor networks, rendering them more suitable for control applications. As mentioned before, this Thesis is centered around techniques for the improvement of performance of distributed control systems in which several elements are connected through a fieldbus that may be subject to packet drops. The first three approaches are directly related to this topic, with the first two approaching the problem from an architectural standpoint, whereas the third one does so from more theoretical grounds. The fourth approach ensures that the approaches to this and similar problems that can be found in the literature that try to achieve goals similar to objectives of this Thesis, can do so without causing other problems that may invalidate the solutions in question. Then, the thesis presents an approach to the problem dealt with in it, which is centered in the efficient generation of the transmission patterns that are used in the aforementioned approaches.

Dependable wireless real-time communications for open environments

Wireless communication technologies have become widely adopted, appearing in heterogeneous applications ranging from tracking victims, responders and equipments in disaster scenarios to machine health monitoring in networked manufacturing systems. Very often, applications demand a strictly bounded timing response, which, in distributed systems, is generally highly dependent on the performance of the underlying communication technology. These systems are said to have real-time timeliness requirements since data communication must be conducted within predefined temporal bounds, whose unfulfillment may compromise the correct behavior of the system and cause economic losses or endanger human lives. The potential adoption of wireless technologies for an increasingly broad range of application scenarios has made the operational requirements more complex and heterogeneous than before for wired technologies. On par with this trend, there is an increasing demand for the provision of cost-effective distributed systems with improved deployment, maintenance and adaptation features. These systems tend to require operational flexibility, which can only be ensured if the underlying communication technology provides both time and event triggered data transmission services while supporting on-line, on-the-fly parameter modification. Generally, wireless enabled applications have deployment requirements that can only be addressed through the use of batteries and/or energy harvesting mechanisms for power supply. These applications usually have stringent autonomy requirements and demand a small form factor, which hinders the use of large batteries. As the communication support may represent a significant part of the energy requirements of a station, the use of power-hungry technologies is not adequate. Hence, in such applications, low-range technologies have been widely adopted. In fact, although low range technologies provide smaller data rates, they spend just a fraction of the energy of their higher-power counterparts. The timeliness requirements of data communications, in general, can be met by ensuring the availability of the medium for any station initiating a transmission. In controlled (close) environments this can be guaranteed, as there is a strict regulation of which stations are installed in the area and for which purpose. Nevertheless, in open environments, this is hard to control because no a priori abstract knowledge is available of which stations and technologies may contend for the medium at any given instant. Hence, the support of wireless real-time communications in unmanaged scenarios is a highly challenging task. Wireless low-power technologies have been the focus of a large research effort, for example, in the Wireless Sensor Network domain. Although bringing extended autonomy to battery powered stations, such technologies are known to be negatively influenced by similar technologies contending for the medium and, especially, by technologies using higher power transmissions over the same frequency bands. A frequency band that is becoming increasingly crowded with competing technologies is the 2.4 GHz Industrial, Scientific and Medical band, encompassing, for example, Bluetooth and ZigBee, two lowpower communication standards which are the base of several real-time protocols. Although these technologies employ mechanisms to improve their coexistence, they are still vulnerable to transmissions from uncoordinated stations with similar technologies or to higher power technologies such as Wi- Fi, which hinders the support of wireless dependable real-time communications in open environments. The Wireless Flexible Time-Triggered Protocol (WFTT) is a master/multi-slave protocol that builds on the flexibility and timeliness provided by the FTT paradigm and on the deterministic medium capture and maintenance provided by the bandjacking technique. This dissertation presents the WFTT protocol and argues that it allows supporting wireless real-time communication services with high dependability requirements in open environments where multiple contention-based technologies may dispute the medium access. Besides, it claims that it is feasible to provide flexible and timely wireless communications at the same time in open environments. The WFTT protocol was inspired on the FTT paradigm, from which higher layer services such as, for example, admission control has been ported. After realizing that bandjacking was an effective technique to ensure the medium access and maintenance in open environments crowded with contention-based communication technologies, it was recognized that the mechanism could be used to devise a wireless medium access protocol that could bring the features offered by the FTT paradigm to the wireless domain. The performance of the WFTT protocol is reported in this dissertation with a description of the implemented devices, the test-bed and a discussion of the obtained results.