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.

Optimal alarms systems and its application to financial time series

This thesis focuses on the application of optimal alarm systems to non linear time series models. The most common classes of models in the analysis of real-valued and integer-valued time series are described. The construction of optimal alarm systems is covered and its applications explored. Considering models with conditional heteroscedasticity, particular attention is given to the Fractionally Integrated Asymmetric Power ARCH, FIAPARCH(p; d; q) model and an optimal alarm system is implemented, following both classical and Bayesian methodologies. Taking into consideration the particular characteristics of the APARCH(p; q) representation for financial time series, the introduction of a possible counterpart for modelling time series of counts is proposed: the INteger-valued Asymmetric Power ARCH, INAPARCH(p; q). The probabilistic properties of the INAPARCH(1; 1) model are comprehensively studied, the conditional maximum likelihood (ML) estimation method is applied and the asymptotic properties of the conditional ML estimator are obtained. The final part of the work consists on the implementation of an optimal alarm system to the INAPARCH(1; 1) model. An application is presented to real data series.

Integer-valued APARCH processes in the analysis of time series of counts

The Asymmetric Power Arch representation for the volatility was introduced by Ding et al.(1993) in order to account for asymmetric responses in the volatility in the analysis of continuous-valued financial time series like, for instance, the log-return series of foreign exchange rates, stock indices or share prices. As reported by Brannas and Quoreshi (2010), asymmetric responses in volatility are also observed in time series of counts such as the number of intra-day transactions in stocks. In this work, an asymmetric power autoregressive conditional Poisson model is introduced for the analysis of time series of counts exhibiting asymmetric overdispersion. Basic probabilistic and statistical properties are summarized and parameter estimation is discussed. A simulation study is presented to illustrate the proposed model. Finally, an empirical application to a set of data concerning the daily number of stock transactions is also presented to attest for its practical applicability in data analysis.