LQG control policy design against agent identity privacy problem

This thesis project studies the agent identity privacy problem in the scalar linear quadratic Gaussian (LQG) control system. For the agent identity privacy problem in the LQG control, privacy models and privacy measures have to be established first. It depends on a trajectory of correlated data rather than a single observation. I propose here privacy models and the corresponding privacy measures by taking into account the two characteristics. The agent identity is a binary hypothesis: Agent A or Agent B. An eavesdropper is assumed to make a hypothesis testing on the agent identity based on the intercepted environment state sequence. The privacy risk is measured by the Kullback-Leibler divergence between the probability distributions of state sequences under two hypotheses. By taking into account both the accumulative control reward and privacy risk, an optimization problem of the policy of Agent B is formulated. The optimal deterministic privacy-preserving LQG policy of Agent B is a linear mapping. A sufficient condition is given to guarantee that the optimal deterministic privacy-preserving policy is time-invariant in the asymptotic regime. An independent Gaussian random variable cannot improve the performance of Agent B. The numerical experiments justify the theoretic results and illustrate the reward-privacy trade-off. Based on the privacy model and the LQG control model, I have formulated the mathematical problems for the agent identity privacy problem in LQG. The formulated problems address the two design objectives: to maximize the control reward and to minimize the privacy risk. I have conducted theoretic analysis on the LQG control policy in the agent identity privacy problem and the trade-off between the control reward and the privacy risk.Finally, the theoretic results are justified by numerical experiments. From the numerical results, I expected to have some interesting observations and insights, which are explained in the last chapter.

Divergence patterns in Fucus seaweeds (Phaeophyceae) in the northern Baltic Sea and in the Tjongspollen area

To be able to interpret patterns of biodiversity it is important to understand the processes by which new species evolve and how closely related species remain reproductively isolated and ecologically differentiated. Divergence and differentiation can vary during speciation and it can be seen in different stages. Groups of closely related taxa constitute important case studies to understand species and new biodiversity formation. However, it is important to assess the divergence among them at different organismal levels and from an integrative perspective. For this purpose, this study used the brown seaweeds genus Fucus as a model to study speciation, as they constitute a good opportunity to study divergence at different stages. We investigated the divergence patterns in Fucus species from two marginal areas (northern Baltic Sea and the Tjongspollen area), based on phenetic, phylogenetic and biological taxonomical criteria that are respectively characterised by algal morphology, allele frequencies of five microsatellite loci and levels of secondary polyphenolic compounds called phlorotannins. The results from this study showed divergence at morphological and genetic levels to certain extent but complete lack of divergence at biochemical level (i.e. constitutive phlorotannin production) in the Baltic Sea or Norway. Morphological divergence was clearly evident in Tjongspollen (Norway) among putative taxa as they were identified in the field and this divergence corresponds with their neutral genetic divergence. In the Baltic, there are some distinguishable patterns in the morphology of the swedish and finnish individuals according to locality to certain extent but not among putative taxa within localities. Likewise, these morphological patterns have genetic correspondence among localities but not within each locality. At the biochemical level, measured by the phlorotannin contents there were neither evidence of divergence in Norway or the Baltic Sea nor any discernable aggregation pattern among or within localities. Our study have contributed with further understanding of the Baltic Sea Fucus system and its intriguingly rapid and recent divergence as well as of the Tjongspollen area systems where formally undescribed individuals have been observed for the first time; in fact they appear largely differentiated and they may well warrant a new species status. In current times, climate change threatens, peripheral ecosystems, biodiversity, and increased knowledge of processes generating and maintaining biodiversity in those ecosystems seem particularly important and needed.