The present thesis addresses the problem of stabilisability of a linear time invariant (LTI) output feedback control loop in the presence of a communication link. The communication link itself can be either located between the controller and the plant or between the plant and the controller. The communication link is assumed to be an additive coloured Gaussian noise channel with (or without) bandwidth limitation (memory) in the continuous-(or discrete-)time domain. The requirement for stabilisability of the feedback loop is then characterised as a lower bound on the channel signal to noise ratio (SNR). This lower bound is tight and it will depend on the channel model, plant and channel model NMP zeros, plant time delay and plant unstable poles. Performance requirements are also investigated, by loop shaping in the continuous-time domain, whilst a linear quadratic Gaussian (LQG) control approach is suggested for the discrete-time domain. / PhD Doctorate

This thesis considers the application of information inequalities, Cramér-Rao type bounds, based on Fisher information, to linear systems. These tools are used to study the trade-offs between learning and performance in two application areas: adaptive control and control systems security. In the first part of the thesis, we study stochastic adaptive control of linear quadratic regulators (LQR). Here, information inequalities are used to derive instance-dependent  regret lower bounds. First, we consider a simplified version of LQR, a memoryless reference tracking model, and show how regret can be linked to a cumulative estimation error. This is then exploited to derive a regret lower bound in terms of the Fisher information generated by the experiment of the optimal policy. It is shown that if the optimal policy has ill-conditioned Fisher information, then so does any low-regret policy. This is combined with a Cramér-Rao bound to give a regret lower bound on the order of magnitude square-root T in the time-horizon  for a class of instances we call uninformative. The lower bound holds for all policies which depend smoothly on the underlying parametrization. Second, we extend these results to the general LQR model, and to arbitrary affine parametrizations of the instance parameters. The notion of uninformativeness is generalized to this situation to give a structure-dependent rank condition for when logarithmic regret is impossible. This is done by reduction of regret to a cumulative Bellman error. Due to the quadratic nature of LQR, this Bellman error turns out to be a quadratic form, which again can be interpreted as an estimation error. Using this, we prove a local minimax regret lower bound, of which the proof relies on relating the minimax regret to a Bayesian estimation problem, and then using Van Trees' inequality. Again, it is shown that an appropriate information quantity of any low regret policy is similar to that of the optimal policy and that any uninformative instance suffers local minimax regret at least on the order of magnitude square-root T. Moreover, it shown that the notion of uninformativeness when specialized to certain well-understood scenarios yields a tight characterization of square-root-regret. In the second part of this thesis, we study control systems security problems from a Fisher information point of view. First, we consider a secure state estimation problem and characterize the maximal impact an adversary can cause by means of least informative distributions -- those which maximize the Cramér-Rao bound. For a linear measurement equation, it is shown that the least informative distribution, subjected to variance and sparsity constraints, can be solved for by a semi-definite program, which becomes mixed-integer in the presence of sparsity constraints. Furthermore, by relying on well-known results on minimax and robust estimation, a game-theoretic interpretation for this characterization of the maximum impact is offered. Last, we consider a Fisher information regularized minimum variance control objective, to study the trade-offs between parameter privacy and control performance. It is noted that this can be motivated for instance by learning-based attacks, in which case one seeks to leak as little information as possible to a system-identification adversary. Supposing that the feedback law is linear, the noise distribution minimizing the trace of Fisher information subject to a state variance penalty is found to be conditionally Gaussian. / <p>QC 20210310</p><p>QC 20210310</p>

A full Strouhal number thermo-acoustic model is purposed for the feedback control of self excited noise driven combustors. The inclusion of time delays in the volumetric heat release perturbation models create unique behavioral characteristics which are not properly reproduced within current low Strouhal number thermo acoustic models. New analysis tools using probability density functions are introduced which enable exact expressions for the statistics of a time delayed system. Additionally, preexisting tools from applied mathematics and control theory for spectral analysis of time delay systems are introduced to the combustion community. These new analysis tools can be used to extend sensitivity function analysis used in control theory to explain limits to control effectiveness in self-excited combustors. The control effectiveness of self-excited combustors with actuator constraints are found to be most sensitive to the location of non-minimum phase zeros. Modeling the non-minimum phase zeros correctly require accurate volumetric heat release perturbation models. Designs that removes non-minimum phase zeros are more likely to have poles in the right hand complex plane. As a result, unstable combustors are inherently more responsive to feedback control.

Dans le contexte actuel où l’évolution des systèmes sans-fil est jugée importante, il estnécessaire de pouvoir réduire les pollutions électromagnétiques qui limitent l’acceptabilité descommunications et la cohabitation des systèmes. D’une façon générale, les besoins de contrôle durayonnement des antennes miniatures répondent donc à une demande croissante pour améliorer lesportées mais aussi pour limiter les interférences dans les systèmes sans-fil. Ces dernières années,malgré le développement connu dans les domaines des antennes, la question du contrôle durayonnement des antennes miniatures connait plusieurs barrières empêchant leur déploiementtechnologique. L’approche retenue dans le cadre de cette thèse est le développement de nouveauxconcepts de contrôle du rayonnement des antennes miniatures par la mise en oeuvre de différentestechniques. Cette étude a pour objectif de soulever quelques questions concernant un sujet d’étude peuexploré. / In the current context where the evolution of communicating objects is important indifferent growing fields such as: localization, wireless multimedia systems, etc., controlling theradiation pattern of antennas is one of the most important issues for future radio communicationsystems. In recent years, despite the growth experienced in the areas of antennas, the issue of smallantennas radiation control knows several barriers preventing their deployment. This thesis focuses onthe analysis of the problem of controlling the radiation pattern of small antennas and aims to raisesome questions about a little-explored subject of study. This work gives an approach using differenttechniques to develop new concepts of controlling the radiation pattern of antennas.

We address the question of performance of large-scale networks with distributed feedback control. We consider networked dynamical systems with single and double integrator dynamics, subject to distributed disturbances. We focus on two types of problems. First, we consider problems modeled over regular lattice structures. Here, we treat consensus and vehicular formation problems and evaluate performance in terms of measures of “global order”, which capture the notion of network coherence. Second, we consider electric power networks, which we treat as dynamical systems modeled over general graphs. Here, we evaluate performance in terms of the resistive power losses that are incurred in maintaining network synchrony. These losses are associated with transient power flows that are a consequence of “local disorder” caused by lack of synchrony. In both cases, we characterize fundamental limitations to performance as networks become large. Previous studies have shown that such limitations hold for coherence in networks with regular lattice structures. These imply that connections in 3 spatial dimensions are necessary to achieve full coherence, when the controller uses static feedback from relative measurements in a local neighborhood. We show that these limitations remain valid also with dynamic feedback, where each controller has an internal memory state. However, if the controller can access certain absolute state information, dynamic feedback can improve performance compared to static feedback, allowing also 1-dimensional formations to be fully coherent. For electric power networks, we show that the transient power losses grow unboundedly with network size. However, in contrast to previous results, performance does not improve with increased network connectivity. We also show that a certain type of distributed dynamic feedback controller can improve performance by reducing losses, but that their scaling with network size remains an important limitation. / <p>QC 20160504</p>