Gradient Methods for Large-Scale and Distributed Linear Quadratic Control

This thesis considers methods for synthesis of linear quadratic controllers for large-scale, interconnected systems. Conventional methods that solve the linear quadratic control problem are only applicable to systems with moderate size, due to the rapid increase in both computational time and memory requirements as the system size increases. The methods presented in this thesis show a much slower increase in these requirements when faced with system matrices with a sparse structure. Hence, they are useful for control design for systems of large order, since they usually have sparse systems matrices. An equally important feature of the methods is that the controllers are restricted to have a distributed nature, meaning that they respect a potential interconnection structure of the system. The controllers considered in the thesis have the same structure as the centralized LQG solution, that is, they are consisting of a state predictor and feedback from the estimated states. Strategies for determining the feedback matrix and predictor matrix separately, are suggested. The strategies use gradient directions of the cost function to iteratively approach a locally optimal solution in either problem. A scheme to determine bounds on the degree of suboptimality of the partial solution in every iteration, is presented. It is also shown that these bounds can be combined to give a bound on the degree of suboptimality of the full output feedback controller. Another method that treats the synthesis of the feedback matrix and predictor matrix simultaneously is also presented. The functionality of the developed methods is illustrated by an application, where the methods are used to compute controllers for a large deformable mirror, found in a telescope to compensate for atmospheric disturbances. The model of the mirror is obtained by discretizing a partial differential equation. This gives a linear, sparse representation of the mirror with a very large state space, which is suitable for the methods presented in the thesis. The performance of the controllers is evaluated using performance measures from the adaptive optics community

Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPs in short-term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks.Comment: 31 page

Decentralized Control of Large Collaborative Swarms using Random Finite Set Theory

Controlling large swarms of robotic agents presents many challenges including, but not limited to, computational complexity due to a large number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm's configuration. The contribution of this work is to decentralize Random Finite Set (RFS) control of large collaborative swarms for control of individual agents. The RFS control formulation assumes that the topology underlying the swarm control is complete and uses the complete graph in a centralized manner. To generalize the control topology in a localized or decentralized manner, sparse LQR is used to sparsify the RFS control gain matrix obtained using iterative LQR. This allows agents to use information of agents near each other (localized topology) or only the agent's own information (decentralized topology) to make a control decision. Sparsity and performance for decentralized RFS control are compared for different degrees of localization in feedback control gains which show that the stability and performance compared to centralized control do not degrade significantly in providing RFS control for large collaborative swarms.Comment: arXiv admin note: text overlap with arXiv:1810.0069

The State-of-the-Art Survey on Optimization Methods for Cyber-physical Networks

Cyber-Physical Systems (CPS) are increasingly complex and frequently integrated into modern societies via critical infrastructure systems, products, and services. Consequently, there is a need for reliable functionality of these complex systems under various scenarios, from physical failures due to aging, through to cyber attacks. Indeed, the development of effective strategies to restore disrupted infrastructure systems continues to be a major challenge. Hitherto, there have been an increasing number of papers evaluating cyber-physical infrastructures, yet a comprehensive review focusing on mathematical modeling and different optimization methods is still lacking. Thus, this review paper appraises the literature on optimization techniques for CPS facing disruption, to synthesize key findings on the current methods in this domain. A total of 108 relevant research papers are reviewed following an extensive assessment of all major scientific databases. The main mathematical modeling practices and optimization methods are identified for both deterministic and stochastic formulations, categorizing them based on the solution approach (exact, heuristic, meta-heuristic), objective function, and network size. We also perform keyword clustering and bibliographic coupling analyses to summarize the current research trends. Future research needs in terms of the scalability of optimization algorithms are discussed. Overall, there is a need to shift towards more scalable optimization solution algorithms, empowered by data-driven methods and machine learning, to provide reliable decision-support systems for decision-makers and practitioners

Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area