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1. Controllability of Sobolev-Type Linear Ensemble Systems

   https://doi.org/10.1109/CDC45484.2021.9683659  

   Zhang, W; Tie, L; Li, J.-S. (December 2021, 60th IEEE Conference on Decision and Control)

   Systems composed of large ensembles of isolated or interacted dynamic units are prevalent in nature and engineered infrastructures. Linear ensemble systems are inarguably the simplest class of ensemble systems and have attracted intensive attention to control theorists and practionars in the past years. Comprehensive understanding of dynamic properties of such systems yet remains far-fetched and requires considerable knowledge and techniques beyond the reach of modern control theory. In this paper, we explore the classes of linear ensemble systems with system matrices that are not globally diagonalizable. In particular, we focus on analyzing their controllability properties under a Sobolev space setting and develop conditions under which uniform controllability of such ensemble systems is equivalent to that of their diagonalizable counterparts. This development significantly facilitates controllability analysis for linear ensemble systems through examining diagonalized linear systems. 

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2. Finite Sample Identification of Bilinear Dynamical Systems

   Sattar, Yahya; Oymak, Samet; Ozay, Necmiye (January 2022, Proceedings of the IEEE Conference on Decision Control)

   Bilinear dynamical systems are ubiquitous in many different domains and they can also be used to approximate more general control-affine systems. This motivates the problem of learning bilinear systems from a single trajectory of the system’s states and inputs. Under a mild marginal meansquare stability assumption, we identify how much data is needed to estimate the unknown bilinear system up to a desired accuracy with high probability. Our sample complexity and statistical error rates are optimal in terms of the trajectory length, the dimensionality of the system and the input size. Our proof technique relies on an application of martingale small-ball condition. This enables us to correctly capture the properties of the problem, specifically our error rates do not deteriorate with increasing instability. Finally, we show that numerical experiments are well-aligned with our theoretical results. 

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3. Sparse Linear Ensemble Systems and Structural Controllability

   https://doi.org/10.1109/TAC.2021.3097289  

   Chen, Xudong (July 2021, IEEE Transactions on Automatic Control)

   The paper introduces and solves a structural controllability problem for continuum ensembles of linear time-invariant systems. All the individual linear systems of an ensemble are sparse, governed by the same sparsity pattern. Controllability of an ensemble system is, by convention, the capability of using a common control input to simultaneously steer every individual systems in it. A sparsity pattern is structurally controllable if it admits a controllable linear ensemble system. A main contribution of the paper is to provide a graphical condition that is necessary and sufficient for a sparsity pattern to be structurally controllable. Like other structural problems, the property of being structural controllable is monotone. We provide a complete characterization of minimal sparsity patterns as well. 

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4. A Randomized Distributed Kaczmarz Algorithm and Anomaly Detection

   https://doi.org/10.3390/axioms11030106  

   Keinert, Fritz; Weber, Eric S. (March 2022, Axioms)

   The Kaczmarz algorithm is an iterative method for solving systems of linear equations. We introduce a randomized Kaczmarz algorithm for solving systems of linear equations in a distributed environment, i.e., the equations within the system are distributed over multiple nodes within a network. The modification we introduce is designed for a network with a tree structure that allows for passage of solution estimates between the nodes in the network. We demonstrate that the algorithm converges to the solution, or the solution of minimal norm, when the system is consistent. We also prove convergence rates of the randomized algorithm that depend on the spectral data of the coefficient matrix and the random control probability distribution. In addition, we demonstrate that the randomized algorithm can be used to identify anomalies in the system of equations when the measurements are perturbed by large, sparse noise. 

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5. A Distributed-Parameter Control System Using Electromagnetic Images Stimulation for Human-Machine Perception Interface

   https://doi.org/10.1115/DSCC2018-9217  

   Li, Min; Lee, Kok-Meng (September 2018, Proceedings of the ASME 2018 Dynamic Systems and Control Conference)

   This article develops a new human-machine perception interface method to convert visual patterns to accurate eddy-current stimulation using an electromagnet (EM) array. The eddy-current stimulation is formulated as a feedforward controller design. In this paper, a state-space model for the eddy-current stimulation is derived for design and analysis of the controller. Unlike traditional methods where the distributed parameter systems are often modeled using partial differential equations and solved numerically using numerical methods such as finite element analysis, the model presented here offers closed-form solutions in state-space representation. The novel approach enables the applications of the well-established control theory for analyzing the system controllability. The feasibility and accuracy of the feedforward control method are numerically illustrated and validated by generating the stimulation with two types of patterns, which provides an essential base for future research of human-machine perception interface. 

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