Generalization Of Linear Systems Research Articles

Linear systems with a canonical polyadic decomposition constrained solution: Algorithms and applications

SummaryReal‐life data often exhibit some structure and/or sparsity, allowing one to use parsimonious models for compact representation and approximation. When considering matrix and tensor data, low‐rank models such as the (multilinear) singular value decomposition, canonical polyadic decomposition (CPD), tensor train, and hierarchical Tucker model are very common. The solution of (large‐scale) linear systems is often structured in a similar way, allowing one to use compact matrix and tensor models as well. In this paper, we focus on linear systems with a CPD‐constrained solution (LS‐CPD). Our main contribution is the development of optimization‐based and algebraic methods to solve LS‐CPDs. Furthermore, we propose a condition that guarantees generic uniqueness of the obtained solution. We also show that LS‐CPDs provide a broad framework for the analysis of multilinear systems of equations. The latter are a higher‐order generalization of linear systems, similar to tensor decompositions being a generalization of matrix decompositions. The wide applicability of LS‐CPDs in domains such as classification, multilinear algebra, and signal processing is illustrated.

Blood glucose regulation in diabetics. A flatness based nonlinear control simulation study

Flat systems are a generalization of linear systems, but the techniques used for controlling flat systems are much different than many of the existing techniques for linear systems. In this paper we present the flatness-based control of blood glucose regulation in human system. A non-near model, he Bergman Minimal Model, is used o represent he dynamics of blood regulation in humans and because of the flatness property, he system variables can be expressed as functions of he at output and heir time derivatives and a control aw developed.

Outer Invariance Entropy for Linear Systems on Lie Groups

Linear systems on Lie groups are a natural generalization of linear systems on Euclidian spaces. For such systems, this paper studies what happens with the outer invariance entropy introduced by Colonius and Kawan [SIAM J. Control Optim., 48 (2009), pp. 1701--1721]. It is shown that, as for the linear Euclidean case, the outer invariance entropy is given by the sum of the positive real parts of the eigenvalues of a linear derivation $\mathcal{D}$ that is associated to the drift of the system.

On robustness in control and LTI identification: Near-linearity and non-conic uncertainty

Robustness issues are studied in the context of linear models in linear controller design and in system identification when the true system is nonlinear. The notion of nearly linear system is generalized to include time-varying and open-loop unstable systems. This class of systems, although it presents the simplest possible (global) generalization of linear systems, is in many ways nontrivial for the purpose of linear controller design and linear model identification from input–output data. This is mainly due to the presence of non-conic uncertainty, which is not included in standard treatments of robust control theory and stochastic system identification theory. Signal distribution theory, a realistic non-stochastic signal analysis tool, is used to study the limiting least squares estimates of linear finite impulse response (FIR) and autoregressive with external input (ARX) model parametrizations for two classes of nonlinear systems. Some connections to worst-case analysis of linear model identification are also discussed.