Related papers: Feedback classification of linear systems over von…
As a key method in dealing with uncertainties, feedback has been understood fairly well in classical control theory. But for quantum control systems, the capability of measurement-based feedback control (MFC) has not been investigated…
Finitely generated Z-modules have canonical decompositions. When such modules are given in a finitely presented form there is a classical algorithm for computing a canonical decomposition. This is the algorithm for computing the Smith…
Conic linear programs, among them semidefinite programs, often behave pathologically: the optimal values of the primal and dual programs may differ, and may not be attained. We present a novel analysis of these pathological behaviors. We…
Prediction-based transformation is applied to control-affine systems with distributed input delays. Transformed system state is calculated as a prediction of the system's future response to the past input with future input set to zero.…
It has been known in the robotics literature since about 1995 that, in polar coordinates, the nonholonomic unicycle is asymptotically stabilizable by smooth feedback, even globally. We introduce a modular design framework that selects the…
In an unnormalized Krylov subspace framework for solving symmetric systems of linear equations, the orthogonal vectors that are generated by a Lanczos process are not necessarily on the form of gradients. Associating each orthogonal vector…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…
Macroscopic observables in a quantum spin system are given by sequences of spatial means of local elements $\frac{1}{2n+1}\sum_{j=-n}^n\gamma_j(A_{i}), \; n\in{\mathbb N},\; i=1,...,m$ in a UHF algebra. One of their properties is that they…
We examine whether metrological resolution beyond coherent states is a nonclassical effect. We show that this is true for linear detection schemes but false for nonlinear schemes, and propose a very simple experimental setup to test it. We…
For a general class of dynamical systems (of which the canonical continuous and uniform discrete versions are but special cases), we prove that there is a state feedback gain such that the resulting closed-loop system is uniformly…
A badly approximable system of affine forms is determined by a matrix and a vector. We show Kleinbock's conjecture for badly approximable systems of affine forms: for any fixed vector, the set of badly approximable systems of affine forms…
We propose a new controllability property for linear time varying control systems in finite dimension: the nonuniform complete controllability, which is halfway between the classical Kalman's properties of complete controllability and…
This paper studies the Kalman decomposition for linear quantum systems. Contrary to the classical case, the coordinate transformation used for the decomposition must belong to a specific class of transformations as a consequence of the laws…
The trace regression model, a direct extension of the well-studied linear regression model, allows one to map matrices to real-valued outputs. We here introduce an even more general model, namely the partial-trace regression model, a family…
The rules of canonical quantization normally offer good results, but sometimes they fail, e.g., leading to quantum triviality ($=$ free) for certain examples that are classically nontrivial ($\ne$ free). A new procedure, called Enhanced…
Let G be a complex connected reductive group. The representation ring R(G) admits a canonical filtration defined in terms of the lambda-structure. We compute the associated graded ring gr R(G) (over Q) and the Chern classes of a…
In this note, we propose a method to under-approximate finite-time reachable sets and tubes for a class of continuous-time linear uncertain systems. The class under consideration is the linear time-varying (LTV) class with integrable…
Randomized benchmarking (RB) is the gold standard for experimentally evaluating the quality of quantum operations. The current framework for RB is centered on groups and their representations, but this can be problematic. For example,…
The invariant classification of superintegrable systems is reviewed and utilized to construct singular limits between the systems. It is shown, by construction, that all superintegrable systems on conformally flat, 3D complex Riemannian…
This paper demonstrates the first application of feedback linearization to replicator dynamics, driving the evolution of non-convergent evolutionary games to systems with guaranteed global asymptotic stability.