Related papers: A Rigorous Computational Approach to Linear Respon…
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
This paper investigates adaptive model predictive control (MPC) for a class of constrained linear systems with unknown model parameters. This is also posed as the dual control problem consisting of system identification and regulation. We…
Density matrix perturbation theory based on recursive Fermi-operator expansions provides a computationally efficient framework for time-independent response calculations in quantum chemistry and materials science. From a perturbation in the…
The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response…
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
Late-lumping feedback design for infinite-dimensional linear systems with unbounded input operators is considered. The proposed scheme is suitable for the approximation of backstepping and flatness-based designs and relies on a…
This paper studies the theoretical construction and analytic error estimation of complex Bessel function-based conformal mappings in regions with randomly perturbed boundaries. First, we construct a conformal mapping applicable to such…
We establish an algorithm to learn feedback maps from data for a class of robust model predictive control (MPC) problems. The algorithm accounts for the approximation errors due to the learning directly at the synthesis stage, ensuring…
We address a specific but recurring problem related to sampled linear systems. In particular, we provide a numerical method for the rigorous verification of constraint satisfaction for linear continuous-time systems between sampling…
Linear response theory asserts that sufficiently small external biases produce currents proportional to the applied force and forms the theoretical foundation of nonequilibrium transport. Here we demonstrate that linear response can break…
The paper deals with local robust feedback synthesis for systems with multidimensional control and unknown bounded perturbations. Using V.~I.~Korobov's controllability function method, we construct a bounded control which steers an…
We propose a novel approach to design a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertain system is modeled as linear parameter varying with additive disturbance. Set bounds for the system…
The goal of response theory, in each of its many statistical mechanical formulations, is to predict the perturbed response of a system from the knowledge of the unperturbed state and of the applied perturbation. A new recent angle on the…
This theoretical work considers the following conundrum: linear response theory is successfully used by scientists in numerous fields, but mathematicians have shown that typical low-dimensional dynamical systems violate the theory's…
Perturbative expansions in physical applications are generically divergent, and their physical content can be studied using Borel analysis. Given just a finite number of terms of such an expansion, this input data can be analyzed in…
This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…
The diamond and completely bounded norms for linear maps play an increasingly important role in quantum information science, providing fundamental stabilized distance measures for differences of quantum operations. Based on the theory of…
In this paper, we derive closed-form expressions for implicit controlled invariant sets for discrete-time controllable linear systems with measurable disturbances. In particular, a disturbance-reactive (or disturbance feedback) controller…
From previous work arXiv:2010.09811, the semiclassical backreaction equation in 1+1 dimensions was solved and a criterion was implemented to assess the validity of the semiclassical approximation in this case. The criterion involves the…
This is the third part of four series papers, aiming at the delay compensation for the abstract linear system (A,B,C). Both the input delay and output delay are investigated. We first propose a full state feedback control to stabilize the…