相关论文: Integral Quadratic Constraints: Exact Convergence …
A point-to-point integrated sensing and communication (ISAC) system is considered where a transmitter conveys a message to a receiver over a discrete memoryless channel (DMC) and simultaneously estimates the state of the channel through the…
Consider a truncated circular unitary matrix which is a $p_n$ by $p_n$ submatrix of an $n$ by $n$ circular unitary matrix by deleting the last $n-p_n$ columns and rows. Jiang and Qi (2017) proved that the maximum absolute value of the…
A new notion of integrability called the multi-dimensional consistency for the integrable systems with the Lagrangian 1-form structure is captured in the geometrical language for quantum level. A zero-curvature condition, which implies the…
Quadratic invariance is a condition which has been shown to allow for optimal decentralized control problems to be cast as convex optimization problems. The condition relates the constraints that the decentralization imposes on the…
In this paper, we address the problem of computing the maximal admissible robust positive invariant (MARPI) set for discrete-time linear time-varying systems with parametric uncertainties and additive disturbances. The system state and…
Consider a square random matrix with independent and identically distributed entries of mean zero and unit variance. We show that as the dimension tends to infinity, the spectral radius is equivalent to the square root of the dimension in…
We examine the utility of the quadratic pseudospectrum in photonics and condensed matter. Specifically, the quadratic pseudospectrum represents a method for approaching systems with incompatible observables, as it both minimizes the…
An autonomous dynamical system is described by a system of second order differential equations whose solution gives the trajectories of the system. The solution is facilitated by the use of first integrals (FIs) that are used to reduce the…
Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the waveguide. Due to geometry, coupling for each microring…
A definition of frequency (cycles per unit-time) based on an approximate reconstruction of the phase-space trajectory of an oscillator from a signal is introduced. It is shown to be invariant under linear filtering, and therefore…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
The word stable is used to describe a situation when mathematical objects that almost satisfy an equation are close to objects satisfying it exactly. We study operator-algebraic forms of stability for unitary representations of groups and…
Consider a square matrix with independent and identically distributed entries of zero mean and unit variance. It is well known that if the entries have a finite fourth moment, then, in high dimension, with high probability, the spectral…
Decoherence represents a major obstacle towards realizing reliable quantum technologies. Identifying states that can be uphold against decoherence by purely coherent means, i.e., {\it stabilizable states}, for which the dissipation-induced…
Shaped pulses obtained by optimal control theory often possess unphysically broad spectra. In principle, the spectral width of a pulse can be restricted by an additional constraint in the optimization functional. However, it has so far been…
In this paper, we present an equivalent convex optimization formulation for discrete-time stochastic linear systems subject to linear chance constraints, alongside a tight convex relaxation for quadratic chance constraints. By lifting the…
In this paper, we propose a novel safety-critical control framework for a chain of integrators subject to both matched and mismatched perturbations. The core of our approach is a linear, time-varying state-feedback design that…
Starting from a solution of the problem of a mechanical oscillator coupled to a scalar field inside a reflecting sphere of radius $R$, we study the behaviour of the system in free space as the limit of an arbitrarily large radius in the…
This paper focuses on adaptive control of the discrete-time linear quadratic regulator (adaptive LQR). Recent literature has made significant contributions in proving non-asymptotic convergence rates, but existing approaches have a few…
This paper addresses an open problem in the area of linear quadratic optimal control. We consider the regular, infinite-horizon, stability-modulo-a-subspace, indefinite linear quadratic problem under the assumption that the dynamics are…