Related papers: Universal regular control for generic semilinear s…
Controlled commands -- computations whose execution depends on a separate input -- play a central role in reversible Boolean circuits and quantum circuits. However, existing formalisms typically treat control only implicitly, entangled with…
As is well-known, the classical PID control plays a dominating role in various control loops of industrial processes. However, a theory that can explain the rationale why the linear PID can successfully deal with the ubiquitous uncertain…
Universal approximation theorems establish the expressive capacity of neural network architectures. For dynamical systems, existing results are limited to finite time horizons or systems with a globally stable equilibrium, leaving…
We prove a general multidimensional invariance principle for a family of U-statistics based on freely independent non-commutative random variables of the type $U_n(S)$, where $U_n(x)$ is the $n$-th Chebyshev polynomial and $S$ is a standard…
This work presents several improvements to the closed-loop stability verification framework using semialgebraic sets and convex semidefinite programming to examine neural-network-based control systems regulating nonlinear dynamical systems.…
A class of models of long waves in dispersive media with coupled quadratic nonlinearities on a periodic domain $\mathbb{T}$ are studied. We used two distributed controls, supported in $\omega\subset\mathbb{T}$ and assumed to be generated by…
In this paper we consider kinetically constrained models (KCM) on $\mathbb Z^2$ with general update families $\mathcal U$. For $\mathcal U$ belonging to the so-called "critical class" our focus is on the divergence of the infection time of…
This paper addresses the problem of tracking control for robotic vehicles equipped with pivoted unidirectional actuators. Starting from a baseline robust controller that assumes unconstrained inputs, we redesign the control law to be…
Output feedback controlled synchronization problems for a class of nonlinear unstable systems under information constraints imposed by limited capacity of the communication channel are analyzed. A binary time-varying coder-decoder scheme is…
We establish that if a scheme can control a time-independent system arbitrarily coupled to a generic finite bath over a short period of time $T$ with control precision $O(T^{N+1})$, it can also realize the control with the same order of…
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…
We investigate a new class of nonlinear control systems of O.D.E., which are not feedback linearizable in general. Our class is a generalization of the well-known feedback linearizable systems, and moreover it is a generalization of the…
We show that a bilinear control system is approximately controllable if and only if it is controllable in $\mathbb{R}^{n}\setminus\{0\}$. We approach this problem by looking at the foliation made by the orbits of the system, and by showing…
A cross-dimensional Euclidian space ($\Omega$) is proposed for the state space of dimension varying (control) systems. It is shown that the topological structure of $\Omega$ is consistent with all $\mathbb{R}^n$, which are the state spaces…
Since the classical proportional-integral-derivative (PID) controller is the most widely and successfully used ones in industrial processes, it is of vital importance to investigate theoretically the rationale of this ubiquitous controller…
It is shown that if one can perform a restricted set of fast manipulations on a quantum system, one can implement a large class of dynamical evolutions by effectively removing or introducing selected Hamiltonians. The procedure can be used…
An important result in the theory of quantum control is the "universality" of $2$-local unitary gates, i.e. the fact that any global unitary evolution of a system of $L$ qudits can be implemented by composition of $2$-local unitary gates.…
In this paper, we present a novel decentralized controller to drive multiple unmanned aerial vehicles (UAVs) into a symmetric formation of regular polygon shape surrounding a mobile target. The proposed controller works for time-varying…
We provide bounds on the error between dynamics of an infinite dimensional bilinear Schr\"odinger equation and of its finite dimensional Galerkin approximations. Standard averaging methods are used on the finite dimensional approximations…
In this paper, we consider the problems of approximating uncertainties and feedback control for a class of nonlinear systems without full-known states, and two approximation methods are proposed: universal approximation using integral-chain…