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In this paper, a novel design scheme is introduced to solve the optimal control problem for nonlinear systems with unsymmetrical and state-dependent input constraints. By introducing an initial stabilizing control policy as the baseline of…
Unitary designs are unitary ensembles that emulate Haar-random unitary statistics. They provide a vital tool for studying quantum randomness and have found broad applications in quantum technologies. However, existing research has focused…
There exist many examples of systems which have some symmetries, and which one may monitor with symmetry preserving controls. Since symmetries are preserved along the evolution, full controllability is not possible, and controllability has…
In [15] we proposed a set of sufficient conditions for the approximate controllability of a discrete-spectrum bilinear Schr\"odinger equation. These conditions are expressed in terms of the controlled potential and of the eigenpairs of the…
We consider the general bilinear control systems in three-dimensional Euclidean space which satisfy the LARC and have an open control set U; and give sufficient controllability conditions for corresponding projected systems on…
This work provides a framework for data-driven control of discrete time systems with unknown input-output dynamics and outputs controllable by the inputs. This framework leads to stable and robust real-time control of the system such that a…
This paper deals with the problem of robust output regulation of systems governed by nonlinear contraction semigroups. After adding an integral action to the system, we design a feedback law based on the so-called forwarding approach. For…
One of the most important and useful examples in discrete geometry is a finite sequence of points on the moment curve $\gamma(t)=(t,t^2,t^3,\dots ,t^d)$ or, more generally, on a {\it strictly monotone curve} in $\mathbb R^d$. These…
Infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain with full boundary control and without internal damping are studied. This class of systems includes models of beams and waves as well as the transport…
It is shown that a simple modification of the dimensional regularization allows to compute in a consistent and gauge invariant way any diagram with less than four loops in the SO(10) unified model. The method applies also to the Standard…
Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin…
We provide sufficient conditions for the approximate controllability of infinite-dimensional quantum control systems corresponding to form perturbations of the drift Hamiltonian modulated by a control function. We rely on previous results…
We identify a \emph{universal functional form} that governs anticoncentration in random quantum circuits-one that holds across diverse circuit architectures and depths, and crucially remains valid even at finite system sizes and shallow…
We consider a class of optimal control problems on networks that generically permits a reduction to a universal set of reference problems without differential constraints that may be solved analytically. The derivation shows that input…
Since the classical proportional-integral-derivative (PID) controller has continued to be the most widely used feedback methods in engineering systems by far, it is crucial to investigate the working mechanism of PID in dealing with…
The capability of recurrent neural networks to approximate trajectories of a random dynamical system, with random inputs, on non-compact domains, and over an indefinite or infinite time horizon is considered. The main result states that…
In this paper, we study the global approximate multiplicative controllability for nonlinear degenerate parabolic Cauchy-Neumann problems. First, we will obtain embedding results for weighted Sobolev spaces, that have proved decisive in…
Inspired by the adaptation phenomenon of neuronal firing, we propose the regularity normalization (RN) as an unsupervised attention mechanism (UAM) which computes the statistical regularity in the implicit space of neural networks under the…
The aim of this paper is to set up appropriate uniform convergence spaces in which to reformulate and enrich the Order Completion Method for nonlinear PDEs. In this regard, we consider an appropriate space ML(X) of normal lower…
A semigroup A is an abelian semigroup with identity 0. A set of positives in A is an ordered down-directed set P containing with every r an element r/2 with r/2 + r/2 = r. A continuity space is an abstract set X equipped with a map d : XxX…