Related papers: Rational observers of rational systems
Complex systems are often composed of many small communicating components called modules. We investigate the synthesis of supervisory controllers for modular systems under partial observation that, as the closed-loop system, realize the…
Program synthesis techniques construct or infer programs from user-provided specifications, such as input-output examples. Yet most specifications, especially those given by end-users, leave the synthesis problem radically ill-posed,…
In this paper, we consider a control synthesis problem for a class of polynomial dynamical systems subject to bounded disturbances and with input constraints. More precisely, we aim at synthesizing at the same time a controller and an…
We address an inverse problem in non-Archimedean dynamics: given a finite discrete dynamical system (equivalently, a functional graph on $N$ states), construct a continuous $p$-adic dynamical system whose residue-level behavior reproduces…
The discovery of a small cosmological constant has stimulated interest in the measure problem. One should expect to be a typical observer, but defining such a thing is difficult in the vastness of an eternally inflating universe. We propose…
A rational function is the ratio of two complex polynomials in one variable without common roots. Its degree is the maximum of the degrees of the numerator and the denominator. Rational functions belong to the same class if one turns into…
Abstraction and realization are bilateral processes that are key in deriving intelligence and creativity. In many domains, the two processes are approached through rules: high-level principles that reveal invariances within similar yet…
Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs…
Two related numerical schemes for the realization of the Mortensen observer or minimum energy estimator for the state reconstruction of non-linear dynamical systems subject to deterministic disturbances are proposed and compared. Both…
We identify a new observability concept, called relative observability, in supervisory control of discrete-event systems under partial observation. A fixed, ambient language is given, relative to which observability is tested. Relative…
We discuss first order systems of rational difference equations which have the property that lines through the origin are mapped into lines through the origin. We call such systems projective systems of rational difference equations and we…
We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by…
Synthesizer is a fast, flexible, modular, and extensible Python package that empowers astronomers to turn theoretical galaxy models into realistic synthetic observations - including spectra, photometry, images, and spectral cubes - with a…
The duality between controllability and observability enables methods developed for full-state control to be applied to full-state estimation, and vice versa. In applications in which control or estimation of all state variables is…
For obtaining causal inferences that are objective, and therefore have the best chance of revealing scientific truths, carefully designed and executed randomized experiments are generally considered to be the gold standard. Observational…
Various methods are nowadays available to design observers for broad classes of systems, where the primary focus is on establishing the convergence of the estimated states. Nevertheless, the question of the tuning of the observer to achieve…
This article focuses on the development of functional unknown input observers for systems with arbitrary relative degree. Two distinct approaches are presented to address this challenge. The first approach is tailored to a class of…
A major issue with using deep learning models in sensitive applications is that they provide no explanation for their output. To address this problem, unsupervised selective rationalization produces rationales alongside predictions by…
Given a holonomic sequence $F(n)$, we characterize rational functions $r(n)$ so that $r(n)F(n)$ can be summable. We provide upper and lower bounds on the degree of the numerator of $r(k)$ and show the denominator of $r(n)$ can be read from…
Real-world phenomena can often be conveniently described by dynamical systems (that is, ODE systems in the state-space form). However, if one observes the state of the system only partially, the observed quantities (outputs) and the inputs…