Design of observers for systems with rational output function

This note presents an approach for the design of asymptotic state observers for systems characterized by output functions that are ratios of polynomials in the state. The case of linear and bilinear input-state dynamics is considered, and conditions for exponential error decay are provided. The first step towards the construction of the observer is to show that the dynamics of a system in the considered class can be embedded into the dynamics of a system of higher dimension, with time-varying linear state dynamics and linear output map. The construction of the observer here proposed exploits the structure of the extended system. The solution of a Riccati differential equation provides the observer gain

Design of observers for systems with rational output function

Abstract-This note presents an approach for the design of asymptotic state observers for systems characterized by output functions that are ratios of polynomials in the state. The case of linear and bilinear input-state dynamics is considered, and conditions for exponential error decay are provided. The first step towards the construction of the observer is to show that the dynamics of a system in the considered class can be embedded into the dynamics of a system of higher dimension, with time-varying linear state dynamics and linear output map. The construction of the observer here proposed exploits the structure of the extended system. The solution of a Riccati differential equation provides the observer gain

Verification of Information Flow Properties under Rational Observation

Information flow properties express the capability for an agent to infer information about secret behaviours of a partially observable system. In a language-theoretic setting, where the system behaviour is described by a language, we define the class of rational information flow properties (RIFP), where observers are modeled by finite transducers, acting on languages in a given family $\mathcal{L}$. This leads to a general decidability criterion for the verification problem of RIFPs on $\mathcal{L}$, implying PSPACE-completeness for this problem on regular languages. We show that most trace-based information flow properties studied up to now are RIFPs, including those related to selective declassification and conditional anonymity. As a consequence, we retrieve several existing decidability results that were obtained by ad-hoc proofs.Comment: 19 pages, 7 figures, version extended from AVOCS'201

A Possible Approach to Inclusion of Space and Time in Frame Fields of Quantum Representations of Real and Complex Numbers

This work is based on the field of reference frames based on quantum representations of real and complex numbers described in other work. Here frame domains are expanded to include space and time lattices. Strings of qukits are described as hybrid systems as they are both mathematical and physical systems. As mathematical systems they represent numbers. As physical systems in each frame the strings have a discrete Schrodinger dynamics on the lattices. The frame field has an iterative structure such that the contents of a stage j frame have images in a stage j-1 (parent) frame. A discussion of parent frame images includes the proposal that points of stage j frame lattices have images as hybrid systems in parent frames. The resulting association of energy with images of lattice point locations, as hybrid systems states, is discussed. Representations and images of other physical systems in the different frames are also described.Comment: Paper has been greatly revised and shortened to 26 pages, 2 figures, per referees comment

The Problem of Confirmation in the Everett Interpretation

I argue that the Oxford school Everett interpretation is internally incoherent, because we cannot claim that in an Everettian universe the kinds of reasoning we have used to arrive at our beliefs about quantum mechanics would lead us to form true beliefs. I show that in an Everettian context, the experimental evidence that we have available could not provide empirical confirmation for quantum mechanics, and moreover that we would not even be able to establish reference to the theoretical entities of quantum mechanics. I then consider a range of existing Everettian approaches to the probability problem and show that they do not succeed in overcoming this incoherence