On the observer canonical form for Nonlinear Time-Delay Systems

6 pagesInternational audienceNecessary and sufficient geometric conditions for the equivalence of a nonlinear time-delay system with one output, under bicausal change of coordinates and output transformation, to a linear weakly observable time-delay system up to output injection are given. These conditions are derived through the use of the Extended Lie Bracket operator recently introduced in the literature for dealing with time-delay systems. The results presented show how this operator is useful in the analysis of this class of nonlinear systems

Probability around the Quantum Gravity. Part 1: Pure Planar Gravity

In this paper we study stochastic dynamics which leaves quantum gravity equilibrium distribution invariant. We start theoretical study of this dynamics (earlier it was only used for Monte-Carlo simulation). Main new results concern the existence and properties of local correlation functions in the thermodynamic limit. The study of dynamics constitutes a third part of the series of papers where more general class of processes were studied (but it is self-contained), those processes have some universal significance in probability and they cover most concrete processes, also they have many examples in computer science and biology. At the same time the paper can serve an introduction to quantum gravity for a probabilist: we give a rigorous exposition of quantum gravity in the planar pure gravity case. Mostly we use combinatorial techniques, instead of more popular in physics random matrix models, the central point is the famous $\alpha =-7/2$ exponent.Comment: 40 pages, 11 figure

Chaotic dynamical systems associated with tilings of RN\R^N

In this chapter, we consider a class of discrete dynamical systems defined on the homogeneous space associated with a regular tiling of $\R^N$, whose most familiar example is provided by the $N-$dimensional torus \T ^N. It is proved that any dynamical system in this class is chaotic in the sense of Devaney, and that it admits at least one positive Lyapunov exponent. Next, a chaos-synchronization mechanism is introduced and used for masking information in a communication setup

Physics Without Physics: The Power of Information-theoretical Principles

David Finkelstein was very fond of the new information-theoretic paradigm of physics advocated by John Archibald Wheeler and Richard Feynman. Only recently, however, the paradigm has concretely shown its full power, with the derivation of quantum theory (Chiribella et al., Phys. Rev. A 84:012311, 2011; D'Ariano et al., 2017) and of free quantum field theory (D'Ariano and Perinotti, Phys. Rev. A 90:062106, 2014; Bisio et al., Phys. Rev. A 88:032301, 2013; Bisio et al., Ann. Phys. 354:244, 2015; Bisio et al., Ann. Phys. 368:177, 2016) from informational principles. The paradigm has opened for the first time the possibility of avoiding physical primitives in the axioms of the physical theory, allowing a refoundation of the whole physics over logically solid grounds. In addition to such methodological value, the new information-theoretic derivation of quantum field theory is particularly interesting for establishing a theoretical framework for quantum gravity, with the idea of obtaining gravity itself as emergent from the quantum information processing, as also suggested by the role played by information in the holographic principle (Susskind, J. Math. Phys. 36:6377, 1995; Bousso, Rev. Mod. Phys. 74:825, 2002). In this paper I review how free quantum field theory is derived without using mechanical primitives, including space-time, special relativity, Hamiltonians, and quantization rules. The theory is simply provided by the simplest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the three following simple principles: homogeneity, locality, and isotropy. The inherent discrete nature of the informational derivation leads to an extension of quantum field theory in terms of a quantum cellular automata and quantum walks. A simple heuristic argument sets the scale to the Planck one, and the observed regime is that of small wavevectors ...Comment: 34 pages, 8 figures. Paper for in memoriam of David Finkelstei

Doubly-Special Relativity: Facts, Myths and Some Key Open Issues

I report, emphasizing some key open issues and some aspects that are particularly relevant for phenomenology, on the status of the development of "doubly-special" relativistic ("DSR") theories with both an observer-independent high-velocity scale and an observer-independent small-length/large-momentum scale, possibly relevant for the Planck-scale/quantum-gravity realm. I also give a true/false characterization of the structure of these theories. In particular, I discuss a DSR scenario without modification of the energy-momentum dispersion relation and without the $\kappa$-Poincar\'e Hopf algebra, a scenario with deformed Poincar\'e symmetries which is not a DSR scenario, some scenarios with both an invariant length scale and an invariant velocity scale which are not DSR scenarios, and a DSR scenario in which it is easy to verify that some observable relativistic (but non-special-relativistic) features are insensitive to possible nonlinear redefinitions of symmetry generators.Comment: This is the preprint version of a paper prepared for a special issue "Feature Papers: Symmetry Concepts and Applications" of the journal Symmetr

Exponentially Stable Adaptive Observation for Systems Parameterized by Unknown Physical Parameters

The method to design exponentially stable adaptive observers is proposed for linear time-invariant systems parameterized by unknown physical parameters. Unlike existing adaptive solutions, the system state-space matrices A, B are not restricted to be represented in the observer canonical form to implement the observer. The original system description is used instead, and, consequently, the original state vector is obtained. The class of systems for which the method is applicable is identified via three assumptions related to: (i) the boundedness of a control signal and all system trajectories, (ii) the identifiability of the physical parameters of A and B from the numerator and denominator polynomials of a system input/output transfer function and (iii) the complete observability of system states. In case they are met and the regressor is finitely exciting, the proposed adaptive observer, which is based on the known GPEBO and DREM procedures, ensures exponential convergence of both system parameters and states estimates to their true values. Detailed analysis for stability and convergence has been provided along with simulation results to validate the developed theory.Comment: 8 pages, 2 figure