On the structure of kinematic systems with complete symmetry

This paper provides a new perspective on the structure of kinematic systems with complete symmetry. These systems naturally occur as models for mechanical systems with symmetry, for example flying or submersible robots. The configuration space of such systems is a homogeneous space of the symmetry Lie group, and it is well known that their kinematics can be lifted to equivariant kinematics on the symmetry group thus allowing global state observer constructions. We provide explicitly checkable sufficient differential-algebraic conditions on the symmetry that will lead to a lifted system in the form of standard left or right invariant kinematics on the symmetry group. Previously known conditions for one of these two cases required finding a velocity lift map with particular properties for which there was no general construction known.This work was partially supported by the Australian Research Council through the ARC Discovery Project DP160100783 “Sensing a complex world: Infinite dimensional observer theory for robots”

Sliding mode observers for a class of LPV systems

In this paper, a new framework for the synthesis of a class of sliding mode observers for affine linear parameter varying (LPV) systems is proposed. The sliding mode observer is synthesized by selecting the design freedom via LMIs. Posing the problem from a small gain perspective allows existing numerical techniques from the literature to be used for the purpose of synthesizing the observer gains. In particular, the framework allows affine parameterdependent Lyapunov functions to be considered for analyzing the stability of the state estimation error dynamics, to help reduce design conservatism. Initially a variable structure observer formulation is proposed, but by imposing further constraints on the LMIs, a stable sliding mode is introduced, which can force and maintain the output estimation error to be zero in finite time. The efficacy of the scheme is demonstrated using an LPV model of the short period dynamics of an aircraft and demonstrates simultaneous asymptotic estimation of the states and disturbances

Revisiting consistency conditions for quantum states of systems on closed timelike curves: an epistemic perspective

There has been considerable recent interest in the consequences of closed timelike curves (CTCs) for the dynamics of quantum mechanical systems. A vast majority of research into this area makes use of the dynamical equations developed by Deutsch, which were developed from a consistency condition that assumes that mixed quantum states uniquely describe the physical state of a system. We criticise this choice of consistency condition from an epistemic perspective, i.e., a perspective in which the quantum state represents a state of knowledge about a system. We demonstrate that directly applying Deutsch's condition when mixed states are treated as representing an observer's knowledge of a system can conceal time travel paradoxes from the observer, rather than resolving them. To shed further light on the appropriate dynamics for quantum systems traversing CTCs, we make use of a toy epistemic theory with a strictly classical ontology due to Spekkens and show that, in contrast to the results of Deutsch, many of the traditional paradoxical effects of time travel are present.Comment: 10 pages, 6 figures, comments welcome; v2 added references and clarified some points; v3 published versio

If physics is an information science, what is an observer?

Interpretations of quantum theory have traditionally assumed a "Galilean" observer, a bare "point of view" implemented physically by a quantum system. This paper investigates the consequences of replacing such an informationally-impoverished observer with an observer that satisfies the requirements of classical automata theory, i.e. an observer that encodes sufficient prior information to identify the system being observed and recognize its acceptable states. It shows that with reasonable assumptions about the physical dynamics of information channels, the observations recorded by such an observer will display the typical characteristics predicted by quantum theory, without requiring any specific assumptions about the observer's physical implementation.Comment: 30 pages, comments welcome; v2 significant revisions - results unchange

From Knowledge, Knowability and the Search for Objective Randomness to a New Vision of Complexity

Herein we consider various concepts of entropy as measures of the complexity of phenomena and in so doing encounter a fundamental problem in physics that affects how we understand the nature of reality. In essence the difficulty has to do with our understanding of randomness, irreversibility and unpredictability using physical theory, and these in turn undermine our certainty regarding what we can and what we cannot know about complex phenomena in general. The sources of complexity examined herein appear to be channels for the amplification of naturally occurring randomness in the physical world. Our analysis suggests that when the conditions for the renormalization group apply, this spontaneous randomness, which is not a reflection of our limited knowledge, but a genuine property of nature, does not realize the conventional thermodynamic state, and a new condition, intermediate between the dynamic and the thermodynamic state, emerges. We argue that with this vision of complexity, life, which with ordinary statistical mechanics seems to be foreign to physics, becomes a natural consequence of dynamical processes.Comment: Phylosophica