Verification of periodically controlled hybrid systems: Application to an autonomous vehicle

This article introduces Periodically Controlled Hybrid Automata (PCHA) for modular specification of embedded control systems. In a PCHA, control actions that change the control input to the plant occur roughly periodically, while other actions that update the state of the controller may occur in the interim. Such actions could model, for example, sensor updates and information received from higher-level planning modules that change the set point of the controller. Based on periodicity and subtangential conditions, a new sufficient condition for verifying invariant properties of PCHAs is presented. For PCHAs with polynomial continuous vector fields, it is possible to check these conditions automatically using, for example, quantifier elimination or sum of squares decomposition. We examine the feasibility of this automatic approach on a small example. The proposed technique is also used to manually verify safety and progress properties of a fairly complex planner-controller subsystem of an autonomous ground vehicle. Geometric properties of planner-generated paths are derived which guarantee that such paths can be safely followed by the controller. © 2012 ACM.

Periodically controlled hybrid systems verifying a controller for an autonomous vehicle

This paper introduces Periodically Controlled Hybrid Automata (PCHA) for describing a class of hybrid control systems. In a PCHA, control actions occur roughly periodically while internal and input actions may occur in the interim changing the discrete-state or the setpoint. Based on periodicity and subtangential conditions, a new sufficient condition for verifying invariance of PCHAs is presented. This technique is used in verifying safety of the planner-controller subsystem of an autonomous ground vehicle, and in deriving geometric properties of planner generated paths that can be followed safely by the controller under environmental uncertainties.

On the existence of Zeno behavior in hybrid systems with non-isolated zeno equilibria

This paper presents proof-certificate based sufficient conditions for the existence of Zeno behavior in hybrid systems near non-isolated Zeno equilibria. To establish these conditions, we first prove sufficient conditions for Zeno behavior in a special class of hybrid systems termed first quadrant interval hybrid systems. The proof-certificate sufficient conditions are then obtained through a collection of functions that effectively "reduce" a general hybrid system to a first quadrant interval hybrid system. This paper concludes with an application of these ideas to Lagrangian hybrid systems, resulting in easily verifiable sufficient conditions for Zeno behavior. © 2008 IEEE.

The vibro-acoustic analysis of built-up systems using a hybrid method with parametric and non-parametric uncertainties

An existing hybrid finite element (FE)/statistical energy analysis (SEA) approach to the analysis of the mid- and high frequency vibrations of a complex built-up system is extended here to a wider class of uncertainty modeling. In the original approach, the constituent parts of the system are considered to be either deterministic, and modeled using FE, or highly random, and modeled using SEA. A non-parametric model of randomness is employed in the SEA components, based on diffuse wave theory and the Gaussian Orthogonal Ensemble (GOE), and this enables the mean and variance of second order quantities such as vibrational energy and response cross-spectra to be predicted. In the present work the assumption that the FE components are deterministic is relaxed by the introduction of a parametric model of uncertainty in these components. The parametric uncertainty may be modeled either probabilistically, or by using a non-probabilistic approach such as interval analysis, and it is shown how these descriptions can be combined with the non-parametric uncertainty in the SEA subsystems to yield an overall assessment of the performance of the system. The method is illustrated by application to an example built-up plate system which has random properties, and benchmark comparisons are made with full Monte Carlo simulations. © 2012 Elsevier Ltd. All rights reserved.

Non-relativistic conformal symmetries in fluid mechanics

The symmetries of a free incompressible fluid span the Galilei group, augmented with independent dilations of space and time. When the fluid is compressible, the symmetry is enlarged to the expanded Schrodinger group, which also involves, in addition, Schrodinger expansions. While incompressible fluid dynamics can be derived as an appropriate non-relativistic limit of a conformally invariant relativistic theory, the recently discussed conformal Galilei group, obtained by contraction from the relativistic conformal group, is not a symmetry. This is explained by the subtleties of the non-relativistic limit.

Non-commutative oscillator with Kepler-type dynamical symmetry

A 3-dimensional non-commutative oscillator with no mass term but with an appropriate momentum-dependent potential admits a conserved Runge-Lenz vector, derived from the dual description in momentum space. The trajectories lie on ellipses. The dynamical symmetry allows for an algebraic determination of the bound-state spectrum and extends to o(4,2). (c) 2010 Elsevier B.V. All rights reserved.

An Autonomous Sailing Robot for Ocean Observation

Sauze, C. and Neal, M. 'An Autonomous Sailing Robot for Ocean Observation', in proceedings of TAROS 2006, Guildford, UK, Sept 4-6th 2006, pages 190-197.

On the Size Distribution of Autonomous Systems

This paper explores reasons for the high degree of variability in the sizes of ASes that have recently been observed, and the processes by which this variable distribution develops. AS size distribution is important for a number of reasons. First, when modeling network topologies, an AS size distribution assists in labeling routers with an associated AS. Second, AS size has been found to be positively correlated with the degree of the AS (number of peering links), so understanding the distribution of AS sizes has implications for AS connectivity properties. Our model accounts for AS births, growth, and mergers. We analyze two models: one incorporates only the growth of hosts and ASes, and a second extends that model to include mergers of ASes. We show analytically that, given reasonable assumptions about the nature of mergers, the resulting size distribution exhibits a power law tail with the exponent independent of the details of the merging process. We estimate parameters of the models from measurements obtained from Internet registries and from BGP tables. We then compare the models solutions to empirical AS size distribution taken from Mercator and Skitter datasets, and find that the simple growth-based model yields general agreement with empirical data. Our analysis of the model in which mergers occur in a manner independent of the size of the merging ASes suggests that more detailed analysis of merger processes is needed.

Simultaneous Learning of Non-Linear Manifold and Dynamical Models for High-Dimensional Time Series

The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. The model structure setup and parameter learning are done using a variational Bayesian approach, which enables automatic Bayesian model structure selection, hence solving the problem of over-fitting. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.

Localization in systems of non-identical oscillators

A singular perturbation method is applied to a non-conservative system of two weakly coupled strongly nonlinear non-identical oscillators. For certain parameters, localized solutions exist for which the amplitude of one oscillator is an order of magnitude smaller than the other. It is shown that these solutions are described by coupled equations for the phase difference and scaled amplitudes. Three types of localized solutions are obtained as solutions to these equations which correspond to phase locking, phase drift, and phase entrainment. Quantitative results for the phases and amplitudes of the oscillators and the stability of these phenomena are expressed in terms of the parameters of the model.

Plankton indicators and ocean observing systems: support to the marine ecosystem state assessment

Ecological indicators are used extensively as tools to manage environmental resources. In the oceans, indicators of plankton can be measured using a variety of observing systems including: mooring stations, ships, autonomous floats and ocean colour remote sensing. Given the broad range of temporal and spatial sampling resolutions of these different observing systems, as well as discrepancies in measurements obtained from different sensors, the estimation and interpretation of plankton indicators can present significant challenges. To provide support to the assessment of the state of the marine ecosystem, we propose a suite of plankton indicators and subsequently classify them in an ecological framework that characterizes key attributes of the ecosystem. We present two case studies dealing with plankton indicators of biomass, size structure and phenology, estimated using the most spatially extensive and longest in situ and remote-sensing observations. Discussion of these studies illustrates how some of the challenges in estimating and interpreting plankton indicators may be addressed by using for example relative measurement thresholds, interpolation procedures and delineation of biogeochemical provinces. We demonstrate that one of the benefits attained, when analyzing a suite of plankton indicators classified in an ecological framework, is the elucidation of non-trivial changes in composition, structure and functioning of the marine ecosystem.

Stability of 5-aminolevulinic acid in novel non-aqueous gel and patch-type systems intended for topical application.

Aminolevulinic acid (ALA) stability within topical formulations intended for photodynamic therapy (PDT) is poor due to dimerisation to pyrazine-2,5-dipropionic acid (PY). Most strategies to improve stability use low pH vehicles, which can cause cutaneous irritancy. To overcome this problem, a novel approach is investigated that uses a non-aqueous vehicle to retard proton-induced charge separation across the 4-carbonyl group on ALA and lessen nucleophilic attack that leads to condensation dimerisation. Bioadhesive anhydrous vehicles based on methylvinylether-maleic anhydride copolymer patches and poly(ethyleneglycol) or glycerol thickened poly(acrylic acid) gels were formulated. ALA stability fell below pharmaceutically acceptable levels after 6 months, with bioadhesive patches stored at 5°C demonstrating the best stability by maintaining 86.2% of their original loading. Glycerol-based gels maintained 40.2% in similar conditions. However, ALA loss did not correspond to expected increases in PY, indicating the presence of another degradative process that prevented dimerisation. Nuclear magnetic resonance (NMR) analysis was inconclusive in respect of the mechanism observed in the patch system, but showed clearly that an esterification reaction involving ALA and both glycerol and poly(ethyleneglycol) was occurring. This was especially marked in the glycerol gels, where only 2.21% of the total expected PY was detected after 204 days at 5°C. Non-specific esterase hydrolysis demonstrated that ALA was recoverable from the gel systems, further supporting esterified binding within the gel matrices. It is conceivable that skin esterases could duplicate this finding upon topical application of the gel and convert these derivatives back to ALA in situ, provided skin penetration is not affected adversely.