Nonlinear Robust Observer Design Using An Invariant Manifold Approach

This paper presents a method to design a reduced order observer using an invariant manifold approach. The main advantages of this method are that it enables a systematic design approach, and (unlike most nonlinear observer design methods), it can be generalized over a larger class of nonlinear systems. The method uses specific mapping functions in a way that minimises the error dynamics close to zero. Another important aspect is the robustness property which is due to the manifold attractivity: an important feature when an observer is used in a closed loop control system. A two degree-of-freedom system is used as an example. The observer design is validated using numerical simulation. Then experimental validation is carried out using hardware-in-the-loop testing. The proposed observer is then compared with a very well known nonlinear observer based on the off-line solution of the Riccati equation for systems with Lipschitz type nonlinearity. In all cases, the performance of the proposed observer is shown to be very high

Robust model predictive control for dynamics compensation in real-time hybrid simulation

Hybrid simulation is an efficient method to obtain the response of an emulated system subjected to dynamic excitation by combining loading-rate-sensitive numerical and physical substructures. In such simulations, the interfaces between physical and numerical substructures are usually implemented using transfer systems, i.e., an arrangement of actuators. To guarantee high fidelity of the simulation outcome, conducting hybrid simulation in hard real-time is required. Albeit attractive, real-time hybrid simulation comes with numerous challenges, such as the inherent dynamics of the transfer system used, along with communication interrupts between numerical and physical substructures, that introduce time delays to the overall hybrid model altering the dynamic response of the system under consideration. Hence, implementation of adequate control techniques to compensate for such delays is necessary. In this study, a novel control strategy is proposed for time delay compensation of actuator dynamics in hard real-time hybrid simulation applications. The method is based on designing a transfer system controller consisting of a robust model predictive controller along with a polynomial extrapolation algorithm and a Kalman filter. This paper presents a proposed tracking controller first, followed by two virtual real-time hybrid simulation parametric case studies, which serve to validate the performance and robustness of the novel control strategy. Real-time hybrid simulation using the proposed control scheme is demonstrated to be effective for structural performance assessment

Partial synchronization of non-identical chaotic systems via adaptive control, with applications to modelling coupled nonlinear systems

We consider the coupling of two nonidentical dynamical systems using an adaptive feedback linearization controller to achieve partial synchronization between the two systems. In addition we consider the case where an additional feedback signal exists between the two systems, which leads to bidirectional coupling. We demonstrate the stability of the adaptive controller, and use the example of coupling a Chua system with a Lorenz system, both exhibiting chaotic motion, as an example of the coupling technique. A feedback linearization controller is used to show the difference between unidirectional and bidirectional coupling. We observe that the adaptive controller converges to the feedback linearization controller in the steady state for the Chua– Lorenz example. Finally we comment on how this type of partial synchronization technique can be applied to modeling systems of coupled nonlinear subsystems. We show how such modeling can be achieved where the dynamics of one system is known only via experimental time series measurements

Radio observations of the cool gas, dust, and star formation in the first galaxies

We summarize cm through submm observations of the host galaxies of z ~ 6 quasars. These observations reveal the cool molecular gas (the fuel for star formation), the warm dust (heated by star formation), the fine structure line emission (tracing the CNM and PDRs), and the synchrotron emission. Our results imply active star formation in ~ 30% of the host galaxies, with star formation rates ~ 10^3 M_sun/year, and molecular gas masses ~ 10^10 M_sun. Imaging of the [CII] emission from the most distant quasar reveals a 'maximal starburst disk' on a scale ~ 1.5 kpc. Gas dynamical studies suggest a departure of these galaxies from the low-z M_{BH} -- M_{bulge} relation, with the black holes being, on average, 15 times more massive than expected. Overall, we are witnessing the co-eval formation of massive galaxies and supermassive black holes within 1 Gyr of the Big Bang.Comment: First Stars and Galaxies: Challenges in the Next Decade, AIP, 2010; Austin TX (eds Whelan, Bromm, Yoshida); 7 page

A Meta-Learning Approach to Population-Based Modelling of Structures

A major problem of machine-learning approaches in structural dynamics is the frequent lack of structural data. Inspired by the recently-emerging field of population-based structural health monitoring (PBSHM), and the use of transfer learning in this novel field, the current work attempts to create models that are able to transfer knowledge within populations of structures. The approach followed here is meta-learning, which is developed with a view to creating neural network models which are able to exploit knowledge from a population of various tasks to perform well in newly-presented tasks, with minimal training and a small number of data samples from the new task. Essentially, the method attempts to perform transfer learning in an automatic manner within the population of tasks. For the purposes of population-based structural modelling, the different tasks refer to different structures. The method is applied here to a population of simulated structures with a view to predicting their responses as a function of some environmental parameters. The meta-learning approach, which is used herein is the model-agnostic meta-learning (MAML) approach; it is compared to a traditional data-driven modelling approach, that of Gaussian processes, which is a quite effective alternative when few data samples are available for a problem. It is observed that the models trained using meta-learning approaches, are able to outperform conventional machine learning methods regarding inference about structures of the population, for which only a small number of samples are available. Moreover, the models prove to learn part of the physics of the problem, making them more robust than plain machine-learning algorithms. Another advantage of the methods is that the structures do not need to be parametrised in order for the knowledge transfer to be performed

Model selection and parameter estimation in structural dynamics using approximate Bayesian computation

This paper will introduce the use of the approximate Bayesian computation (ABC) algorithm for model selection and parameter estimation in structural dynamics. ABC is a likelihood-free method typically used when the likelihood function is either intractable or cannot be approached in a closed form. To circumvent the evaluation of the likelihood function, simulation from a forward model is at the core of the ABC algorithm. The algorithm offers the possibility to use different metrics and summary statistics representative of the data to carry out Bayesian inference. The efficacy of the algorithm in structural dynamics is demonstrated through three different illustrative examples of nonlinear system identification: cubic and cubic-quintic models, the Bouc-Wen model and the Duffing oscillator. The obtained results suggest that ABC is a promising alternative to deal with model selection and parameter estimation issues, specifically for systems with complex behaviours

System identification of a mechanical system with impacts using model reference adaptive control

A single degree of freedom mechanical spring-mass system was considered where the motion of the mass is constrained by an adjustable rigid impact stop. A model reference adaptive control algorithm combined with interspike interval techniques was used to consider the viability of identifying system parameters when impacts are present. The unmodified adaptive control algorithm destabilizes during vibro-impact motion, so three modified control algorithms were tested experimentally. The first, the gain reset, was found to be of limited use and system identification could not be successfully carried out. The second and third used a gain pause strategy. The second algorithm used acceleration triggering and represented an improvement on the gain reset method. The third approach used displacement triggering and was found to be partially successful in identifying system parameters in the presence of vibro-impact motion

COLDz: Karl G. Jansky Very Large Array discovery of a gas-rich galaxy in COSMOS

The broad spectral bandwidth at mm and cm-wavelengths provided by the recent upgrades to the Karl G. Jansky Very Large Array (VLA) has made it possible to conduct unbiased searches for molecular CO line emission at redshifts, z > 1.31. We present the discovery of a gas-rich, star-forming galaxy at z = 2.48, through the detection of CO(1-0) line emission in the COLDz survey, through a sensitive, Ka-band (31 to 39 GHz) VLA survey of a 6.5 square arcminute region of the COSMOS field. We argue that the broad line (FWHM ~570 +/- 80 km/s) is most likely to be CO(1-0) at z=2.48, as the integrated emission is spatially coincident with an infrared-detected galaxy with a photometric redshift estimate of z = 3.2 +/- 0.4. The CO(1-0) line luminosity is L'_CO = (2.2 +/- 0.3) x 10^{10} K km/s pc^2, suggesting a cold molecular gas mass of M_gas ~ (2 - 8)x10^{10}M_solar depending on the assumed value of the molecular gas mass to CO luminosity ratio alpha_CO. The estimated infrared luminosity from the (rest-frame) far-infrared spectral energy distribution (SED) is L_IR = 2.5x10^{12} L_solar and the star-formation rate is ~250 M_solar/yr, with the SED shape indicating substantial dust obscuration of the stellar light. The infrared to CO line luminosity ratio is ~114+/-19 L_solar/(K km/s pc^2), similar to galaxies with similar SFRs selected at UV/optical to radio wavelengths. This discovery confirms the potential for molecular emission line surveys as a route to study populations of gas-rich galaxies in the future