Model-free tracking control of complex dynamical trajectories with machine learning.

Nonlinear tracking control enabling a dynamical system to track a desired trajectory is fundamental to robotics, serving a wide range of civil and defense applications. In control engineering, designing tracking control requires complete knowledge of the system model and equations. We develop a model-free, machine-learning framework to control a two-arm robotic manipulator using only partially observed states, where the controller is realized by reservoir computing. Stochastic input is exploited for training, which consists of the observed partial state vector as the first and its immediate future as the second component so that the neural machine regards the latter as the future state of the former. In the testing (deployment) phase, the immediate-future component is replaced by the desired observational vector from the reference trajectory. We demonstrate the effectiveness of the control framework using a variety of periodic and chaotic signals, and establish its robustness against measurement noise, disturbances, and uncertainties.

Reservoir computing as digital twins for nonlinear dynamical systems.

We articulate the design imperatives for machine learning based digital twins for nonlinear dynamical systems, which can be used to monitor the "health" of the system and anticipate future collapse. The fundamental requirement for digital twins of nonlinear dynamical systems is dynamical evolution: the digital twin must be able to evolve its dynamical state at the present time to the next time step without further state input-a requirement that reservoir computing naturally meets. We conduct extensive tests using prototypical systems from optics, ecology, and climate, where the respective specific examples are a chaotic CO2 laser system, a model of phytoplankton subject to seasonality, and the Lorenz-96 climate network. We demonstrate that, with a single or parallel reservoir computer, the digital twins are capable of a variety of challenging forecasting and monitoring tasks. Our digital twin has the following capabilities: (1) extrapolating the dynamics of the target system to predict how it may respond to a changing dynamical environment, e.g., a driving signal that it has never experienced before, (2) making continual forecasting and monitoring with sparse real-time updates under non-stationary external driving, (3) inferring hidden variables in the target system and accurately reproducing/predicting their dynamical evolution, (4) adapting to external driving of different waveform, and (5) extrapolating the global bifurcation behaviors to network systems of different sizes. These features make our digital twins appealing in applications, such as monitoring the health of critical systems and forecasting their potential collapse induced by environmental changes or perturbations. Such systems can be an infrastructure, an ecosystem, or a regional climate system.

A Dynamic Escape Problem of Molecular Motors.

Animal skeletal muscle exhibits very interesting behavior at near-stall forces (when the muscle is loaded so strongly that it can barely contract). Near this physical limit, the myosin II proteins may be unable to reach advantageous actin binding sites through simple attractive forces. It has been shown that the advantageous utilization of thermal agitation is a likely source for an increased force-production capacity and reach in myosin-V (a processing motor protein), and here we explore the dynamics of a molecular motor without hand-over-hand motion including Brownian motion to show how local elastic energy well boundaries may be overcome. We revisit a spatially two-dimensional mechanical model to illustrate how thermal agitation can be harvested for useful mechanical work in molecular machinery inspired by this biomechanical phenomenon without rate functions or empirically inspired spatial potential functions. Additionally, the model accommodates variable lattice spacing, and it paves the way for a full three-dimensional model of cross-bridge interactions where myosin II may be azimuthally misaligned with actin binding sites. With potential energy sources based entirely on realizable components, this model lends itself to the design of artificial, molecular-scale motors.

Carbon nanotubes within polymer matrix can synergistically enhance mechanical energy dissipation.

Safe operation and health of structures relies on their ability to effectively dissipate undesired vibrations, which could otherwise significantly reduce the life-time of a structure due to fatigue loads or large deformations. To address this issue, nanoscale fillers, such as carbon nanotubes (CNTs), have been utilized to dissipate mechanical energy in polymer-based nanocomposites through filler-matrix interfacial friction by benefitting from their large interface area with the matrix. In this manuscript, for the first time, we experimentally investigate the effect of CNT alignment with respect to reach other and their orientation with respect to the loading direction on vibrational damping in nanocomposites. The matrix was polystyrene (PS). A new technique was developed to fabricate PS-CNT nanocomposites which allows for controlling the angle of CNTs with respect to the far-field loading direction (misalignment angle). Samples were subjected to dynamic mechanical analysis, and the damping of the samples were measured as the ratio of the loss to storage moduli versus CNT misalignment angle. Our results defied a notion that randomly oriented CNT nanocomposites can be approximated as a combination of matrix-CNT representative volume elements with randomly aligned CNTs. Instead, our results points to major contributions of stress concentration induced by each CNT in the matrix in proximity of other CNTs on vibrational damping. The stress fields around CNTs in PS-CNT nanocomposites were studied via finite element analysis. Our findings provide significant new insights not only on vibrational damping nanocomposites, but also on their failure modes and toughness, in relation to interface phenomena.

Blocking Oxidation Failures of Carbon Nanotubes through Selective Protection of Defects.

The selective growth of Al2 O3 islands over defect sites on the surface of carbon nanotubes significantly increases the oxidation breakdown threshold to 6.8 W cm(-2) , more than double than that of unprotected films. The elevated input power enables thermoacoustic emissions at loud audible sound pressure levels of 90.1 dB, which are inaccessible with the unprotected films.

Spectral decomposition of nonlinear systems with memory.

We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.

Identification of energy dissipation mechanisms in CNT-reinforced nanocomposites.

In this paper we present our recent findings on the mechanisms of energy dissipation in polymer-based nanocomposites obtained through experimental investigations. The matrix of the nanocomposite was polystyrene (PS) which was reinforced with carbon nanotubes (CNTs). To study the mechanical strain energy dissipation of nanocomposites, we measured the ratio of loss to storage modulus for different CNT concentrations and alignments. CNT alignment was achieved via hot-drawing of PS-CNT. In addition, CNT agglomeration was studied via a combination of SEM imaging and Raman scanning. We found that at sufficiently low strains, energy dissipation in composites with high CNT alignment is not a function of applied strain, as no interfacial slip occurs between the CNTs and PS. However, below the interfacial slip strain threshold, damping scales monotonically with CNT content, which indicates the prevalence of CNT-CNT friction dissipation mechanisms within agglomerates. At higher strains, interfacial slip also contributes to energy dissipation. However, the increase in damping with strain, especially when CNT agglomerates are present, does not scale linearly with the effective interface area between CNTs and PS, suggesting a significant contribution of friction between CNTs within agglomerates to energy dissipation at large strains. In addition, for the first time, a comparison between the energy dissipation in randomly oriented and aligned CNT composites was made. It is inferred that matrix plasticity and tearing caused by misorientation of CNTs with the loading direction is a major cause of energy dissipation. The results of our research can be used to design composites with high energy dissipation capability, especially for applications where dynamic loading may compromise structural stability and functionality, such as rotary wing structures and antennas.

Energy dissipation due to interfacial slip in nanocomposites reinforced with aligned carbon nanotubes.

Interfacial slip mechanisms of strain energy dissipation and vibration damping of highly aligned carbon nanotube (CNT) reinforced polymer composites were studied through experimentation and complementary micromechanics modeling. Experimentally, we have developed CNT-polystyrene (PS) composites with a high degree of CNT alignment via a combination of twin-screw extrusion and hot-drawing. The aligned nanocomposites enabled a focused study of the interfacial slip mechanics associated with shear stress concentrations along the CNT-PS interface induced by the elastic mismatch between the filler and matrix. The variation of storage and loss modulus suggests the initiation of the interfacial slip occurs at axial strains as low as 0.028%, primarily due to shear stress concentration along the CNT-PS interface. Through micromechanics modeling and by matching the model with the experimental results at the onset of slip, the interfacial shear strength was evaluated. The model was then used to provide additional insight into the experimental observations by showing that the nonlinear variation of damping with dynamic strain can be attributed to slip-stick behavior. The dependence of the interfacial load-transfer reversibility on the dynamic strain history and characteristic time scale was experimentally investigated to demonstrate the relative contribution of van der Waals (vdW) interactions, mechanical interlocking, and covalent bonding to shear interactions.