IPMC-based actuators: An approach for measuring a linear form of its static equation

Ionic Polymer-Metal Composites (IPMCs) are smart materials used as actuators, sensors, and energy harvesters. They are known as a subset of Electroactive Polymers (EAPs). IPMCs structure is layered with one polymer layer and two of electrodes. In this paper, the actuation behavior of an IPMC sample with platinum electrodes and Nafion-117 polymer is of the interest and two diverse methods have been applied; This microelectromechanical system which is used in this paper is manufactured initially, and then the experimental method was applied besides the finite element method. According to the experimental analysis, the maximum displacement of a cantilever model of the IPMC in various lengths and different amounts of voltages is measured and recorded. The experimental method is used to validate the finite element method results. By using Linear Regression with the Ordinary-Least- Squares method, a linear equation is derived that will provide the maximum displacement of a cantilever beam model of the IPMC in varying lengths and different applied Voltages. This equation can be a special-occasion alteration for the specific application of Poisson- Nernst-Plank equation. This multi-input linear equation can predict ionic polymer-metal composite attitude accurately.

A robust finite-time model reference adaptive controller for arbitrary order disturbed LTI systems

This manuscript deals with the trajectory-tracking problem for linear time-invariant systems with parameter uncertainties and time-dependent external perturbations. A robust finite-time model reference adaptive controller is proposed. In the absence of external perturbations, the proposed controller ensures finite-time convergence to zero of the tracking and parameter identification errors. In presence of time-dependent external perturbations, the tracking and parameter identification errors converge to a region around the origin in a finite time. The convergence proofs are developed based on Lyapunov and input-to-state stability theory. Finally, simulation results in an academic example and a flexible-joint robot manipulator show the feasibility of the proposed approach.

Dynamic event-triggered distributed observer for linear systems

This paper investigates a dynamic event-triggered distributed observer for linear systems including two groups of local observers: one can access the local outputs and another cannot. By the detectability decomposition, the proposed observer contains a detectable sub-state (DSS) observer and a distributed undetectable sub-state (USS) observer. The dynamic event-triggered mechanism (DETM) for the outputs only requires a copy of the DSS observer with low dimension. Besides, only the USS estimate is transmitted to the neighbors which can reduce the communication burden. Positive minimum inter-event times are prescribed previously in the DETMs, and piece-wise dynamics for internal dynamic variables are employed. By modeling the error systems as hybrid systems, the exponential stability of the proposed observer is assured with the utilization of time-triggering method and event-triggering method.

Feasibility of sparse large Lotka-Volterra ecosystems

Consider a large ecosystem (foodweb) with n species, where the abundances follow a Lotka-Volterra system of coupled differential equations. We assume that each species interacts with [Formula: see text] other species and that their interaction coefficients are independent random variables. This parameter d reflects the connectance of the foodweb and the sparsity of its interactions especially if d is much smaller that n. We address the question of feasibility of the foodweb, that is the existence of an equilibrium solution of the Lotka-Volterra system with no vanishing species. We establish that for a given range of d, namely [Formula: see text] or [Formula: see text] with an extra condition on the sparsity structure, there exists an explicit threshold depending on n and d and reflecting the strength of the interactions, which guarantees the existence of a positive equilibrium as the number of species n gets large. From a mathematical point of view, the study of feasibility is equivalent to the existence of a positive solution [Formula: see text] (component-wise) to the equilibrium linear equation: [Formula: see text]where [Formula: see text] is the [Formula: see text] vector with components 1 and [Formula: see text] is a large sparse random matrix, accounting for the interactions between species. The analysis of such positive solutions essentially relies on large random matrix theory for sparse matrices and Gaussian concentration of measure. The stability of the equilibrium is established. The results in this article extend to a sparse setting the results obtained by Bizeul and Najim in Bizeul and Najim (2021).

LMI-based consensus of linear multi-agent systems by reduced-order dynamic output feedback

This work proposes new conditions for consensus of homogeneous multi-agent systems subjected to exogenous disturbances in directed communication graphs by dynamic output feedback protocols. The agents under investigation are described as linear dynamics, and the communication network is such that each agent receives as information only the output of neighbor agents. The synchronization problem is rewritten as an output feedback stabilization without requiring the Laplacian matrix to be diagonalizable. As the main appeal, we propose new necessary and sufficient conditions for the design of dynamic output feedback controllers of arbitrary order - including static output feedback as a particular case - and sufficient Linear Matrix Inequalities (LMIs) for H_∞ consensus. Numerical experiments illustrate the effectiveness of the proposed approach.

A reinterpretation of critical flicker-frequency (CFF) data reveals key details about light adaptation and normal and abnormal visual processing

Our ability to see flicker has an upper frequency limit above which flicker is invisible, known as the "critical flicker frequency" (CFF), that typically grows with light intensity (I). The relation between CFF and I, the focus of nearly 200 years of research, is roughly logarithmic, i.e., CFF ∝ log(I)-a relation called the Ferry-Porter law. However, why this law should occur, and how it relates to the underlying physiology, have never been adequately explained. Over the past two decades we have measured CFF in normal observers and in patients with retinal gene defects. Here, we reanalyse and model our data and historical CFF data. Remarkably, CFF-versus-I functions measured under a wide range of conditions in patients and in normal observers all have broadly similar shapes when plotted in double-logarithmic coordinates, i.e., log (CFF)-versus-log(I). Thus, the entire dataset can be characterised by horizontal and vertical logarithmic shifts of a fixed-shape template. Shape invariance can be predicted by a simple model of visual processing built from a sequence of low-pass filters, subtractive feedforward stages and gain adjustment (Rider, Henning & Stockman, 2019). It depends primarily on the numbers of visual processing stages that approach their power-law region at a given intensity and a frequency-independent gain reduction at higher light levels. Counter-intuitively, the CFF-versus-I relation depends primarily on the gain of the visual response rather than its speed-a conclusion that changes our understanding and interpretation of human flicker perception. The Ferry-Porter "law" is merely an approximation of the shape-invariant template.

Erasure decoding of convolutional codes using first-order representations

It is well known that there is a correspondence between convolutional codes and discrete-time linear systems over finite fields. In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. In this kind of channel, which is important due to its use for data transmission over the Internet, the receiver knows if a received symbol is correct. We study the decoding problem using the state space description of a convolutional code, and this provides in a natural way additional information. With respect to previously known decoding algorithms, our new algorithm has the advantage that it is able to reduce the decoding delay as well as the computational effort in the erasure recovery process. We describe which properties a convolutional code should have in order to obtain a good decoding performance and illustrate it with an example.

Resilient Reachability for Linear Systems

A fault-tolerant system is able to reach its goal even when some of its components are malfunctioning. This paper examines tolerance to a specific type of malfunction: the loss of control authority over actuators. Namely, we investigate whether the desired target set for a linear system remains reachable under any undesirable input. Contrary to robust control, we assume that the undesirable inputs can be observed in real time, and subsequently allow the control inputs to depend on these undesirable inputs. Building on previous work on reachability with undesirable inputs, this paper develops a reachability condition for linear systems, and obtains a formula that describes reachability of the goal set for driftless linear systems by computing the minimum of a concave-convex objective function. From this formulation we establish two novel sufficient conditions for resilient reachability.

Validating Linear Systems Analysis for Laminar fMRI: Temporal Additivity for Stimulus Duration Manipulations

Advancements in ultra-high field (7 T and higher) magnetic resonance imaging (MRI) scanners have made it possible to investigate both the structure and function of the human brain at a sub-millimeter scale. As neuronal feedforward and feedback information arrives in different layers, sub-millimeter functional MRI has the potential to uncover information processing between cortical micro-circuits across cortical depth, i.e. laminar fMRI. For nearly all conventional fMRI analyses, the main assumption is that the relationship between local neuronal activity and the blood oxygenation level dependent (BOLD) signal adheres to the principles of linear systems theory. For laminar fMRI, however, directional blood pooling across cortical depth stemming from the anatomy of the cortical vasculature, potentially violates these linear system assumptions, thereby complicating analysis and interpretation. Here we assess whether the temporal additivity requirement of linear systems theory holds for laminar fMRI. We measured responses elicited by viewing stimuli presented for different durations and evaluated how well the responses to shorter durations predicted those elicited by longer durations. We find that BOLD response predictions are consistently good predictors for observed responses, across all cortical depths, and in all measured visual field maps (V1, V2, and V3). Our results suggest that the temporal additivity assumption for linear systems theory holds for laminar fMRI. We thus show that the temporal additivity assumption holds across cortical depth for sub-millimeter gradient-echo BOLD fMRI in early visual cortex.

Clinical vision and molecular loss: Integrating visual psychophysics with molecular genetics reveals key details of normal and abnormal visual processing

Over the past two decades we have developed techniques and models to investigate the ways in which known molecular defects affect visual performance. Because molecular defects in retinal signalling invariably alter the speed of visual processing, our strategy has been to measure the resulting changes in flicker sensitivity. Flicker measurements provide not only straightforward clinical assessments of visual performance but also reveal fundamental details about the functioning of both abnormal and normal visual systems. Here, we bring together our past measurements of patients with pathogenic variants in the GNAT2, RGS9, GUCA1A, RPE65, OPA1, KCNV2 and NR2E3 genes and analyse the results using a standard model of visual processing. The model treats flicker sensitivity as the result of the actions of a sequence of simple processing steps, one or more of which is altered by the genetic defect. Our analyses show that most defects slow down the visual response directly, but some speed it up. Crucially, however, other steps in the processing sequence can make compensatory adjustments to offset the abnormality. For example, if the abnormal step slows down the visual response, another step is likely to speed up or attenuate the response to rebalance system performance. Such compensatory adjustments are probably made by steps in the sequence that usually adapt to changing light levels. Our techniques and modelling also allow us to tease apart stationary and progressive effects, and the localised molecular losses help us to unravel and characterise individual steps in the normal and abnormal processing sequences.

Path-dependent connectivity, not modularity, consistently predicts controllability of structural brain networks

The human brain displays rich communication dynamics that are thought to be particularly well-reflected in its marked community structure. Yet, the precise relationship between community structure in structural brain networks and the communication dynamics that can emerge therefrom is not well understood. In addition to offering insight into the structure-function relationship of networked systems, such an understanding is a critical step toward the ability to manipulate the brain's large-scale dynamical activity in a targeted manner. We investigate the role of community structure in the controllability of structural brain networks. At the region level, we find that certain network measures of community structure are sometimes statistically correlated with measures of linear controllability. However, we then demonstrate that this relationship depends on the distribution of network edge weights. We highlight the complexity of the relationship between community structure and controllability by performing numerical simulations using canonical graph models with varying mesoscale architectures and edge weight distributions. Finally, we demonstrate that weighted subgraph centrality, a measure rooted in the graph spectrum, and which captures higher order graph architecture, is a stronger and more consistent predictor of controllability. Our study contributes to an understanding of how the brain's diverse mesoscale structure supports transient communication dynamics.

Boolean network analysis through the joint use of linear algebra and algebraic geometry

Among the various phenomena that can be modeled by Boolean networks, i.e., discrete-time dynamical systems with binary state variables, gene regulatory interactions are especially well known. Therefore, the analysis of Boolean networks is critical, e.g., to identify genetic pathways and to predict the effects of mutations on the cell functionality. Two methodologies (i.e., the semi-tensor product and the Gröbner bases over finite fields) have recently been proposed to tackle the problem of determining cycles and attractors (with the corresponding basin of attraction) for such systems. Here, it is shown that, by suitably coupling methodologies taken from these two fields (i.e., linear algebra and algebraic geometry), it is not only possible to determine cycles and attractors, but also to find closed-form solutions of the Boolean network. Such a goal is pursued by finding an immersion that recasts the Boolean dynamics in a linear form and by computing the closed-form solution of the latter system. The effectiveness of this technique is demonstrated by fully computing the solutions of the Boolean network modeling the differentiation of the Th-lymphocyte, a type of white blood cells involved in the human adaptive immune system.

Model individualization for artificial pancreas

BACKGROUND AND OBJECTIVE

The inter-subject variability characterizing the patients affected by type 1 diabetes mellitus makes automatic blood glucose control very challenging. Different patients have different insulin responses, and a control law based on a non-individualized model could be ineffective. The definition of an individualized control law in the context of artificial pancreas is currently an open research topic. In this work we consider two novel identification approaches that can be used for individualizing linear glucose-insulin models to a specific patient.

METHODS

The first approach belongs to the class of black-box identification and is based on a novel kernel-based nonparametric approach, whereas the second is a gray-box identification technique which relies on a constrained optimization and requires to postulate a model structure as prior knowledge. The latter is derived from the linearization of the average nonlinear adult virtual patient of the UVA/Padova simulator. Model identification and validation are based on in silico data collected during simulations of clinical protocols designed to produce a sufficient signal excitation without compromising patient safety. The identified models are evaluated in terms of prediction performance by means of the coefficient of determination, fit, positive and negative max errors, and root mean square error.

RESULTS

Both identification approaches were used to identify a linear individualized glucose-insulin model for each adult virtual patient of the UVA/Padova simulator. The resulting model simulation performance is significantly improved with respect to the performance achieved by a linear average model.

CONCLUSIONS

The approaches proposed in this work have shown a good potential to identify glucose-insulin models for designing individualized control laws for artificial pancreas.

H2 control of linear uncertain systems considering input quantization with encoder/decoder mismatch

In this paper, an H2 control design for linear uncertain systems with input quantization in the presence of more general encoder/decoder mismatch is investigated. The construction of the control law includes two parts: linear part and nonlinear part. The gain of the linear part is derived from linear matrix inequalities (LMIs), and the linear part of the control law is designed for achieving the H2 performance against system characteristic matrix uncertainty and encoder/decoder mismatch. The nonlinear part is designed to eliminate the influence of external disturbance and quantization error. Finally, examples are provided to illustrate the effectiveness of the proposed method.

Properties of blocked linear systems

This paper presents a systematic study on the properties of blocked linear systems that have resulted from blocking discrete-time linear time invariant systems. The main idea is to explore the relationship between the blocked and the unblocked systems. Existing results are reviewed and a number of important new results are derived. Focus is given particularly on the zero properties of the blocked system as no such study has been found in the literature.