Time-varying Case Research Articles

Flow separation on flapping and rotating profiles with spanwise gradients

The growth of leading-edge vortices (LEV) on analogous flapping and rotating profiles has been investigated experimentally. Three time-varying cases were considered: a two-dimensional reference case with a spanwise-uniform angle-of-attack variation α; a case with increasing α towards the profile tip (similar to flapping flyers); and a case with increasing α towards the profile root (similar to rotor blades experiencing an axial gust). It has been shown that the time-varying spanwise angle-of-attack gradient produces a vorticity gradient, which, in combination with spanwise flow, results in a redistribution of circulation along the profile. Specifically, when replicating the angle-of-attack gradient characteristic of a rotor experiencing an axial gust, the spanwise-vorticity gradient is aligned such that circulation increases within the measurement domain. This in turn increases the local LEV growth rate, which is suggestive of force augmentation on the blade. Reversing the relative alignment of the spanwise-vorticity gradient and spanwise flow, thereby replicating that arrangement found in a flapping flyer, was found to reduce local circulation. From this, we can conclude that spanwise flow can be arranged to vary LEV growth to prolong lift augmentation and reduce the unsteadiness of cyclic loads.

Distance-Based Cycle-Free Persistent Formation: Global Convergence and Experimental Test With a Group of Quadcopters

In this paper, distributed formation control for multi-agent systems is considered. The proposed control laws are designed to globally obtain and keep the desired formation in a two-dimensional space. It is assumed that the local frames of the agents are not aligned with each other and each agent does not know the orientation of others’ coordinate frames. Further, the agent measures only relative positions of neighbors with respect to the local reference frame. Therefore, the control of the system is completely decentralized and the global convergence is achieved without the global reference frame. The stability and convergence of the system are analyzed mathematically and the experiment using quadcopters is performed to verify the results of the theoretical analysis. In addition, the ambiguity problem and time-varying velocity case are also handled and discussed.

Time-Varying Coefficient Estimation in SURE Models: Application to Portfolio Management

This paper provides a detailed analysis of the asymptotic properties of a kernel estimator for a Seemingly Unrelated Regression Equations model with time-varying coefficients (tv-SURE) under very general conditions. Theoretical results together with a simulation study differentiates the cases for which the estimation of a tv-SURE outperforms the estimation of a Single Regression Equations model with time-varying coefficients (tv-SRE). The study shows that Zellner's results cannot be straightforwardly extended to the time-varying case. The tv-SURE is applied to the Fama and French five-factor model using data from four different international markets. Finally, we provide the estimation under cross-restriction and discuss a testing procedure.

The Relationship between Age of Air and the Diabatic Circulation of the Stratosphere

AbstractThe strength of the Brewer–Dobson circulation is difficult to estimate using observations. Trends in the age of stratospheric air, deduced from observations of transient tracers, have been used to identify trends in the circulation, but there are ambiguities in the relationship between age and the strength of the circulation. This paper presents a steady-state theory and a time-dependent extension to relate age of air directly to the diabatic circulation of the stratosphere. In steady state, it is the difference between the age of upwelling and downwelling air through an isentrope and not the absolute value of age that is a measure of the strength of the diabatic circulation through that isentrope. For the time-varying case, expressions for other terms that contribute to the age budget are derived. An idealized atmospheric general circulation model with and without a seasonal cycle is used to test the time-dependent theory and to find that these additional terms are small upon annual averaging. The steady-state theory holds as well for annual averages of a seasonally varying model as for a perpetual-solstice model. These results are a step toward using data to quantify the strength of the diabatic circulation.

Heat Flow Dynamics in Thermal Systems Described by Diffusive Representation

The objective of this paper is to analyze the dynamics of heat flow in thermal structures working under constant temperature operation. This analysis is made using the tools of sliding mode controllers. The theory is developed considering that the thermal system can be described using diffusive representation. The experimental corroboration has been made with a prototype of a wind sensor for Mars atmosphere being controlled by a thermal sigma–delta modulator. This sensor structure allows to analyze the time-varying case experimentally since changes in wind conditions imply changes in the corresponding thermal models. The diffusive symbols of the experimental structures have been obtained from open-loop measurements in which pseudorandom binary sequences of heat are injected in the sensor. With the proposed approach, it is possible to predict heat flux transient waveforms in systems described by any arbitrary number of poles. This allows for the first time the analysis of lumped and distributed systems without any limitation on the number of poles describing it.

Sampled-Data Stabilization for Fuzzy Genetic Regulatory Networks with Leakage Delays.

This paper deals with the sampled-data stabilization problem for Takagi-Sugeno (T-S) fuzzy genetic regulatory networks with leakage delays. A novel Lyapunov-Krasovskii functional (LKF) is established by the non-uniform division of the delay intervals with triplex and quadruplex integral terms. Using such LKFs for constant and time-varying delay cases, new stability conditions are obtained in the T-S fuzzy framework. Based on this, a new condition for the sampled-data controller design is proposed using a linear matrix inequality representation. A numerical result is provided to show the effectiveness and potential of the developed design method.

Consensus in the Presence of Multiple Opinion Leaders: Effect of Bounded Confidence

The problem of analyzing the performance of networked agents exchanging evidence in a dynamic network has recently grown in importance. This problem has relevance in signal and data fusion network applications and in studying opinion and consensus dynamics in social networks. Due to its capability of handling a wider variety of uncertainties and ambiguities associated with evidence, we use the framework of Dempster-Shafer (DS) theory to capture the opinion of an agent. We then examine the consensus among agents in dynamic networks in which an agent can utilize either a cautious or receptive updating strategy. In particular, we examine the case of bounded confidence updating where an agent exchanges its opinion only with neighboring nodes possessing 'similar' evidence. In a fusion network, this captures the case in which nodes only update their state based on evidence consistent with the node's own evidence. In opinion dynamics, this captures the notions of Social Judgment Theory (SJT) in which agents update their opinions only with other agents possessing opinions closer to their own. Focusing on the two special DS theoretic cases where an agent state is modeled as a Dirichlet body of evidence and a probability mass function (p.m.f.), we utilize results from matrix theory, graph theory, and networks to prove the existence of consensus agent states in several time-varying network cases of interest. For example, we show the existence of a consensus in which a subset of network nodes achieves a consensus that is adopted by follower network nodes. Of particular interest is the case of multiple opinion leaders, where we show that the agents do not reach a consensus in general, but rather converge to 'opinion clusters'. Simulation results are provided to illustrate the main results.

A novel control algorithm for the self-organized fission behavior of flocking system with time delay

This paper studies the self-organized fission control problem for flocking system with time delay. Both constant and time-varying time delay cases are considered. Firstly, a novel information coupling degree (ICD) based fission control algorithm, which is able to split a coherent flock into multiple sub-groups under conflict external stimuli, is proposed. Then, for the case of constant time delay, the sufficient conditions for the fission control algorithm is derived using Lyapunov-Razumikhin theorem. For the case of time-varying time delay, Lyapunov-Krasovskii functional method is adopted to obtain the sufficient conditions for the fission control algorithm in terms of linear matrix inequalities (LMIs). Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

Max-min Fair Rate Allocation and Routing in Energy Harvesting Networks: Algorithmic Analysis

This paper considers max-min fair rate allocation and routing in energy harvesting networks where fairness is required among both the nodes and the time slots. Unlike most previous work on fairness, we focus on multihop topologies and consider different routing methods. We assume a predictable energy profile and focus on the design of efficient and optimal algorithms that can serve as benchmarks for distributed and approximate algorithms. We first develop an algorithm that obtains a max-min fair rate assignment for any routing that is specified at the input. We then turn to the problem of determining a “good” routing. For time-invariable unsplittable routing, we develop an algorithm that finds routes that maximize the minimum rate assigned to any node in any slot. For fractional routing, we derive a combinatorial algorithm for the time-invariable case with constant rates. We show that the time-variable case is at least as hard as the 2-commodity feasible flow problem and design an FPTAS to combat the high running time. Finally, we show that finding an unsplittable routing or a routing tree that provides lexicographically maximum rate assignment (i.e., the best in the max-min fairness terms) is NP-hard, even for a time horizon of a single slot. Our analysis provides insights into the problem structure and can be applied to other related fairness problems.

Relativistic analysis of field-kinetic and canonical electromagnetic systems

We demonstrate the relativistic electromagnetic force and power distributions of the field-kinetic and canonical electromagnetic subsystems with respect to light normally incident upon a moving, lossless magnetodielectric slab of material. Time-averaged and time-varying studies are preformed to demonstrate the continuum mathematical approach and discern between the physical characteristics of both field-kinetic and canonical subsystems. It is shown that when considering time-averaged fields, both subsystems are equivalent and thereby yield equivalent electromagnetic force and power results. The time-varying case demonstrates the differences between the field-kinetic and canonical subsystems, where the field-kinetic subsystem attempts to distort the media and the canonical subsystem satisfies global conservation principles.

Sufficient conditions to stabilize time-varying nonlinear sampled-data systems via approximation

Summary This paper investigates the problem of stabilizing a time-varying nonlinear sampled-data system based on its approximate models. Given a time-varying nonlinear sampled-data system, we make use of the approximate models of the system at each sampling instant to build a time-varying approximate model with which an appropriate controller is designed. This paper provides some sufficient conditions under which a controller stabilizing the approximate models can also stabilize the exact sampled-data system under any sufficiently small sampling period. With this method, we do not need to compute the complicated exact discrete-time model of the concerned system and significantly simplify the controller design. The major contribution of this method lies in extending the available results regarding the time-invariant sampled-data systems to the time-varying case. Moreover, this method enables us to analyze the influence of the precision of approximate models on the system performance. Copyright © 2016 John Wiley & Sons, Ltd.

Event-based state estimation of linear dynamic systems with unknown exogenous inputs

In this work, an event-based optimal state estimation problem for linear-time varying systems with unknown inputs is investigated. By treating the unknown input as a process with a non-informative prior, the event-based minimum mean square error (MMSE) estimator is obtained in a recursive form. It is shown that for the general time-varying case, the closed-loop matrix of the optimal event-based estimator is exponentially stable and the estimation error covariance matrix is asymptotically bounded for each sample path of the event-triggering process. The results are also extended to the multiple sensor scenario, where each sensor is allowed to have its own event-triggering condition. The efficiency of the proposed results is illustrated by a numerical example and comparative simulation with the MMSE estimators obtained based on time-triggered measurements. The results are potentially applicable to event-based secure state estimation of cyber-physical systems.

Backstepping-based boundary observer for a class of time-varying linear hyperbolic PIDEs

In this paper, a Luenberger-type boundary observer is presented for a class of distributed-parameter systems described by time-varying linear hyperbolic partial integro-differential equations. First, known limitations due to the minimum observation time for simple transport equations are restated for the considered class of systems. Then, the backstepping method is applied to determine the unknown observer gain term. By avoiding the framework of Gevrey-functions, which is typically used for the time-varying case, it is shown that the backstepping method can be employed without severe limitations on the regularity of the time-varying terms. A modification of the underlying Volterra transformation ensures that the observer error dynamics is equivalent to the behavior of a predefined exponentially stable target system. The magnitude of the observer gain term can be traded for lower decay rates of the observer error. After the theoretic results have been proven, the effectiveness of the proposed design is demonstrated by simulation examples.

Singular perturbation margin and generalised gain margin for nonlinear time-invariant systems

ABSTRACTIn this paper, singular perturbation margin (SPM) and generalised gain margin (GGM) are proposed as the classical phase margin and gain margin like stability metrics for nonlinear systems established from the view of the singular perturbation and the regular perturbation, respectively. The problem of SPM and GGM assessment of a nonlinear nominal system is formulated. The SPM and GGM formulations are provided as the functions of radius of attraction (ROA), which is introduced as a conservative measure of the domain of attraction (DOA). Furthermore, the ROA constrained SPM and GGM analysis are processed through two stages: (1) the SPM and GGM assessment for nonlinear systems at the equilibrium point, based on the SPM and GGM equilibrium theorems, including time-invariant and time-varying cases (Theorem 5.3, Theorem 5.2, Theorem 5.4 and Theorem 5.5); (2) the establishment of the relationship between the SPM or GGM and the ROA for nonlinear time-invariant systems through the construction of the Lyapunov function for the singularly perturbed model (Theorem 6.1 and Section 6.2.3).

Stability Criteria for Nonlinearly Perturbed Load Frequency Systems With Time-Delay

In this paper, new criteria are presented for ascertaining delay-dependent stability of networked multi-area load frequency control (LFC) systems with feedback loop delay in presence of unknown and time-varying exogenous load disturbance. The proposed stability criteria are based on Lyapunov-Krasovskii (LK) functional approach, and they are expressed in linear matrix inequality (LMI) framework. Since the unknown exogenous load disturbance in the power system (cause) ultimately affects the evolution of the state variables of the system (effect), in the reported stability criteria, the load disturbance is mathematically modelled as a norm-bounded nonlinear time-varying function of current and delayed state vectors, and subsequently incorporated into the delay-dependent stability analysis. Two cases of time-delays are considered in the stability analysis: time-varying single feedback-loop delay element and time-invariant multiple feedback-loop delay elements. In addition, to realize less conservative stability criteria with minimal number of decision variables, in the stability analysis, tighter integral inequalities, viz., reciprocal convex combination lemma (for time-varying delay case) and Jenson integral inequality (for time-invariant delay case) are employed. The proposed results are illustrated on standard benchmark LFC systems, and supported suitably by simulation results.

Robust optimal current control for grid‐connected three‐phase pulse‐width modulated converters

This study deals with the current control of three-phase inverters connected to the grid by means of LCL filters. The control action is given by the feedback of the filter states, in coordinates αβ0, and of the internal states of resonant controllers. The control gains are computed by means of an optimal linear quadratic regulator that is robust to uncertain and time-varying parameters related to the grid impedance at the point of common coupling. As contributions, one has the detailed proof of a robust discrete linear quadratic control, showing its applicability also for the time-varying case, the experimental validation of the results in terms of the total harmonic distortion and harmonic limits for the grid injected current, according to the IEEE 1547 standard, and the analysis of the ℋ∞ norm of the closed-loop system for several values of grid inductance, indicating a value of grid inductance for which one has best performance for the time-invariant case. For comparison, a conventional state feedback controller is designed and implemented, showing the limitation of the non-robust strategy.

Robust [formula omitted] and [formula omitted] memory filter design for linear uncertain discrete-time delay systems

This paper is concerned with the problems of robust full-order H2 and H∞ filter design for linear uncertain discrete-time systems with multiple state delays. The uncertain parameters affecting the matrices of the system are supposed to be time-invariant and to belong to a polytopic domain. The main novelty is the fact that the filter contains an arbitrary number of past states and past output measures of the system, yielding a filtering system with memory. Linear matrix inequality relaxations based on polynomially parameter-dependent Lyapunov matrices and slack variables are proposed for the H2 and H∞ filter design. Due to the extra dynamics introduced through the delayed states, the robust memory filter is able to provide less conservative results in terms of the H∞ and the H2 performance when compared to the memoryless case. Throughout the paper, the multiple delays are considered to be fixed and time-invariant, but an extension of the conditions to cope with unknown delays belonging to a given interval is also presented for both time-varying and time-invariant delay cases. Numerical examples are given to demonstrate the improvements of the proposed approach with respect to other methods from the literature.

Filtering Continuous-Time Linear Systems With Time-Varying Measurement Delay

We consider the filtering problem of LTI continuous-time systems with known and bounded measurement delays. The aim of the technical note is the design of a finite-dimensional sub-optimal filter whose performance in terms of the estimation error is comparable to optimal infinite-dimensional approaches. We show that the proposed approach allows for a precise characterization of the relationship between measurement delay and the covariance of the estimation error. In the time-varying case no restrictive hypotheses on the delay function are needed. The proposed filter can therefore be applied to delay functions for which traditional infinite-dimensional approaches cannot be straightforwardly applied.

Stable LPV realisation of the Smith predictor

The paper is concerned with the control of a linear plant with an output delay. As is known, when the plant parameters do not vary in time, the transfer function approach can be used to find a high-performing controller with the Smith-predictor structure. Such an approach in the domain of the Laplace transform is not directly applicable in the time-variant case. Nevertheless, it is shown that the transfer function of the Smith controller valid for constant values of the parameters can be realised in such a way that closed-loop stability, as well as point-wise optimal performance, is ensured also when the parameters vary with time. The suggested technique is applied to the control of a heat exchanger whose varying parameters include a measurement delay.

Reaching a consensus: a discrete nonlinear time-varying case

In this paper, we have considered a nonlinear protocol for a structured time-varying and synchronous multi-agent system. By means of cubic triple stochastic matrices, we present an opinion sharing dynamics of the multi-agent system as a trajectory of a non-homogeneous system of cubic triple stochastic matrices. We show that the multi-agent system eventually reaches to a consensus if either of the following two conditions is satisfied: (1) every member of the group people has a positive subjective distribution on the given task after some revision steps or (2) all entries of some cubic triple stochastic matrix are positive.