Finite Period Of Time Research Articles

Finite-time adaptive neural control for nonstrict-feedback stochastic nonlinear systems with input delay and output constraints

This paper addresses a novel finite-time adaptive neural control (FTANC) problem for nonstrict-feedback stochastic nonlinear systems (NSFSNS), in which the input delay and output constrained problems are considered simultaneously. First, the Pade approximation technique is adopted to transform the delay input system into a delay-free one. Second, the stochastic nonlinear mapping technique is developed to solve the symmetric and asymmetric output constraints in the system. Then, the adaptive neural controller is designed based on backstepping technique, such that the closed-loop systems are semi-globally practical finite-time stable (SGPFTS) in probability, and the tracking error converges to a small neighborhood of the origin after a finite period of time. Two simulation examples show the effectiveness of the proposed approach.

PROBLEMS OF STABILITY OF LINEAR NON-STATIONARY SYSTEMS ON A FINITE TIME INTERVAL

When studying various processes taking place in real life, we have to deal with one of the most important concepts - the concept of stability of movement. The foundations of the theory of stability of motion were developed at the end of the last century by the great Russian scientist A. M. Lyapunov. As is known, Lyapunov stability is considered on an infinite time interval, which is a serious obstacle for many applications, since most of the objects of research function for a finite period of time. The concept of stability, introduced for an unlimited period of time, cannot be used to evaluate the properties of motion within a finite period of time. The study of motion stability by analyzing solutions of the corresponding equations is permissible and makes sense only if the mathematical model of physical reality is fully adequate. The purpose of this work is to study the stability and stabilization of the motion of linear non-stationary systems.

On a Brownian motion conditioned to stay in an open set

UDC 519.21 Distribution of a Brownian motion conditioned to start from the boundary of an open set and to stay in for a finite period of time is studied. Characterizations of such distributions in terms of certain singular stochastic differential equations are obtained. Results are applied to the study of boundaries of clusters in some coalescing stochastic flows on

Solvability of Pseudoparabolic Equations with Non-Linear Boundary Condition

The work is devoted to the fundamental problem of studying the solvability of the initial-boundary value problem for a pseudo-parabolic equation (also called Sobolev type equations) with a fairly smooth boundary. In this paper, the initial-boundary value problem for a quasilinear equation of a pseudoparabolic type with a nonlinear Neumann–Dirichlet boundary condition is studied. From a physical point of view, the initial-boundary-value problem we are considering is a mathematical model of quasi-stationary processes in semiconductors and magnetics, taking into account the most diverse physical factors. Many approximate methods are suitable for finding eigenvalues and eigenfunctions of tasks boundary conditions of which are linear with respect to the function and its derivatives. Among these methods, Galerkin’s method leads to the simplest calculations. In the paper, by means of the Galerkin method the existence of a weak solution of a pseudoparabolic equation in a bounded domain is proved. The use of the Galerkin approximations allows us to get an estimate above the time of the solution existence. Using Sobolev ’s attachment theorem, a priori solution estimates are obtained. The local theorem of the existence of the solution has been proved. The uniqueness of the weak generalized solution of the initial-boundary value problem of quasi-linear equations of pseudoparabolic type is proved on the basis of a priori estimates.A special place in the theory of nonlinear equations is taken by the range of studies of unlimited solutions, or, as they are otherwise called, modes with exacerbation. Nonlinear evolutionary problems that allow unlimited solutions are globally intractable: solutions increase indefinitely over a finite period of time. Sufficient conditions have been obtained for the destruction of its solution over finite time in a limited area with a nonlinear Neumann–Dirichle boundary condition.

Swift Trust in Ad Hoc Teams: A Cognitive Task Analysis of Intelligence Operators in Multi-Domain Command and Control Contexts

Trust is important for establishing successful relationships and performance outcomes. In some contexts, however, rich information such as knowledge of and experience with a teammate is not available to inform one’s trust. Yet, parties in these contexts are expected to work together toward common goals for a relatively brief and finite period of time. This research investigated the antecedents to quickly-formed trust (often referred to as swift trust) in fast-paced, time-constrained contexts. We conducted a cognitive task analysis (CTA) based on 11 structured interviews of subject-matter experts (SMEs) in Intelligence (Intel)—a heterogeneous job category comprising distributed and co-located personnel within multi-domain command and control (MDC2) environments. Eight antecedents to swift trust emerged from these interviews (i.e., ability, integrity, benevolence, communication, mission-focus, self-awareness, shared perspectives/experiences, and calm), with further analysis implying that swift trust is a relevant and emergent state in MDC2 that facilitates reliance. These findings offer implications for teams operating in high-risk distributed contexts and should be expanded through basic experimental investigations as well as applied initiatives.

Spontaneous Color Polarization as A Modus Originis of the Dynamic Aether

We suggest the phenomenological model of emergence of the dynamic aether as a result of decay of the SU(N) symmetric field configuration containing the multiplet of vector fields. The scenario of the transition to the dynamic aether, which is characterized by one unit timelike vector field that is associated with the aether velocity, is based on the idea of spontaneous color polarization analogous to the spontaneous electric polarization in ferroelectric materials. The mechanism of spontaneous color polarization is described in the framework of anisotropic cosmological model of the Bianchi-I type; it involves consideration of the idea of critical behavior of the eigenvalues of the tensor of color polarization in the course of the Universe accelerated expansion. The interim stage of transition from the color aether to the canonic dynamic aether takes the finite period of time, the duration of which is predetermined by the phenomenologically introduced critical value of the expansion scalar.

SOLVABILITY OF THE INITIAL-BOUNDARY VALUE PROBLEM FOR THE QUASILINEAR EQUATION OF HEAT CONDUCTIVITY IN DOMAINS THAT CAN BE TRANSFORMED INTO RECTANGLES

In this paper, we study the initial-boundary-value problem for the quasilinear heat equation in regions that are reduced to rectangular. Mathematical modeling of many processes taking place in the real world leads to the study of the problems of equations of mathematical physics, when the areas are not rectangular. The theory of nonlinear problems is an actively developing section of the theory of modern differential equations. In the theory of nonlinear equations, a special place is occupied by the study of unbounded solutions or, in other words, modes with exacerbation. Nonlinear evolutionary problems that allow unlimited solutions are globally unsolvable: solutions grow unlimitedly over a finite period of time. In this paper, the initial-boundary-value problem for the quasilinear heat equation in regions that can be reduced to rectangular ones, the existence of a solution is proved by the Galerkin method. The uniqueness of the solution was proved by the obtained a priori estimates. Sufficient conditions for the destruction of the solution in a finite time in a bounded domain are obtained. The exponential decay of the solution with an infinite increase in time is proved. In the final time, it was proved that the solution is localized, i.e. disappears (nullifies).

Dynamics of a predator–prey model with generalized Holling type functional response and mutual interference

Mutual interference and prey refuge are important drivers of predator–prey dynamics. The “exponent” or degree of mutual interference has been under much debate in theoretical ecology. In the present work, we investigate the interplay of the mutual interference exponent, and prey refuge, on the behavior of a predator–prey model with a generalized Holling type functional response — considering in particular the “non-smooth” case. This model can also be used to model an infectious disease where a susceptible population, moves to an infected class, after being infected by the disease. We investigate dynamical properties of the system and derive conditions for the occurrence of saddle–node, transcritical and Hopf-bifurcations. A sufficient condition for finite time extinction of the prey species has also been derived. In addition, we investigate the effect of a prey refuge on the population dynamics of the model and derive conditions such that the prey refuge would yield persistence of the population. We provide additional verification of our analytical results via numerical simulations. Our findings are in accordance with classical experimental results in ecology (Gause, 1934), that show that extinction of predator and prey populations is possible in a finite time period — but that bringing in refuge can effectively yield persistence.

Finite-time ruin probabilities under large-claim reinsurance treaties for heavy-tailed claim sizes

AbstractWe investigate the probability that an insurance portfolio gets ruined within a finite time period under the assumption that the r largest claims are (partly) reinsured. We show that for regularly varying claim sizes the probability of ruin after reinsurance is also regularly varying in terms of the initial capital, and derive an explicit asymptotic expression for the latter. We establish this result by leveraging recent developments on sample-path large deviations for heavy tails. Our results allow, on the asymptotic level, for an explicit comparison between two well-known large-claim reinsurance contracts, namely LCR and ECOMOR. Finally, we assess the accuracy of the resulting approximations using state-of-the-art rare event simulation techniques.

Material Engineering and Design of a Relativistic Engine: How to Avoid Radiation Losses

In a previous paper [1] we have shown that Newton’s third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot exceed the speed of light at vacuum, causing the total force in the system to not add up to zero. This was demonstrated in a specific example of two current loops with time dependent currents in at least one of the loops [1], or in one-time dependent loop current and a permanent magnet assembly [2, 3]. A relativistic engine was thus suggested. Since the system is affected by a total force for a finite period of time this means that the system acquires mechanical momentum and energy, the question then arises how to accommodate the law of momentum and energy conservation. The subject of momentum conversation was discussed in [4], while a preliminary discussion of the subject of electric energy conservation is given in [5, 6]. Here we discuss some of the radiation losses associated with the engine and their implications on the energy balance.

Problem of damping oscillations of a mechanical system with integral memory

The paper considers a mechanical system defined by a linear system of integro-differential equations with nonlocal convolution type terms. The problem of controllability is studied for various types of control (boundary and volume-distributed control) and various types of kernels. These kernels simulate the aftereffect of the system. It is proved that in some cases there is no possibility of damping the oscillations of the system for arbitrary initial conditions. In this work, those cases are distinguished when there is the possibility of damping oscillations over a finite period of time for any initial conditions.

Suppression of Oscillations of Thin Plate by Bounded Control Acting to the Boundary

The problem of the exact bounded control of transverse vibrations of a thin plate is considered. Control actions are applied to the boundary of the plate, which fills a certain bounded domain on the plane. The purpose of the control is to completely stop oscillations in a finite time period.

Solving predictive control problem of fast‐varying multivariable systems by incorporating unknown active dynamics generated by real‐time adaptive learning machine

AbstractNot only adaptive predictive control of switched systems is a computationally intensive procedure, it also involves various challenges in addressing the problems of robust stabilization and precise tracking. This study proposes new strategies to deal with the aforementioned issues (namely safe and precise control alongside with reduction of computational burden). The first contribution of this work is reduction of conservatism for described class of systems. Control of switched systems with undetectable switching signals is often conducted in worst case switching configuration to ensure robustness, which potentially results in conservative design. The issue of conservativeness is intensified in multi input‐multi output (MIMO) dynamical systems due to increased dimensions. However, attaining a robust control scheme for all switching configurations while ensuring precise response is inherently paradoxical. To overcome this issue, this study proposes a new dual‐mode algorithm where control modes corresponding to safety and precision are activated at appropriate stages of system response. This is conducted based on incorporation of an adaptive fuzzy‐wavelet neural network identification scheme in predictive control of MIMO switched systems. However, as convergence of the adaptive algorithm to actual system is attained after a finite period of time, a safe‐mode control algorithm is proposed to maintain quality of transient response in convergence period. In other words, the proposed algorithm operates in safe and precise control modes to ensure robust stability in the convergence period and non‐conservative design in steady‐state. Second major contribution of the work is reduction of calculation burden based on incorporation of a suboptimal control algorithm. To this end, we propose a predictive control scheme based on a suboptimal gradient‐descent based controller, calculating feasible stabilizing inputs instead of optimal inputs. Effects of dynamical variations are incorporated in the model predictive control framework for increased compatibility with high‐speed switching dynamics. Then, based on incorporation of dual‐mode algorithm, precise steady‐state performance is attained while preventing notable perturbations in dynamical discontinuities at switching.

Caring for older adults with multiple myeloma during the COVID-19 Pandemic: Perspective from the International Forum for Optimizing Care of Older Adults with Myeloma

The novel coronavirus (SARS-CoV-2, COVID-19) was first identified in the province of Wuhan, China in December 2019 [1], following the emergence of new cases of pneumonia of unknown etiology. Since then, the manifestations of COVID-19 infections have ranged from asymptomatic to severe respiratory infections, with increased morbidity in older adults including those with co-morbidities and cancer [2,3]. Presently, global mortality is reported at 4.7%, but this varies widely by location, from 0.7% in Germany to 10.8% in Italy [4]. As of April 13, 2020, the number of infections continues to rise well beyond the 1.9 million cases, and approximately 120,000 COVID-19-related deaths that have already occurred globally [5]. Multiple myeloma (MM) is a malignant plasma cell dyscrasia which predominantly affects older and often frail adults. Although tremendous gains have been made for older adults with MM, infections, including respiratory infections, significantly impact the rate of early mortality in these patients [6,7]. Furthermore, older adults with MM have age-associated vulnerabilities leading to heterogeneity in outcomes [8]. The complexity of caring for older patients have increased substantially during this pandemic, due to concern about their risk of severe morbidity of COVID19 infection. Optimal strategies for these patients will involve staging the malignancy/aging, while simultaneously considering the local prevalence of COVID-19 infection. Herein, we discuss strategies for the risk reduction of COVID-19 transmission, treatment stratification of anti-myeloma therapy and discussion regarding goals of care for older adults with MM during the COVID-19 pandemic.

Distributed finite-time bipartite consensus of multi-agent systems on directed graphs: Theory and experiment in nano-quadcopters formation

This work deals with the analysis and protocol design problems of finite-time consensus for multi-agent systems on signed and directed networks. A new distributed protocol with two reciprocal fractional power feedbacks of local consensus error has been proposed to remove the influence of initial states on the consensus time. By introducing a well-structured Lyapunov function, the technical difficulty arising from the asymmetrical Laplacian matrices of directed graphs is circumvented. Furthermore, it is shown that the feasibility of this proposed protocol can be extended to directed graphs with a spanning tree by mathematical induction method. The upper bounds of the finite-time periods are given under the circumstances of directed networks with a spanning tree apart from the strongly-connected ones. This new protocol is then extended to the application of finite-time bipartite formation control of multi-agent systems. Simulations and experiments of bipartite formation of multiple nano-quadcopters are implemented to prove the validity and practicability of this new protocol. In the experiment, a novel fuzzy logic is also introduced to realize the group collision avoidance of all nano-quadcopters.

Coordinated Influence on the Opinions of Social Network Members

This paper studies a model of coordinated influence in a social network in which several members, called players, can jointly affect the opinions of other members, called agents, during a finite period of time. The model is treated as a cooperative dynamic game. The influence of players is expressed by declaring their opinions which are then considered and weighted by the agents to form their own opinions. The goal is to find the declared opinions of players focusing only on associated costs as well as on the average deviation of agents beliefs from the desired ones. Under coordination, the total costs of players are distributed using the Shapley value. If there is no information about the degrees of trust of agents to each other, these degrees are estimated using a centrality measure. Numerical simulation is performed for a well-known social network of a university karate club and for a lattice graph often used for modeling of spatial networks.

On the Huygens principle in the Puu model

We consider the macroeconomic model of T. Puu, describing the fluctuations of gross income in a given region. With a special combination of savings and investment rates, income deviations will take place only for a finite period of time, after which the income will return to a stationary state. This e˙ect is known in mathematical physics as the Huygens principle. We investigated this model using statistical methods of data analysis. The obtained results suggest that the Huygens effect hypothesis in certain historical periods of the Russian economy is plausible. We have also considered the structure of the set of stationary zeros for nontrivial solutions to a stationary equation.

Adaptive finite‐time tracking control for robotic manipulators with funnel boundary

SummaryThe finite‐time tracking control problem with the output‐constraint property of robotic manipulators subjected to system uncertainties is addressed. Specifically, the radial basis function neural network is employed to compensate for system uncertainties. The finite‐time stability theorem is used for the backstepping design process, by which the limit of the settling time is set. A funnel boundary is used to limit the output overshoot. The proposed controller guarantees that all the signals are semi‐globally practically finite‐time bounded, while the tracking errors are enveloped by the funnel boundary. The performance of the proposed control method is illustrated by a numerical simulation of a 3‐DOF manipulator. It is shown that the tracking errors are bounded by prescribed funnel boundaries. In the meantime, the manipulator is stabilized within a finite period of time.

Optimal Sensor and Relay Nodes Power Scheduling for Remote State Estimation with Energy Constraint.

We study the sensor and relay nodes’ power scheduling problem for the remote state estimation in a Wireless Sensor Network (WSN) with relay nodes over a finite period of time given limited communication energy. We also explain why the optimal infinite time and energy case does not exist. Previous work applied a predefined threshold for the error covariance gap of two contiguous nodes in the WSN to adjust the trade-off between energy consumption and estimation accuracy. However, instead of adjusting the trade-off, we employ an algorithm to find the optimal sensor and relay nodes’ scheduling strategy that achieves the smallest estimation error within the given energy limit under our model assumptions. Our core idea is to unify the sensor-to-relay-node way of error covariance update with the relay-node-to-relay-node way by converting the former way of the update into the latter, which enables us to compare the average error covariances of different scheduling sequences with analytical methods and thus finding the strategy with the minimal estimation error. Examples are utilized to demonstrate the feasibility of converting. Meanwhile, we prove the optimality of our scheduling algorithm. Finally, we use MATLAB to run our algorithm and compute the average estimation error covariance of the optimal strategy. By comparing the average error covariance of our strategy with other strategies, we find that the performance of our strategy is better than the others in the simulation.

Can we use linear response theory to assess geoengineering strategies?

Geoengineering can control only some climatic variables but not others, resulting in side-effects. We investigate in an intermediate-complexity climate model the applicability of linear response theory (LRT) to the assessment of a geoengineering method. This application of LRT is twofold. First, our objective (O1) is to assess only the best possible geoengineering scenario by looking for a suitable modulation of solar forcing that can cancel out or otherwise modulate a climate change signal that would result from a rise in carbon dioxide concentration [CO2] alone. Here, we consider only the cancellation of the expected global mean surface air temperature Δ⟨[Ts]⟩. It is in fact a straightforward inverse problem for this solar forcing, and, considering an infinite time period, we use LRT to provide the solution in the frequency domain in closed form as fs(ω)=(Δ⟨[Ts]⟩(ω)-χg(ω)fg(ω))/χs(ω), where the χ's are linear susceptibilities. We provide procedures suitable for numerical implementation that apply to finite time periods too. Second, to be able to utilize LRT to quantify side-effects, the response with respect to uncontrolled observables, such as regional averages ⟨Ts⟩, must be approximately linear. Therefore, our objective (O2) here is to assess the linearity of the response. We find that under geoengineering in the sense of (O1), i.e., under combined greenhouse and required solar forcing, the asymptotic response Δ⟨[Ts]⟩ is actually not zero. This turns out not to be due to nonlinearity of the response under geoengineering, but rather a consequence of inaccurate determination of the linear susceptibilities χ. The error is in fact due to a significant quadratic nonlinearity of the response under system identification achieved by a forced experiment. This nonlinear contribution can be easily removed, which results in much better estimates of the linear susceptibility, and, in turn, in a fivefold reduction in Δ⟨[Ts]⟩ under geoengineering practice. This correction dramatically improves also the agreement of the spatial patterns of the predicted linear and the true model responses. However, considering (O2), such an agreement is not perfect and is worse in the case of the precipitation patterns as opposed to surface temperature. Some evidence suggests that it could be due to a greater degree of nonlinearity in the case of precipitation.