scholarly journals On the Reachability of a Feedback Controlled Leontief-Type Singular Model Involving Scheduled Production, Recycling and Non-Renewable Resources

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2175
Author(s):  
Manuel De la De la Sen ◽  
Asier Ibeas ◽  
Santiago Alonso-Quesada
Keyword(s):  
Renewable Resources ◽  
Finite Time ◽  
Economic Model ◽  
Initial Conditions ◽  
Final Time ◽  
Final State ◽  
Regulation Scheme ◽  
Leontief Model ◽  
Proposed Regulation ◽  
Economic Goods

This paper proposes and studies the reachability of a singular regular dynamic discrete Leontief-type economic model which includes production industries, recycling industries, and non-renewable products in an integrated way. The designed prefixed final state to be reached, under discussed reachability conditions, is subject to necessary additional positivity-type constraints which depend on the initial conditions and the final time for the solution to match such a final prescribed state. It is assumed that the model may be driven by both the demand and an additional correcting control in order to achieve the final targeted state in finite time. Formal sufficiency-type conditions are established for the proposed singular Leontief model to be reachable under positive feedback, correcting controls designed for appropriate demand/supply regulation. Basically, the proposed regulation scheme allows fixing a prescribed final state of economic goods stock in finite time if the model is reachable.

Fractal Boundary Explorations for a Nonlinear Two Degree-of-Freedom System

2012 ◽  
Author(s):  
Benjamin A. M. Owens ◽  
Brian P. Mann
Keyword(s):  
Initial Conditions ◽  
Coupled System ◽  
Basins Of Attraction ◽  
Degree Of Freedom ◽  
Fractal Boundary ◽  
Final State ◽  
Potential Wells ◽  
Mechanical Coupling ◽  
Mass Spring ◽  
Two Degree Of Freedom

This paper explores a two degree-of-freedom nonlinearly coupled system with two distinct potential wells. The system consists of a pair of linear mass-spring-dampers with a non-linear, mechanical coupling between them. This nonlinearity creates fractal boundaries for basins of attraction and forced well-escape response. The inherent uncertainty of these fractal boundaries is quantified for errors in the initial conditions and parameter space. This uncertainty relationship provides a measure of the final state and transient sensitivity of the system.

scholarly journals Study of the influence of initial-state fluctuations on hydrodynamic simulations

2020 ◽  
Vol 245 ◽  
pp. 06005
Author(s):  
Marcin Słodkowski ◽  
Patryk Gawryszewski ◽  
Dominik Setniewski
Keyword(s):  
Initial Conditions ◽  
Graphics Processing Unit ◽  
Heavy Ion ◽  
Processing Unit ◽  
Initial State ◽  
Final State ◽  
Hydrodynamic Simulation ◽  
Hydrodynamic Simulations ◽  
Cartesian Coordinate ◽  
Ion Collision

In this work, we are focusing on assessing the contribution of the initial-state fluctuations of heavy ion collision in the hydrodynamic simulations. We are trying to answer the question of whether the hydrodynamic simulation retains the same level of fluctuation in the final-state as for the initial stage. In another scenario, the hydrodynamic simulations of the fluctuation drowns in the final distribution of expanding matter. For this purpose, we prepared sufficient relativistic hydrodynamic program to study A+A interaction which allows analysing initial-state fluctuations in the bulk nuclear matter. For such an assumption, it is better to use high spatial resolution. Therefore, we applied the (3+1) dimensional Cartesian coordinate system. We implemented our program using parallel computing on graphics cards processors - Graphics Processing Unit (GPU). Simulations were carried out with various levels of fluctuation in initial conditions using the average method of events coming from UrQMD models. Energy density distributions were analysed and the contribution of fluctuations in initial conditions was assessed in the hydrodynamic simulation.

Multicausality and Equifinality

2021 ◽  
pp. 174-177
Author(s):  
Johann Wolfschwenger ◽  
Kevin L. Young
Keyword(s):  
Social Science ◽  
Systems Analysis ◽  
Initial Conditions ◽  
Final State ◽  
Social Phenomena ◽  
Research Traditions ◽  
Causal Processes ◽  
Science Methodology ◽  
Social Science Methodology ◽  
Research Situation

This chapter evaluates multicausality and equifinality, which refer to a research situation whereby an outcome is explained by more than one causal factor. The term ‘equifinality’ stems from systems analysis, and refers to a situation in which ‘the same final state may be reached from different initial conditions and in different ways’. ‘Equifinality’ also appears in related disciplines such as psychology, archaeology, or environmental studies, while ‘multicausality’ is often used in literature on social science methodology. Ultimately, multicausality and equifinality are important reasons why social phenomena are particularly challenging to study. Multicausality and equifinality are often explored by research traditions and methods of social inquiry that approach causal processes through a ‘causes-of-effects’ approach, rather than an ‘effect-of-causes’ approach.

Stochastic storage networks: stationarity and the feedforward case

1997 ◽  
Vol 34 (02) ◽  
pp. 498-507 ◽  
Author(s):  
Offer Kella
Keyword(s):  
Total Variation ◽  
Finite Time ◽  
Initial Conditions ◽  
Stability Conditions ◽  
Input Process ◽  
Stationary Increments ◽  
Stationary Version ◽  
Storage Network ◽  
The Difference ◽  
Storage Networks

We show that for a certain storage network the backward content process is increasing, and when the net input process has stationary increments then, under natural stability conditions, the content process has a stationary version under which the cumulative lost capacities have stationary increments. Moreover, for the feedforward case, we show that under some minimal conditions, two content processes with net input processes which differ only by initial conditions can be coupled in finite time and that the difference of two content processes vanishes in the limit if the difference of the net input processes monotonically approaches a constant. As a consequence, it is shown that for the natural stability conditions, when the net input process has stationary increments, the distribution of the content process converges in total variation to a proper limit, independent of initial conditions.

Effect of an Azimuthal Mean Flow On the Structure and Stability of Thermoacoustic Modes in an Annular Combustor Model with Electroacoustic Feedback

2020 ◽  
Author(s):  
Sylvain C. Humbert ◽  
Jonas Moeck ◽  
Alessandro Orchini ◽  
Christian Oliver Paschereit
Keyword(s):  
Mach Number ◽  
Initial Conditions ◽  
Mean Flow ◽  
Final State ◽  
Mean Velocity ◽  
Acoustic Damping ◽  
Annular Combustor ◽  
The Mean ◽  
High Mach ◽  
The Stability

Abstract Thermoacoustic oscillations in axisymmetric annular combustors are generally coupled by degenerate azimuthal modes, which can be of standing or spinning nature. Symmetry breaking due to the presence of a mean azimuthal flow splits the degenerate thermoacoustic eigenvalues, resulting in pairs of counter-spinning modes with close but distinct frequencies and growth rates. In this study, experiments have been performed using an annular system where the thermoacoustic feedback due to the flames is mimicked by twelve identical electroacoustic feedback loops. The mean azimuthal flow is generated by fans. We investigate the standing/spinning nature of the oscillations as a function of the Mach number for two types of initial states, and how the stability of the system is affected by the mean azimuthal flow. It is found that spinning, standing or mixed modes can be encountered at very low Mach number, but increasing the mean velocity promotes one spinning direction. At sufficiently high Mach number, spinning modes are observed in the limit cycle oscillations. In some cases, the initial conditions have a significant impact on the final state of the system. It is found that the presence of a mean azimuthal flow increases the acoustic damping. This has a beneficial effect on stability: it often reduces the amplitude of the self-sustained oscillations, and can even suppress them in some cases. However, we observe that the suppression of a mode due to the mean flow may destabilize another one. We discuss our findings in relation with an existing low-order model.

A novel adaptive second-order nonsingular terminal sliding mode guidance law design

2020 ◽  
Vol 234 (16) ◽  
pp. 2263-2273
Author(s):  
Shuai Xu ◽  
Min Gao ◽  
Dan Fang ◽  
Yi Wang ◽  
Baochen Li
Keyword(s):  
Finite Time ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Dynamic Control ◽  
Small Neighborhood ◽  
Lyapunov Stability Theory ◽  
Second Order ◽  
Terminal Sliding Mode ◽  
Guidance Law ◽  
Nonsingular Terminal Sliding Mode

Aiming at the problem of missile attacking ground target in pitch plane, combined with a composite fast nonsingular terminal sliding mode, a new adaptive finite-time stable guidance law with attack angle constraint is designed based on the second-order sliding mode control. The improved extended state observer is used to estimate the uncertainties and compensate the control quantity, and the dynamic control gains are designed to avoid the problem about “excessive estimation” of the parameter upper limit. According to the Lyapunov stability theory, it is proved that the system states can converge into a small neighborhood near the equilibrium point in a finite time. Monte Carlo simulation is carried out by randomly generating initial conditions, which proves that the guidance law has strong adaptability to different initial conditions and has good guidance precision.

On the Design of Finite Time Settling Control for Linear Systems

1992 ◽  
Vol 114 (3) ◽  
pp. 359-368 ◽  
Author(s):  
S. Choura
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Finite Time ◽  
Linear Time ◽  
Minimum Energy ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Final State ◽  
Variable Function ◽  
Time Varying Systems

The design of controllers combining feedback and feedforward for the finite time settling control of linear systems, including linear time-varying systems, is considered. The feedforward part transfers the initial state of a linear system to a desired final state in finite time, and the feedback part reduces the effects of uncertainties and disturbances on the system performance. Two methods for determining the feedforward part, without requiring the knowledge of the explicit state solutions, are proposed. In the first method, a numerical procedure for approximating combined controls that drive linear time-varying systems to their final state in finite time is given. The feedforward part is a variable function of time and is selected based on a set of necessary conditions, such as magnitude constraints. In the second method, an analytical procedure for constructing combined controls for linear time-invariant systems is presented, where the feedforward part is accurately determined and it is of the minimum energy control type. It is shown that both methods facilitate the design of the feedforward part of combined controllers for the finite time settling of linear systems. The robustness of driving a linear system to its desired state in finite time is analyzed for three types of uncertainties. The robustness analysis suggests a modification of the feedforward control law to assure the robustness of the control strategy to parameter uncertainties for arbitrary final times.

What is the final size of turbulent mixing zones driven by the Faraday instability?

2017 ◽  
Vol 837 ◽  
pp. 293-319 ◽  
Author(s):  
B.-J. Gréa ◽  
A. Ebo Adou
Keyword(s):  
Large Scale ◽  
Initial Conditions ◽  
Mixing Layer ◽  
Strong Support ◽  
Large Set ◽  
Mixing Zone ◽  
Final Size ◽  
Final State ◽  
Weakly Nonlinear ◽  
Faraday Instability

Miscible fluids of different densities subjected to strong time-periodic accelerations normal to their interface can mix due to Faraday instability effects. Turbulent fluctuations generated by this mechanism lead to the emergence and the growth of a mixing layer. Its enlargement is gradually slowed down as the resonance conditions driving the instability cease to be fulfilled. The final state corresponds to a saturated mixing zone in which the turbulence intensity progressively decays. A new formalism based on second-order correlation spectra for the turbulent quantities is introduced for this problem. This method allows for the prediction of the final mixing zone size and extends results from classical stability analysis limited to weakly nonlinear regimes. We perform at various forcing frequencies and amplitudes a large set of homogeneous and inhomogeneous numerical simulations, extensively exploring the influence of initial conditions. The mixing zone widths, measured at the end of the simulations, are satisfactorily compared to the predictions, and bring a strong support to the proposed theory. The flow dynamics is also studied and reveals the presence of sub-harmonic as well as harmonic modes depending on the initial parameters in the Mathieu phase diagram. Important changes in the flow anisotropy, corresponding to the large scale structures of turbulence, occur. This phenomenon appears directly related to the orientation of the most amplified gravity waves excited in the system, evolving due to the enlargement of the mixing zone.

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