Changes In State Variables Research Articles

Dynamical theory for adaptive systems

Abstract The study of adaptive dynamics, involving many degrees of freedom on two separated timescales, one for fast changes of state variables and another for the slow adaptation of parameters controlling the former’s dynamics is crucial for understanding feedback mechanisms underlying evolution and learning. We present a path-integral approach à la Martin–Siggia–Rose-De Dominicis–Janssen to analyse non-equilibrium phase transitions in such dynamical systems. As an illustration, we apply our framework to the adaptation of gene-regulatory networks under a dynamic genotype-phenotype map: phenotypic variations are shaped by the fast stochastic gene-expression dynamics and are coupled to the slowly evolving distribution of genotypes, each encoded by a network structure. We establish that under this map, genotypes corresponding to reciprocal networks of coherent feedback loops are selected within an intermediate range of environmental noise, leading to phenotypic robustness.

Flatness-based control in successive loops for dual-arm robotic manipulators

Dual-arm robotic manipulators are used in industry and for assisting humans since they enable dexterous handling of objects and more agile and secure execution of pick-and-place, grasping and lifting, or assembling tasks. In this article, a multi-loop flatness-based controller is proposed for the dynamic model of a dual-arm robot. In the considered application, the dual-arm robotic system has to lift and transfer an object under synchronized motion of its two end-effectors while it has also to compensate for the grasping forces between the two end-effectors and the object. The dynamic model of this robotic system is formulated while it is proven that the state-space description of the robot’s dynamics is differentially flat. The control problem for this robotic system is solved with the use of a flatness-based control approach which is implemented in successive loops. To apply the multi-loop flatness-based control method, the state-space model of the dual-arm robotic manipulator is separated into subsystems, which are connected in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input–output linearized flat systems. The state variables of the preceding i-th subsystem become virtual control inputs for the subsequent ( i + 1)-th subsystem. In turn, real control inputs are applied to the last subsystem. The whole control method is implemented in successive loops and its global stability properties are also proven through Lyapunov stability analysis. The multi-loop flatness-based control approach is an exact nonlinear control scheme which (i) does not use approximate linearization of the dynamic model of the controlled system and (ii) does not need changes of state variables and complicated state-space model transformations.

Disorder-to-order transition induced by spontaneous cooling regulation in robotic active matter

Abstract In classical matter systems, typical phase-transition phenomena usually stem from changes in state variables, such as temperature and pressure, induced by external regulations such as heat transfer and volume adjustment. However, in active matter systems, the self-propulsion nature of active particles endows the systems with the ability to induce unique collective-state transitions by spontaneously regulating individual properties to alter the overall states. Based on an innovative robot-swarm experimental system, we demonstrate a field-driven active matter model capable of modulating individual motion behaviors through interaction with a recoverable environmental resource field by the resource perception and consumption. In the simulated model, by gradually reducing the individual resource-conversion coefficient over time, this robotic active matter can spontaneously decrease the overall level of motion, thereby actively achieving a regulation behavior like the cooling-down control. Through simulation calculations, we discover that the spatial structures of this robotic active matter convert from disorder to order during this process, with the resulting ordered structures exhibiting a high self-adaptability on the geometry of the environmental boundaries.

An overview of the NEMO modelling for the BaySys project

This article is intended as an introduction to discuss the development of a modelling framework to examine simulated climate change and river discharge regulation and their combined impact on marine conditions in the Hudson Bay Complex as a contribution to BaySys, a collaborative project between Manitoba Hydro, Hydro-Quebec, the University of Manitoba, the University of Alberta, Université Laval and Ouranos. In support of this work, a sea ice and oceanographic model was improved and then used to further study the effects of freshwater loading and ice cover on the circulation of Hudson Bay. This modelling perspective is based on the Nucleus for European Modelling of the Ocean (NEMO) ocean general circulation model coupled to version 2 of the Louvain-la-Neuve sea ice model (LIM2). The goal of the modelling was to provide a framework and tool for simulating projected changes in marine state and dynamic variables, while also enabling an integration of observations and numerical analyses. A key aspect of this work was the climate-hydrologic-ocean model integration aspect. The inclusion of a biogeochemical model and explicit tidal forcing to examine the evolution of a Canadian marginal sea with century-long integrations was also a novel aspect of the work. Overall, this work examines the NEMO modelling configuration used in BaySys, how it is set up and the experiments carried out. A broader picture evaluation of the model output is made including the BaySys mooring observations, showing that the modelling framework is suitable to examine the posed questions on the role of climate change and river regulation.

Pressure‐Induced Structural and Semiconductor‐Metal‐Superconductor Transitions in a High‐Entropy van der Waals Compound (MnFeCuCdIn)PSe3

AbstractThe properties of the emerging phosphochalcogenide compounds can be tuned by temperature, pressure, and the chemical composition characterized by the compound entropy. However, it is unknown how the entropy of such a compound affects its structural stability and material properties when a state variable changes. In this work, a new layered high‐entropy phosphoselenide compound (MnFeCuCdIn)PSe3 (denoted MPSe3) is prepared and its structural evolution and property changes are studied at pressures up to ≈60 GPa. It is found that the compound undergoes two isostructural changes at ≈10 and 20 GPa, a structural change forming a high‐coordination phase in ≈32–35 GPa, a semiconductor‐to‐metal transition in ≈28–30 GPa at room temperature, and a metal‐to‐superconductor transition in ≈2.5–4.9 K at a pressure from ≈43 to 58 GPa. Combining data from prior studies, it is further found that for the MPSe3‐type medium/high‐entropy compounds, there exists a linear relationship between the structural transition pressure and the cation mixing entropy, and an inverse nearly linear relationship between the superconducting critical temperature and the cation mixing entropy, with the latter due primarily to the decrease in the Debye temperature. These findings will have great importance for developing new complex materials using the evolving entropy engineering.

Age-dependent ventilator-induced lung injury: Mathematical modeling, experimental data, and statistical analysis.

A variety of pulmonary insults can prompt the need for life-saving mechanical ventilation; however, misuse, prolonged use, or an excessive inflammatory response, can result in ventilator-induced lung injury. Past research has observed an increased instance of respiratory distress in older patients and differences in the inflammatory response. To address this, we performed high pressure ventilation on young (2-3 months) and old (20-25 months) mice for 2 hours and collected data for macrophage phenotypes and lung tissue integrity. Large differences in macrophage activation at baseline and airspace enlargement after ventilation were observed in the old mice. The experimental data was used to determine plausible trajectories for a mathematical model of the inflammatory response to lung injury which includes variables for the innate inflammatory cells and mediators, epithelial cells in varying states, and repair mediators. Classification methods were used to identify influential parameters separating the parameter sets associated with the young or old data and separating the response to ventilation, which was measured by changes in the epithelial state variables. Classification methods ranked parameters involved in repair and damage to the epithelial cells and those associated with classically activated macrophages to be influential. Sensitivity results were used to determine candidate in-silico interventions and these interventions were most impact for transients associated with the old data, specifically those with poorer lung health prior to ventilation. Model results identified dynamics involved in M1 macrophages as a focus for further research, potentially driving the age-dependent differences in all macrophage phenotypes. The model also supported the pro-inflammatory response as a potential indicator of age-dependent differences in response to ventilation. This mathematical model can serve as a baseline model for incorporating other pulmonary injuries.

Flatness-based control in successive loops for robotic manipulators and autonomous vehicles

ABSTRACT The control problem for the multivariable and nonlinear dynamics of robotic manipulators and autonomous vehicles is solved with the use of a flatness-based control approach which is implemented in successive loops. The state-space model of these robotic systems is separated into two subsystems, which are connected between them in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input–output linearised flat systems. The state variables of the second subsystem become virtual control inputs for the first subsystem. In turn, exogenous control inputs are applied to the first subsystem. The whole control method is implemented in two successive loops and its global stability properties are also proven through Lyapunov stability analysis. The validity of the control method is confirmed in two case studies: (a) control of a 3-DOF industrial rigid-link robotic manipulator and (b) control of a 3-DOF autonomous underwater vessel. The novel control method can simplify significantly the solution of the nonlinear control problem for robotic manipulators and vehicles. Unlike global linearisation-based control schemes, the proposed flatness-based method in successive loops does not need any changes in state variables of complicated state-space model transformations.

Ecological dynamic regimes: Identification, characterization, and comparison

AbstractUnderstanding ecological dynamics has been a central topic in ecology since its origins. Yet, identifying dynamic regimes remains a research frontier for modern ecology. The concept of ecological dynamic regime (EDR) emerged to emphasize the dynamic property of steady states in nature and refers to the fluctuations of ecosystems around some trend or average. Identifying and characterizing EDRs is of utmost importance in the current context of global change since they form the reference against which post‐disturbance dynamics must be compared to assess ecological resilience. However, the implementation of EDRs in empirical science is still challenging given the high dimensionality and stochasticity of ecological data and the large volume of data required to distinguish stochastic dynamics from general and predictable dynamics. The era of big data and the recent advances in quantitative ecology and data science offer an opportunity to study dynamic regimes using empirical approaches from a new perspective. This paper presents a novel methodological framework to describe EDRs from a set of ecological trajectories defined by the temporal changes of state variables in a multidimensional state space. In our framework, we formally define EDRs and include analytical tools to identify, characterize, and compare EDRs based on their geometric characteristics. More specifically, we propose different ways to identify EDRs from empirical data, develop a new algorithm to identify representative trajectories summarizing the main dynamic patterns, propose a set of metrics to describe the internal distribution of ecological trajectories, and define a dissimilarity index to compare two or more dynamic regimes based on their shape and position in the state space. We used artificial data to illustrate the different elements of our framework and applied our analyses to real data, using permanent sampling plots of Canadian boreal forests as an example. Overall, our framework contributes to filling the gap between theoretical and empirical ecology by providing robust analytical tools to assess ecological resilience and study ecosystem dynamics from a multidimensional perspective and considering the variability of natural systems.

Nonlinear optimal control for permanent magnet synchronous spherical motors

Nonlinear optimal control for permanent magnet synchronous spherical motors

The Florida experience: time for a revitalized and restructured Clean Lakes Program

Canfield, DE Jr., Bachmann RW, Hoyer MV. 2023. The Florida experience: time for a revitalized and restructured Clean Lakes Program. Lake Reserv Manage. 39:191–212. Anthropogenic nonpoint source nutrient enrichment of lakes is a worldwide problem, but inputs from the watershed to Florida lakes may not be as severe as speculated. Long-term trends for total phosphorus (TP), total nitrogen (TN), chlorophyll (Chl), and Secchi disk transparency (SDT), enrichment surrogates, in 381 lakes monitored for 20–43 yr and having extensive management to none demonstrated improvements in trophic conditions following point source removals. Afterward, TP (R2 = 0.85), TN (R2 = 0.49), and Chl (R2 = 0.50) continued to decline significantly (P < 0.05) and SDT (R2 = 0.63) increased. For 99 state-designated “impaired” lakes, TP (R2 = 0.73), TN (R2 = 0.45), and Chl (R2 = 0.44) also declined and SDT (R2 = 0.69) increased. To consider natural background conditions, lakes were assigned to their ambient TP and TN zones. Geometric TP (93%) and TN (82%) zone averages for each lake after removal of point sources remained within each zone’s 95% confidence interval. Individual lake trend analyses documented that ∼80% showed no (most) or an improving trend for the trophic state variables. After correcting for “statistically meaningful” results or to remove false significances, <5% of the lakes had trophic state variable changes associated with eutrophication. If lakes are to be rehabilitated and/or protected to maintain designated uses, exclusive focus on watershed management of nonpoint source nutrients and associated regulatory actions should not be relied on to correct “impairments” in a timely manner. Management priorities should focus on actual causes of impairment and the most effective and efficient approaches for improvement.

On the Foundation and Different Interpretations of Ensemble Sensitivity

Abstract In sensitivity analysis, ensemble sensitivity is defined as the regression coefficients resulting from a simple linear regression of changes of a response function on initial perturbations. One of the interpretations for ensemble sensitivity considers this a simplified version of regression-based adjoint sensitivity called univariate ensemble sensitivity whose derivation involves the so-called diagonal approximation. This approximation, which replaces the analysis error covariance matrix by a diagonal matrix with the same diagonal, helps to avoid inversion of the analysis error covariance, but, at the same time causes confusion in understanding and practical application of ensemble sensitivity. However, some authors have challenged such a controversial interpretation by showing that univariate ensemble sensitivity is multivariate in nature, which raises the necessity for the foundation of ensemble sensitivity. In this study, we have tried to resolve the confusion by establishing a robust foundation for ensemble sensitivity without relying on the controversial diagonality assumption. As employed in some studies, we adopt an impact-based definition for ensemble sensitivity by taking into account probability distributions of analysis perturbations. The mathematical results show that standardized ensemble sensitivity carries in itself three important quantities at the same time: 1) standardized changes of the forecast response with one standard deviation changes of individual state variables, 2) correlations between the forecast response and individual state variables, and 3) the most sensitive analysis perturbation. The theory guarantees validity of ensemble sensitivity, demonstrates its multivariate nature, and explains why ensemble sensitivity is effective in practice.

Modeling and Harmonic Analysis of a Fractional-Order Zeta Converter

The Zeta converter is an essential and widely used high-order converter. The current modeling studies on Zeta converters are based on the model that devices, such as capacitors and inductors, are of integer order. For this reason, this paper takes the Zeta converter as the research object and conducts an in-depth study on its fractional-order modeling. However, the existing modeling and analysis methods have high computational complexity, the analytical solutions of system variables are tedious, and it is difficult to describe the ripple changes of state variables. This paper combines the principle of harmonic balance with the equivalent small parameter method (ESPM); the approximate analytic steady-state solution of the state variable can be obtained in only three iterative steps in the whole solving process. The DC components and ripples of the state variables obtained by the proposed method were compared with those obtained by the Oustaloup’s filter-based approximation method; the symbolic period results obtained by ESPM had sufficient precision because they included more combinations of higher harmonics. Finally, the influence of fractional order on harmonics were analyzed. The obtained results show that the proposed method has the advantage of being less computational and easily describing changes in the ripple of the state variables. The simulation results are provided for validity of the theoretical analysis.

The Strong Tracking Innovation Filter

Sliding innovation filter (SIF) has recently been introduced as a robust strategy for estimation of linear systems. The SIF has been extended to nonlinear systems via analytical linearization. However, as the performance of the extended SIF (ESIF) degrades in the presence of severe nonlinearities, this article has initially developed a derivative-free cubature SIF (CSIF) that uses statistical linearization for the error propagation. In addition, the SIF gain has been reformed to incorporate the innovation covariance matrix, thus reducing the estimation error. Furthermore, the adaptive fading factor has been employed to strengthen the robustness and convergence properties of the CSIF against abrupt changes of state variables. Simulation results of the proposed estimation algorithm named the strong tracking innovation filter (STIF) have been compared to those of the ESIF and the CSIF in different conditions of the modeling error in the dynamic system and statistical characteristics of the system inputs. This comparison has demonstrated the superior performance of the STIF in terms of the convergence rate, estimation accuracy, and the chattering elimination. Integration of the STIF into a sliding mode controller for the concurrent estimation and control of a Mars lander has reconfirmed the robustness and accuracy of the proposed STIF.

Numerical analysis of hybrid nanofluid natural convection in a wavy walled porous enclosure: Local thermal non-equilibrium model

A numerical study of the Buoyancy-driven flow in a porous enclosure, having a bottom heated wavy wall, filled with Cu-Al2O3/water hybrid nanofluid is performed using the local thermal non-equilibrium model. The non-dimensional governing equations of fluid flow and heat transfer are solved using the Galerkin finite element method. The state variables change in the porous enclosure is represented using the Darcy-Brinkman model. The impacts of various effective parameters which include nanoparticle volume fraction (0 ≤ Φ ≤ 0.04), Darcy number (10−5 ≤ Da ≤ 10−2), modified conductivity ratio (0.1 ≤ γ ≤ 1000), the number of undulations (1≤ N ≤ 5) and the amplitude of waviness (0.05 ≤ A ≤ 2). The results showed that the Darcy number is the first controlling parameter on the fluid flow and temperature distributions followed by A, N and γ. Additionally, the heat transfer rate is increased by increasing the thermal conductivity of the nanoparticles reaching its maximum value at Φ = 0.04. Furthermore, by comparing the temperature fields of the fluid phase and solid matrix, it is clear that the effects of the local thermal non-equilibrium are significant at a low modified thermal conductivity ratio and high Darcy number.

Decentralized Control for Balancing the Cell Voltages of a High Conversion Ratio Flying Capacitor Multilevel Converter

This article presents a decentralized control strategy for the balancing of the cell voltages of a flying capacitor multilevel converter, implementing a large number of cells to address a high conversion ratio. The originality of this article is that no reference is required for regulating the capacitor voltages leading to an auto-balance capability. It is composed of several local cell-voltage balancing controllers and a global load-current regulator. For theoretical analysis purposes, a change of state variables is proposed, leading to a new model of the converter. Then, the study of the decentralized balancing method is performed based on a modal analysis of the system. A decoupling of the output current regulation and the cell-voltage balancing loops is proposed, and then observed. The synthesis of the controllers, guaranteeing the stability of the system within a large bandwidth for each mode, is obtained. To address the fault-tolerance requirement, this decentralized control strategy provides an opportunity for auto-reconfiguration, allowing changes in the number of active cells during operation. Simulations of the separated modal responses show the stability and bandwidth of the control loops for dc/dc 500 to 16 V high conversion ratio applications. Experimental results, performed on a 5-cell multilevel converter, demonstrate the validity of the proposed control method.

Assessment of climate change of different meteorological state variables during Indian summer monsoon season

Assessment of climate change of different meteorological state variables during Indian summer monsoon season

Environmental lead reduces the resilience of bald eagle populations

AbstractBald eagles (Haliaeetus leucocephalus) are considered a recovery success in the United States after rebounding from near extirpation due to widespread use of the insecticide dichlorodiphenyltrichloroethane (DDT) in the twentieth century. Although abundances of bald eagles have increased since DDT was banned, other contaminants have remained in the environment with unknown influence on eagle population trends. Ingestion of spent lead (Pb) ammunition, the source of Pb most available to eagles and other scavengers in the United States, is known to kill individual eagles, but the influence of the contaminant on overall population dynamics remains unclear, resulting in longstanding controversy over the continued legality of the use of Pb in terrestrial hunting ammunition. We hypothesized that mortalities from the ingestion of Pb reduced the long‐term growth rate and resiliency of bald eagles in the northeast United States over the last 3 decades. We used Holling's definition of resilience (the ability of a system to absorb changes of state variables, driving variables, and parameters and still persist) to quantify how reduction in survival from Pb‐associated mortalities reduced the likelihood of population persistence. We used a population matrix model and necropsy records gathered between 1990 and 2018 from a 7‐state area to compare population dynamics under current versus hypothetical Pb‐reduced and Pb‐free scenarios. Despite a robust increase in eagle abundances in the northeast United States over that period, we estimated that deaths arising from ingestion of Pb was associated with a 4.2% (females) and 6.3% (males) reduction in the asymptotic long‐term growth rate (lambda). Comparison between real (current) and counterfactual (Pb‐reduced and Pb‐free) population dynamics indicated that the deaths from acute Pb poisoning were additive because the mortality events were associated with marked reduction in annual survival performance of hatchlings and reproductive females. These shifts in survival performance were further associated with a reduction in resilience for hatchling (95.4%) and breeding (81.6%) female eagles. Counterintuitively, the current conditions produced an increase in resilience (68.9%) for immature and non‐breeding female eagles over hypothetical Pb‐free conditions, suggesting that the population of eagles in the northeast United States reorganized (in a population dynamics sense) to ensure population expansion despite additive mortalities associated with Pb. This study can be used by state and federal wildlife managers or non‐governmental organizations to inform policy surrounding the use of lead ammunition or to educate hunters on the population‐scale effects of their ammunition choices.

Robust strong tracking unscented Kalman filter for non‐linear systems with unknown inputs

This paper proposes a state estimation approach ‘robust strong tracking unscented Kalman filter with unknown inputs’ that can be applied to non-linear systems with unknown inputs. Specifically, the non-linear state and measurement equations are linearised by statistical linearisation. Then, the estimation equation of the unknown input is derived based on the weighted least squares method. The multiple suboptimal fading factor is introduced into a priori error covariance matrix to improve the tracking ability for the inaccuracy of the system model and the abrupt change of state variables caused by unknown inputs. Finally, based on the unbiased minimum variance estimation, the unbiased state estimation and the error covariance matrix are derived. Singular value decomposition is performed on the error covariance matrix to improve the stability of the algorithm. Simulated results validate the effectiveness of the proposed method.

A viscosity solution of the Hamilton–Jacobi equation with exponential dependence of Hamiltonian on the momentum

The initial – boundary value problem is considered for the Hamilton-Jacobi of evolutionary type in the case when the state space is one-dimensional. The Hamiltonian depends on the state and momentum variables, and the dependence on the momentum variable is exponential. The problem is considered on fixed bounded time interval, and the state variable changes from a given fixed value to infinity. The initial and boundary functions are subdifferentiable. It is proved that such a problem has a continuous generalized viscosity) solution. The representative formula is given for this solution. Sufficient conditions are indicated under which the generalized solution is unique. Hamilton-Jacobi equations with an exponential dependence on the momentum variable are atypical for theory, but such equations arise in practical problems, for example, in molecular genetics.

Long-Term Water Quality Patterns in an Estuarine Reservoir and the Functional Changes in Relations of Trophic State Variables Depending on the Construction of Serial Weirs in Upstream Reaches.

Water quality degradation is one of the major problems with artificial lakes in estuaries. Long-term spatiotemporal patterns of water quality in a South Korean estuarine reservoir were analyzed using seasonal datasets from 2002 to 2020, and some functional changes in relations of trophic state variables due to the construction of serial weirs in the upper river were also investigated. A total of 19 water quality parameters were used for the study, including indicators of organic matter, nutrients, suspended solids, water clarity, and fecal pollution. In addition, chlorophyll-a (CHL-a) was used to assess algal biomass. An empirical regression model, trophic state index deviation (TSID), and principal component analysis (PCA) were applied. Longitudinal fluctuations in nutrients, organic matter, sestonic CHL-a, and suspended solids were found along the axis of the riverine (Rz), transition (Tz), and lacustrine zones (Lz). The degradation of water quality was seasonally caused by resuspension of sediments, monsoon input due to rainfall inflow, and intensity of Asian monsoon, and was also related to intensive anthropic activities within the catchment. The empirical model and PCA showed that light availability was directly controlled by non-algal turbidity, which was a more important regulator of CHL-a than total nitrogen (TN) and total phosphorus (TP). The TSID supported our hypothesis on the non-algal turbidity. We also found that the construction of serial upper weirs influenced nutrient regime, TSS, CHL-a level, and trophic state in the estuarine reservoir, resulting in lower TP and TN but high CHL-a and high TN/TP ratios. The proportions of both dissolved color clay particles and blue-green algae in the TSID additionally increased. Overall, the long-term patterns of nutrients, suspended solids, and algal biomass changed due to seasonal runoff, turnover time, and reservoir zones along with anthropic impacts of the upper weir constructions, resulting in changes in trophic state variables and their mutual relations in the estuarine reservoir.