Dynamics Of Original System Research Articles

EU land use futures: modelling food, bioenergy and carbon dynamics

This paper presents an original system dynamics model, which aims to assess how changes in diet, agricultural practices, bioenergy and forestry could help reduce greenhouse gas emissions. We demonstrate that changes in types and quantities of food consumed and reductions in food wastes along with sustainable bioenergy and forestry dynamics would materially assist the EU in meeting its 2050 climate mitigation obligations. We find that overall rates of EU-28 greenhouse gas emissions are highly sensitive to the food trade balance, both within and outside the EU. Land use itself is often under-represented as a major option for carbon mitigation in policy strategies, but our results show that it must become a central component aligned with energy system decarbonization if material levels of warming mitigation are to be achieved.

Positive Harris recurrence for degenerate diffusions with internal variables and randomly perturbed time-periodic input

We consider a multidimensional time-homogeneous dynamical system and add a randomly perturbed time-dependent deterministic signal to some of its components, giving rise to a high-dimensional system of stochastic differential equations, which is driven by possibly very low-dimensional noise. Equations of this type commonly occur in biology when modeling neurons or in statistical mechanics for certain Hamiltonian systems. We provide verifiable conditions on the original deterministic dynamical system under which the solution to the respective stochastic system features a point in the interior of its state space, which can be proved to be attainable by deterministic control arguments, and at which a local Hörmander condition holds. Together with a Lyapunov condition, it follows that the corresponding process is positive Harris recurrent.

Output Control by Linear Time-Varying Systems using Parametric Identification Methods

In this paper the problem of control for time-varying linear systems by the output (i.e. without measuring the vector of state variables or derivatives of the output signal) was considered. For the control design, the well-known online procedure for solving the Riccati matrix differential equation is chosen. This procedure involves the synthesis of linear static feedbacks on state variables in the case of known parameters of the plant. If state variables are not measured, then for the observer design using the matrix Riccati differential equation, using the dual scheme, which provides for the transposition of the state matrix and the replacement of the input matrix by the output matrix. It is well known that an observer of state variables built on the basis of a solution of the Riccati matrix differential equation ensures the exponential stability of a closed loop system in the case of uniform observability. Despite the fact that this type of observer can be classified as universal, its have a number of significant drawbacks. The main problem of such observers is the need for accurate knowledge of the parameters and the requirement for uniform observability, which in practice cannot always be realized. Thus, the problem of the new methods design for constructing observers of state variables of linear non-stationary systems is still relevant. Some time ago, a number of methods for the adaptive observers design of state variables for nonlinear systems were proposed. The main idea of the synthesis of observers was based on the transformation of the original dynamic system to a linear regression model containing unknown parameters, which in turn were functions of the initial conditions of the state variables of the control object. This approach in the English language literature is called PEBO. This paper, based on the PEBO method, proposes a new approach for the observers design of state for non-stationary systems. This approach provides the possibility of obtaining monotonic convergence estimates with transient time tuning.

Subharmonic and Combination Resonance of Rotating Pre-deformed Blades Subjected to High Gas Pressure

The present paper deals with the investigation of dynamic responses of a rotating pre-deformed blade in four cases of resonance, including two subharmonic resonances and two combination resonances. The dimensionless gas excitation amplitude is assumed to share the same order with the dimensionless vibration displacement. Four cases of resonance are confirmed by examining the secular terms. The theoretical analysis framework is established for each resonance case based on the method of multiple scales. The original dynamic system is integrated numerically by the Runge–Kutta method. The frequency components and phases obtained from fast Fourier transform of the numerical response are used to verify the theoretical results. For the purpose of contrast, modulation equations are also integrated numerically. In all four resonance cases, the theoretical results agree well with the numerical simulation. Parameter studies are conducted to clarify the effects of system parameters on the perturbation curves. Various results are obtained for the rotating blade. A quasi-saturation phenomenon occurs in both combination resonances of summed type and difference type, and the corresponding limit value of the second-mode response can be reduced by decreasing the external detuning parameter. The quasi-saturation phenomenon of rotating blade only appears with high gas pressure. The subharmonic resonance of second mode and the combination resonance of summed type are hard to excite in practice compared with the other two cases.

Online optimal and adaptive integral tracking control for varying discrete‐time systems using reinforcement learning

SummaryConventional closed‐form solution to the optimal control problem using optimal control theory is only available under the assumption that there are known system dynamics/models described as differential equations. Without such models, reinforcement learning (RL) as a candidate technique has been successfully applied to iteratively solve the optimal control problem for unknown or varying systems. For the optimal tracking control problem, existing RL techniques in the literature assume either the use of a predetermined feedforward input for the tracking control, restrictive assumptions on the reference model dynamics, or discounted tracking costs. Furthermore, by using discounted tracking costs, zero steady‐state error cannot be guaranteed by the existing RL methods. This article therefore presents an optimal online RL tracking control framework for discrete‐time (DT) systems, which does not impose any restrictive assumptions of the existing methods and equally guarantees zero steady‐state tracking error. This is achieved by augmenting the original system dynamics with the integral of the error between the reference inputs and the tracked outputs for use in the online RL framework. It is further shown that the resulting value function for the DT linear quadratic tracker using the augmented formulation with integral control is also quadratic. This enables the development of Bellman equations, which use only the system measurements to solve the corresponding DT algebraic Riccati equation and obtain the optimal tracking control inputs online. Two RL strategies are thereafter proposed based on both the value function approximation and the Q‐learning along with bounds on excitation for the convergence of the parameter estimates. Simulation case studies show the effectiveness of the proposed approach.

Dynamic Kinetic Resolution for Asymmetric Synthesis of L‐Noncanonical Amino Acids from D‐Ser Using Tryptophan Synthase and Alanine Racemase

L‐Ser is often used to synthesize some significant l‐noncanonical α‐amino acids(l‐ncAAs), which are the prevalent intermediates and precursors for functional synthetic compounds. In this study, threonine aldolase from Escherichia coli k‐12 MG1655 has been used to synthesize l‐Ser. In contrast to the maximum catalytic capacity (20 g/L) for l‐threonine aldolase(LTA), d‐Ser was synthesized with high yield (240 g/L) from cheap Gly and paraformaldehyde using d‐threonine aldolase (DTA) from Arthrobacter sp ATCC. In order to fully utilize d‐Ser and expand the resource of l‐Ser, a dynamic kinetic resolution system was constructed to convert d/dl‐Ser to l‐Ser through combining alanine racemase (Alr) from Bacillus subtilis with l‐tryptophan synthase (TrpS) from Escherichia coli k‐12 MG1655, and l‐ncAAs including l‐Trp and l‐Cys derivatives were synthesized with excellent enantioselectivity and in high yields. The results indicated l‐ncAAs could be efficiently synthesized from d‐Ser using this original and green dynamic kinetic resolution system, and the reliable l‐Ser resource has been established from simple and achiral substrates.

Optimal Model Approximation of Linear Time-Invariant Systems Using the Enhanced DE Algorithm and Improved MPPA Method

In this paper, the authors propose a novel model order reduction method integrating evolutionary and conventional approaches for higher-order linear time-invariant single-input–single-output (SISO) and multi-input–multi-output (MIMO) dynamic systems. The proposed method makes use of a differential evolution algorithm with enhanced mutation operation for the determination of reduced order model (ROM) denominator polynomial coefficients. In addition, an improved multi-point Pade approximation method is used to determine the optimal ROM numerator polynomial coefficients. The optimum property of the ROM is measured by minimising the integral square of the step response error between the original high-order dynamic system and the ROM. In the case of the MIMO system reduction approach, an optimal ROM transfer function matrix is determined by minimising a single objective function. This objective function is defined by a linear scalarising of the multi-step error function matrix components $$ \left( {E_{ij} } \right) $$. The proposed method guarantees the preservation of the stability, passivity and accuracy of the original higher-order system in the ROM. The proposed method is validated by applying it to a ninth-order SISO system, as well as to the tenth- and sixth-order linearised single-machine infinite-bus power system model with and without an automatic excitation control system. The simulation results and the comparison of the integral square error and impulse response energy values of the ROM demonstrate the dominance of the proposed method over the latest reduction methods available in the literature.

Stability-preserving model order reduction for linear stochastic Galerkin systems

Mathematical modeling often yields linear dynamical systems in science and engineering. We change physical parameters of the system into random variables to perform an uncertainty quantification. The stochastic Galerkin method yields a larger linear dynamical system, whose solution represents an approximation of random processes. A model order reduction (MOR) of the Galerkin system is advantageous due to the high dimensionality. However, asymptotic stability may be lost in some MOR techniques. In Galerkin-type MOR methods, the stability can be guaranteed by a transformation to a dissipative form. Either the original dynamical system or the stochastic Galerkin system can be transformed. We investigate the two variants of this stability-preserving approach. Both techniques are feasible, while featuring different properties in numerical methods. Results of numerical computations are demonstrated for two test examples modeling a mechanical application and an electric circuit, respectively.

Building a bridge to behavioral economics: countervailing cognitive biases in lifetime saving decisions

AbstractThis research project bridges system dynamics and behavioral economics by importing tools and concepts, such as feedback dynamics, into mainstream behavioral economics research. This project focuses on countervailing cognitive biases, a theory where two competing cognitive biases can interact or even cancel out each other. We apply this concept to a key problem in behavioral economics: the difficulty that people have in making optimal trade‐offs between spending and saving for retirement. The simple model introduced in this paper represents the first iteration in the effort, and provides a proof‐of‐concept model that reproduces theoretical optimal behaviors from behavioral economics. Our exploratory analysis then adds to the simulation two cognitive biases that partially cancel each other out in ways that we had not initially expected. In the next step, we modify our original system dynamics model as an example of how to replace an economic optimization calculation with a decision‐making heuristic involving information feedback.© 2019 System Dynamics Society

New Methods for Optimal Operational Control of Industrial Processes Using Reinforcement Learning on Two Time Scales

Current challenges in industrial processes control include achieving optimum operation for systems with two-time-scale dynamics and unknown models. This paper presents, for the first time, the integration of singular perturbation theory and reinforcement learning to solve this problem. To this end, an optimal operational control (OOC) problem with two time scales is formulated to reach the desired operational indices. Then, a singularly perturbed dynamics for two-time-scale industrial operational processes is developed by introducing a perturbed scale, resulting in the separation of the original system dynamics. Thus, the original optimization problem is decomposed into a reduced slow subproblem and a boundary fast subproblem. The fact that the sum of the separate solutions of these subproblems is approximately equal to the solution of the OOC problem is proven. Then, two $Q$ -learning algorithms are proposed to obtain a composite feedback control. Finally, an industrial thickener example is employed to show the effectiveness of the proposed method.

Quantitative analysis of financial system fragility based on manifold curvature

Manifold curvature is an intrinsic attribute of a dynamical system. By analyzing curvature characteristics of embedding attractor manifold, resistance and resilience of financial dynamic system are investigated in the face of disturbances, thus system fragility is discussed quantitatively from a systemic perspective. First, financial time series data are reconstructed into a high-dimensional phase space, topologically equivalent to its original dynamical system. Then, manifold learning is employed to extract attractor manifold embedding in financial dynamic system. Last, by numerical calculation, the manifold curvature is obtained and further visualized with spatial mapping. In empirical study, Shanghai Composite Index and Dow Jones Industrial Index are adopted as experimental data, and then a more comprehensive understanding about financial systems fragility is obtained by exploring the dynamical properties related to manifold curvature.

Eisenhart lift of 2-dimensional mechanics

The Eisenhart lift is a variant of geometrization of classical mechanics with d degrees of freedom in which the equations of motion are embedded into the geodesic equations of a Brinkmann-type metric defined on (d+2)-dimensional spacetime of Lorentzian signature. In this work, the Eisenhart lift of 2-dimensional mechanics on curved background is studied. The corresponding 4-dimensional metric is governed by two scalar functions which are just the conformal factor and the potential of the original dynamical system. We derive a conformal symmetry and a corresponding quadratic integral, associated with the Eisenhart lift. The energy–momentum tensor is constructed which, along with the metric, provides a solution to the Einstein equations. Uplifts of 2-dimensional superintegrable models are discussed with a particular emphasis on the issue of hidden symmetries. It is shown that for the 2-dimensional Darboux–Koenigs metrics, only type I can result in Eisenhart lifts which satisfy the weak energy condition. However, some physically viable metrics with hidden symmetries are presented.

Alterations and Rearrangements of a Non-autonomous Dynamical System

In this paper, we discuss the dynamics of alterations and rearrangements of a non-autonomous dynamical system generated by the family $${\mathbb {F}}$$ . We prove that while insertion/deletion of a map in the family $${\mathbb {F}}$$ can disturb the dynamics of a system, the dynamics of the system does not change if the map inserted/deleted is feeble open. In the process, we prove that if the inserted/deleted map is feeble open, the altered system exhibits any form of mixing/sensitivity if and only if the original system exhibits the same. We extend our investigations to properties like equicontinuity, minimality, and proximality for the two systems. We prove that any finite rearrangement of a non-autonomous dynamical system preserves the dynamics of original system if the family $${\mathbb {F}}$$ is feeble open. We also give examples to show that the dynamical behavior of a system need be not be preserved under infinite rearrangement.

Global dynamics of the two-dimensional dynamical systems of special type

We study parametic class of two-dimensional discrete dynamical systems, which is a generalization of renormalization group mapping in the hierarchical fermionic model. To analyze global dynamics we develop methods of computer geometry. We reduce original dynamical system to the quadratic projective map and realize two-dimensional projective space as a disk. All fixed points and some invariant sets are described explicitly. With the using of this information we describe the global dynamics of the mapping for selected domains of the parameter space.

Exact analytic solution to nonlinear dynamic system of equations for information propagation in complex networks

We present the exact analytic solution to the nonlinear dynamic system describing the information propagation process in complex networks. The method is to switch to the dynamic system of equations for the new variables defined according to the nonlinear terms appearing in the original dynamic system, and then, after combining relevant consistent condition of solution to reduce the dynamic system of equations for the newly defined variables to the knownly solvable nonlinear Bernoulli differential equation. Numerical comparisons between the purely numerical solution and the exact analytic solution confirm the crosscheck and mutual proof for both of the solutions. The presented exact analytic solution, which does not restrict the coefficients in the original dynamic system to merely constants, is thus suitable for the study of information propagation in networks with evolving structure and changing properties.

Koopman Reduced Order Control for Three Body Problem

In this paper, we use a Circle Restricted Three-Body Problem (CRTBP) to simulate the motion of a satellite. Then we reformulate this problem with the controller into the description using Koopman eigenfunction. Although the original dynamical system is nonlinear, the Koopman eigenfunction behaves linearly. Choosing Jacobi integral as the Koopman eigenfunction and using the zero velocity curve as the reference for control, we are allowed to combine well-developed Linear Quadratic Regulator (LQR) controller to design a nonlinear controller. Using this approach, we design the low thrust orbit transfer strategy for the satellite flying from the earth to the moon or from the earth to the sun.

Estimation of oscillation velocities of oscillator network

The study of the collective behavior of multiscale dynamic processes is currently one of the most urgent problems of nonlinear dynamics. Such systems arise on modelling of many cyclical biological or physical processes. It is of fundamental importance for understanding the basic laws of synchronous dynamics of distributed active subsystems with oscillations, such as neural ensembles, biomechanical models of cardiac or locomotor activity, models of turbulent media, etc. Since the nonlinear oscillations that are observed in such systems have a stable limit cycle , which does not depend on the initial conditions, then a system of interconnected nonlinear oscillators is usually used as a model of multiscale processes. The equations of Lienar type are often used as the main dynamic model of each of these oscillators. In a number of practical control problems of such interconnected oscillators it is necessary to determine the oscillation velocities by known data. This problem is considered as observation problem for nonlinear dynamical system. A new method – a synthesis of invariant relations is used to design a nonlinear observer. The method allows us to represent unknowns as a function of known quantities. The scheme of the construction of invariant relations consists in the expansion of the original dynamical system by equations of some controlled subsystem (integrator). Control in the additional system is used for the synthesis of some relations that are invariant for the extended system and have the attraction property for all of its trajectories. Such relations are considered in observation problems as additional equations for unknown state vector of initial oscillators ensemble. To design the observer, first we introduce a observer for unique oscillator of Lienar type and prove its exponential convergence. This observer is then extended on several coupled Lienar type oscillators. The performance of the proposed method is investigated by numerical simulations.

Rigidity and sensitivity on uniform spaces

In this paper, we introduce the concepts of weak uniformity, uniform rigidity and multi-sensitivity for uniform (not necessarily compact or metric) spaces and obtain some equivalent characterizations of uniform rigidity. In particular, we prove that a dynamical system (X,f) defined on a Hausdorff uniform space is uniformly rigid if and only if (X,fn) is uniformly rigid for some/all n∈N if and only if its hyperspatial dynamical system is uniformly rigid or weakly rigid. Besides, we show that every non-minimal point transitive dynamical system defined on a Hausdorff uniform space with dense Banach almost periodic points is sensitive and obtain the equivalence of the multi-sensitivity between original dynamical system and its hyperspatial dynamical system for Hausdorff uniform spaces.

On the analysis of endogenous growth models with a balanced growth path

This paper is the first that provides a comprehensive toolkit for analyzing deterministic, continuous-time, endogenous growth models with a balanced growth path. Since it is impossible to analyze the original dynamic system of growing variables, I suggest two different methods of transforming the model variables in order to derive a stationary system. The stationary system can then be used to test for the existence and uniqueness of transition paths and to derive transitional dynamics qualitatively (e.g. by phase diagram analysis) and quantitatively (e.g. by numerical simulation). I provide sufficient conditions under which the transformed dynamic system is autonomous, derive the functional form of the transformed system, and provide instructions of how to analyze the stability properties of the transformed system. Furthermore, I show that the class of models for which the method can be applied exhibits a specific pattern of transitional dynamics. Two identical economies that differ only with respect to the endowment of one state variable are shown to grow with the same balanced growth rate in the long-run, but at different levels.

Nonlinear time-optimal trajectory planning for varying-rope-length overhead cranes

PurposeFrom practical perspectives and to improve the working efficiency, trolley transportation and payload hoisting/lowering should be simultaneously controlled. Moreover, in practical crane applications, the transportation time is an important criterion for improving transportation efficiency. Based on these requirements, this paper aims to solve positioning and antiswing control problems and shorten the transportation time for underactuated varying-rope-length overhead cranes.Design/methodology/approachBy choosing trolley acceleration and varying-rope-length acceleration as system inputs, the crane system dynamic model is converted into an equivalent model without linearizing/approximating. Then, based on the converted model and system state constraints, a time-optimal problem is formulated. Further, the original problem is converted into an optimization problem with algebraic constraints which can be conveniently solved. Finally, by solving the optimization problem, the optimal trajectories of system states, including displacements, velocities and accelerations, are obtained.FindingsThis paper first provides a nonlinear time-optimal trajectory planner for varying-rope-length overhead cranes, which achieves accurate and fast trolley positioning and eliminates payload residual swings. Meanwhile, all system states satisfy the given constraints during the entire process. Hardware experimental results show that the proposed time-optimal planner is effective and has better performance compared with existing methods.Originality/valueThis paper proposes a time-optimal trajectory planner for overhead crane systems with hoisting/lowering motion. The proposed planner achieves fast trolley positioning and eliminates payload residual swing with all the system states being constrained within given scopes. The planner is presented based on the original nonlinear system dynamics without linearization/approximation.