Dynamic Input-output System Research Articles

A Multi Objective and Dynamic Input Output Optimization Model and Algorithm

This article analyzes the advantages of the multi-objective dynamic input-output optimization model compared to the single objective dynamic input-output optimization model, and demonstrates the reason why the multi-objective model improves the stability of the solution of the dynamic input-output equation system by constructing a goal programming model. Based on the 2021 and 200 input-output table, a multi-objective dynamic input-output optimization model was established for the actual economic and social development of City A. The model includes five objective functions, including economic growth and comprehensive economic balance, and is solved using the goal programming method. The prediction results of the city's main economic indicators, such as GDP, tertiary output added value, and so on from 2021 to 2025, are presented. This result is basically the same as the results obtained using artificial neural network methods, and is more in line with the actual situation of the city.

Analysis and Control of Macroeconomic Trends Based on the Leontief Model

In the present study, we consolidate the forty-five industrial sectors delineated in the U.S. input-output tables, as disseminated by the OECD, into three overarching sectors: advanced manufacturing, modern services, and a residual category termed ’others.’ We adopt gross fixed capital formation as a proxy for the proportion of net profit allocated to investment, positing that the investment requisite for augmenting output is commensurate with the requisite capital intensity. This framework enables us to forecast the trajectory of total output and GDP, taking into account the interplay of multiple determinants. In addressing the inherent linear control dynamics of the input-output model, we apply classical control theory to regulate the advanced manufacturing sector. By deriving control equations that accommodate multifactorial influences, we substantiate the efficacy of this control mechanism through rigorous numerical analysis. Moreover, we reconceptualize the dynamic input-output system as a game-theoretic model characterized by a saddle-point equilibrium. By leveraging the saddle-point equilibrium strategy, we pioneer an innovative approach to resolving the complexities of dynamic input-output analysis. This methodological innovation not only enhances the precision of our predictions but also contributes a novel perspective to the literature on economic modeling and control theory.

Tracking Control of the Dynamic Input-Output Economic System Based on Data Fusion

In recent years, under the background of stable economic operation, people's research on economic systems has become increasingly popular. The dynamic input-output model reflects the change and development process of the input-output relationship of the economic system over a period of time. The main purpose of tracking control is to design a suitable controller so that the output of the control system can track the output of the reference system as much as possible. In the economic system, data is an important factor. Based on this, this paper mainly studies the tracking control of dynamic input-output economic system based on data fusion. This research takes the data fusion of the dynamic input-output economic system as the starting point and takes the optimal control and tracking of the economic system as the research object of this research. Based on data fusion technology, a new dynamic input-output economic system tracking and control is proposed. This paper studies the finite-time optimal tracking control of linear systems. Through numerical examples, comparing the finite-time and infinite-time optimal control simulation results, it is proved that the algorithm can achieve good tracking control. Experimental data shows that the optimal and suboptimal performance indicators for a limited time are 0.7729412 and 1.5687310, respectively. Therefore, compared with the infinite-time optimal control, the performance loss and the final tracking error of the suboptimal control proposed in this study are reduced.

Game Approach for H∞ Robust Control Strategy to Follow the Production in the Singularly Perturbed Bilinear Dynamic Input-Output Systems

For simulating and analyzing the input and output problem of national economy more accurately, this paper considers the fast and slow production processes during the course of social production development, takes stochastic economic risks into consideration, and constructs a H∞ robust control model to follow the production in the singularly perturbed dynamic input-output systems. Further introducing ideas of noncooperative differential game theory, the H∞ robust control model is transformed into a saddle-point equilibrium game model, and a new method for solving dynamic input-output problem by using saddle-point equilibrium strategies is obtained. A numerical result is presented in the end to illustrate the effectiveness of the method.

A New Algorithm for Construction of Quadratic Volterra Model for a Non-Stationary Dynamic System

The research is dedicated to the integro-power Volterra series application in the description of nonlinear dynamic input-output systems. The paper presents a new algorithm for the identification of Volterra polynomial of the second degree for non-stationary dynamic systems which allow an active experiment using test sets of input signals. A horizontal - axis wind turbine is used for a test case study. The quadratic Volterra polynomials are constructed. They describe the nonlinear dynamics of the angular velocity of the wind turbine components depending on the blade lean angle and wind speed. The practical identification of Volterra kernels was carried out with respect to some random stationary state of a modeled system.

The Control of Leontief Model on Industry Manufacturing Process

The classic Leontief model on industry manufacturing process is investigated. A kind of discrete-time singular dynamic input-output model of industry manufacturing process based on the classic Leontief Model is provided and the stability of this kind of model is researched. By the new mathematic method, the singular dynamic input-output system will not be converted into the general linear system. Finally, a sufficient stability condition under which the discrete-time singular Extended Leontief Model is admissible is proved.

A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure

A new unified modelling framework based on the superposition of additive submodels, functional components, and wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented using a multivariate non-linear function, is initially decomposed into a number of functional components via the well-known analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-the-parameters problem, which can be solved using least-squares type methods. An efficient model structure determination approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to represent high-order and high dimensional non-linear systems.

Stability analysis of the dynamic input-output system

The dynamic input-output model is well known in economic theory and practice. In this paper, the asymptotic stability and balanced growth solutions of the dynamic input-output system are considered. Under some natural assumptions which do not require the technical coefficient matrix to be indecomposable, it has been proved that the dynamic input-output system is not asymptotically stable and the closed dynamic input-output model has a balanced growth solution.

THE NOTION OF STABILITY IN OPEN DYNAMICAL SYSTEMS FROM AN ECOLOGICAL PERSPECTIVE

As opposed to closed systems, the state dynamics of open systems are additionally determined by independently acting external forces called "environment" in ecology. Ecosystems are open dynamical systems whose stability characteristics are commonly described in terms of resistance and resilience of system states towards the “disturbing” effects of external forces. The implicit ideas of invariance and attractivity of specific system states, however, are borrowed from the stability theory of closed dynamical systems and are therefore of limited utility for comprehensive representations of stability characteristics in open dynamical systems. Based on a generic formulation of dynamical input-output systems, it is demonstrated that the notion of adaptation of a system's responses (outputs) to its environment (inputs), when quantified by adaptational valuation functions, provides formulations which establish the desired extension of the ideas of stability known from closed systems. In essence, stability can then be viewed as a system's capacity to immediately or ultimately realize adapted responses. This capacity can conveniently be described for example with the aid of adaptational potentials of system states as described by the set of environments to which adaptation is possible. Regulatory and structural adaptation, which are the two forms of adaptation taking place without and with changes in system state, respectively, are shown to imply a natural hierarchy in adaptational processes. It is suggested that the involved levels of hierarchy be viewed to represent a mechanism for preserving adaptability in ecosystems, which in turn constitutes one of the most crucial components of ecosystem stability.

The State of Dynamical Input–Output Systems as an Operator

A causal input–output system operating for all time from the indefinite past to the indefinite future may be described by a function space for inputs, a function space for outputs, and a causal operator mapping the input space into the output space. The state of such a system at any instant is defined here as an operator from the space of possible future inputs to that of future outputs. This operator is called the natural state. The output space is taken to be a time-shift-invariant normed linear function space, and the input space is either also such a space or a time-shift-invariant subset thereof. There is flexibility allowed in the choice of these spaces. Both the input–output operator and the operator giving the natural state are themselves taken to be elements of normed linear spaces with one of a particular family of norms calledN-power norms. The general development applies to nonlinear and time-varying systems. Continuity and boundedness of the natural state (as an operator) and properties of the natural state and its trajectory as related to the input–output description of the system are investigated. Two examples are presented.

Measuring efficiency of dynamic input-output systems

Abstract Recent methods of data envelopment analysis (DEA) deal mostly with static input-output systems. For dynamic systems with both current and capital inputs, the measurement of efficiency poses new problems due to intemporal effects. Some control-theoretic methods are discussed here by way of generalizing the static framework of data envelopment analysis in terms of dynamic multipliers and stochastic parameters. The dual problems of control and state estimation are analysed in their dynamic aspects, which show the myopic nature of measuring efficiency in a static version of the DEA model.

Minimality of dynamic input-output decoupling for nonlinear systems

In this note we study the strong dynamic input-output decoupling problem for nonlinear systems. Using an algebraic theory for nonlinear control systems, we obtain for a dynamic input-output decouplable nonlinear system a compensator of minimal dimension that solves the decoupling problem.

Rolling plans and the turnpike in a dynamic input-output system: A simulation study

The catenary movement of optimal growth paths toward the turnpike is referred to as the turnpike property. Tsukui and others have demonstrated the robustness of this property using various programming versions of the dynamic input-output system. The turnpike property was clearly observed even in relatively short-term simulations. Hori and others have demonstrated theoretically and qualitatively that a rolling plan with a sufficiently long horizon for its subplan also exhibits the turnpike property. This paper investigates quantitatively the robustness of this property. The tentative conclusion is that five years are a reasonable time span for making a rolling plan in the sense of its proximity to a long-term optimal path.

A Study on Model Reference Adaptive I-O System

Conventional economic planning theories deal with a wide variety of approches to achieve an objective. The basic attempts in these thories have been to maximize or minimize an objective function, say, social welfare or profit of a firm or cost of producing a specific commodity, leading to an optimal policy frame work to achieve the goal.Optimal theoritical policy frame work spelt out in the economic theory to achieve an objective more often is not suitable to the practical situation and the ever changing socio-economic environment.In view of the above-stated reasons a different philosophy from that of the common meaning of optimal approaches is adopted.A new approaches is proposed to clarify how the actual economic growth could be converged towards the reference economic path that is designed theoritically. Towards this objective the theory of model reference adaptive system is applied to a dynamic input-output system, and we propose the new method named “Model Reference Adaptive I-O System”.

Asymptotic properties of projections with applications to stochastic regression problems

Almost sure convergence properties of least-squares estimates in stochastic regression models and an asymptotic theory of related Euclidean projections are developed herein. Applications to autoregressive processes and to dynamic input-output systems are also discussed.

Effect of Sectoral Optimization on Structural Stability of a Single-Period Dynamic Input-Output System

Effect of Sectoral Optimization on Structural Stability of a Single-Period Dynamic Input-Output System

Notion of dynamical input-output systems: causality and state concepts

Abstract A basic mathematical formalism of dynamical systems is presented from the view-point of control engineering. The notion of input-output systems is given in a general logistic format in which most of the detailed system models can be embedded. Concepts of time, time system, causality, and state are introduced. The time system is of a generalized form in which the time domains of component functions of input and output may be different from each other. The causality is a term for the traditional non-anticipation. The state is introduced firstly in a pure form. Then a state representation, state mapping, state transition, and a static output system are formalized. The results of discussion and propositions show close interrelations between the causality, state mapping, and static output system.

A Dynamic Interindustry Model for the Economic Analysis of Pollution Abatement

A two-component model is presented for the analysis of the economic impact of pollution abatement. The primary component is a dynamic input-output system in which the structure of the economy is related to the level of environmental control as well as to time. A submodel, which consists of the various abatement activities within each industry, is used to explore the underlying nature of structural changes which take place as a result of changes in environmental regulations. The usefulness of the overall model for policy and planning purposes is illustrated by an example in which the submodel is transformed into a linear-programming format.

An Open Dynamic System for Long Range Projection of Economic Growth

The dynamic input-output system described below is designed for a specific narrowly defined purpose. It should enable a forecaster or a planner to determine and to display in a compact manageable form the limitations imposed on the passible growth path of a particular economic system by given sets of input-output coefficients describing its changing structural properties over the period of time covered by the envisaged projection.

Turnpike Theorem in a Generalized Dynamic Input-Output System

Turnpike Theorem in a Generalized Dynamic Input-Output System