Control theory and economic policy: Balance and perspectives

This paper provides a selective survey of applications of control theory to the analysis of economic policy problems. We discuss applications of closed-loop control and of optimum control theory, including deterministic, stochastic and decentralized optimum control. Promising areas of mutual cooperation between control theorists and economists such as robust control and dynamic game theory are identified. A critical evaluation is given of different control theory approaches to an empirically useful theory of economic policy.     

Optimal investment policy: An example of a control problem in economic theory

A problem in mathematical economics concerning the optimal investment of resources is solved via the techniques of optimal control theory. Interesting theoretical complications include the simultaneous presence of interdependent control variable inequality constraints, state variable inequality constraints, and singularity conditions. Economic implications of the results are briefly discussed.     

周期性系统的能控性理论

主要探讨周期性系统(包括连续和离散两种情形)的能控性问题，对文献中有关周期为To的连续周期性系统的能控性结论进行了完善，推导出系统能控等价于单周期(0，To)内能控的结论，并将这些结论直接推广到离散周期性系统；然后讨论了离散前后周期性系统能控性保持不变的可能性，证明在采用不等间距采样方式时，离散前后周期性系统的能控性保持不变。     

Controllability distributions and systems approximations: ageometric approach

Given a nonlinear system we determine a relation at an equilibrium between controllability distributions defined for a nonlinear system and a Taylor series approximation of it. The value of such a relation is appreciated if we recall that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant (controllability) distributions. The relation between these distributions at the equilibrium will help us to decide when the solvability conditions of this kind of problems are equivalent for the nonlinear system and its approximation     

有界区域上Petrowsky系统的能控性:极小泛函方法

利用极小泛函方法研究Petrowsky系统的控制问题.通过构造下半连续,严格凸的强制的泛函,把能控性问题,近似能控性问题转化为求泛函极小值存在的问题,从而得到了一些能控制性理论的充分必要条件,这些结果是采用了极小泛函方法得到的,改进了利用乘子方法得到的结果.     

Controllability and local accessibility - a normal form approach

Given a system with an uncontrollable linearization at the origin, we study the controllability of the system at equilibria around the origin. If the uncontrollable mode is nonzero, we prove that the system always has other equilibria around the origin. We also prove that these equilibria are linearly controllable provided a coefficient in the normal form is nonzero. Thus, the system is qualitatively changed from being linearly uncontrollable to linearly controllable when the equilibrium point is moved from the origin to a different one. This is called a bifurcation of controllability. As an application of the bifurcation, systems with a positive uncontrollable mode can be stabilized at a nearby equilibrium point. In the last part of this paper, simple sufficient conditions are proved for local accessibility of systems with an uncontrollable mode. Necessary conditions of controllability and local accessibility are also proved for systems with a convergent normal form.     

Product-form and stochastic Petri nets: a structural approach

Stochastic Petri nets (SPNs) with product-form solution are nets for which there is an analytic expression of the steady-state probabilities with respect to place markings, as it is the case for product-form queueing networks with respect to queue lengths. The most general kind of SPNs with product-form solution introduced by Coleman et al. (and denoted here by -nets) suffers a serious drawback: the existence of such a solution depends on the values of the transition rates. Thus since their introduction, it is an open question to characterize -nets with product-form solution for any values of the rates. A partial characterization has been obtained by Henderson et al. However, this characterization does not hold for every initial marking and it is expressed in terms of the reachability graph. In this paper, we obtain a purely structural characterization of -nets for which a product-form solution exists for any value of probabilistic parameters of the SPN and for any initial marking. This structural characterization leads to the definition of -nets (Stochastic Parametric Product-form Petri nets). We also design a polynomial time (with respect to the size of the net structure) algorithm to check whether a SPN is a -net. Then, we study qualitative properties of -nets and -nets, the non-stochastic versions of -nets and -nets: we establish two results on the complexity bounds for the liveness and the reachability problems, which are central problems in Petri nets theory. This set of results complements previous studies on these classes of nets and improves the applicability of product-form solutions for SPNs.     

Modal control theory and industrial dynamics — a dual approach to the design of policy decisions in a multistage production-inventory system

This paper deals with the problem of designing realistic policy decisions in a Multistage Production-Inventory System (MPIS). First Modal Control Theory has been utilised for the synthesis of control policies in a two-stage production-inventory system. The structure of the resultant control policies, though somewhat idealised, has an underlying implication of central control. Two types of realistic policy decisions are made and tested in Forresters's ID simulation study of the MPIS. It is shown that both the policies result in more attenuated system behaviour than that obtained by Forrester.     

HyperTree: a structural approach to web authoring

The expansion of the World Wide Web (WWW) has created an increasing need for tools capable of supporting WWW authors in composing documents using the HyperText Markup Language (HTML). Currently, most web authors use tools which are basically ordinary text editors and have additional features to facilitate the easy and correct use of HTML tags. This approach places the burden on the web author to design and then create the entire web site in a top-down fashion, without any explicit support for the structural design of the site. In this paper we discuss an alternative structural approach to Web authoring, which is based on the use of the HyperTree hypermedia system as the central authoring tool. The advantages of using HyperTree are two-dimensional. Firstly, web authors can manage a web site as a single complete hypermedia database. For example, HyperTree provides facilities like the automatic creation of indices and the discovery of link inconsistencies. Additionally, it organizes the web pages in an easy to understand hierarchy without using any HTML directly. Secondly, web end-users can benefit from the use of HyperTree, since seeking information in structured web sites is generally less disorientating and develops fewer cognitive overheads. ©1997 John Wiley & Sons, Ltd.     

Asian monetary integration: a structural VAR approach

This paper examines whether forming an optimum currency area (OCA) is viable for the East Asian region by testing the symmetry of underlying structural shocks. A structural vector autoregression (VAR) method is used to identify the underlying shocks and to examine the correlation in shocks for specified sample periods. Decomposition of the variance of shocks and impulse response analysis are used to examine the size and the speed of adjustments to shocks. The results imply that some sub-regions are potential candidates for forming OCAs, as their shocks are correlated and small, and the economies adjust rapidly to such shocks.     

A response surface approach for structural reliability analysis using evidence theory

Evidence theory employs a much more general and flexible framework to quantify the epistemic uncertainty, and thereby it is adopted to conduct reliability analysis for engineering structures recently. However, the large computational cost caused by its discrete property significantly influences the practicability of evidence theory. This paper proposes an efficient response surface (RS) method to evaluate the reliability for structures using evidence theory, and hence improves its applicability in engineering problems. A new design of experiments technique is developed, whose key issue is the search of the important control points. These points are the intersections of the limit-state surface and the uncertainty domain, thus they have a significant contribution to the accuracy of the subsequent established RS. Based on them, a high precise radial basis functions RS to the actual limit-state surface is established. With the RS, the reliability interval can be efficiently computed for the structure. Four numerical examples are investigated to demonstrate the effectiveness of the proposed method.     

Lax-Phillips scattering theory and well-posed linear systems: a coordinate-free approach

We give a further elaboration of the fundamental connections between Lax-Phillips scattering, conservative input/state/output linear systems and Sz.-Nagy-Foias model theory for both the discrete- and continuous-time settings. In particular, for the continuous-time setting, we show how to locate a scattering-conservative L ²-well-posed linear system (in the sense of Staffans and Weiss) embedded in a Lax-Phillips scattering system presented in axiomatic form; conversely, given a scattering-conservative linear system, we show how one can view the space of finite-energy input-state-output trajectories of the system as the ambient space for an associated Lax-Phillips scattering system. We use these connections to give a simple, conceptual proof of the identity of the scattering function of the scattering system with the transfer function of the input-state-output linear system. As an application we show how system-theoretic ideas can be used to arrive at the spectral analysis of the scattering function.     

An energetic and economic simulation for the evaluation of transportation policy

The role of transportation in a regional economy is explored with a simulation model under various levels of energy availability and highway funding. Several policy options are investigated. Increased highway funding did not induce additional urban growth once energy started to be limiting in the whole system. Under these energy-limiting conditions, increases in the proportion of energy alloted to transportation also failed to induce urban growth. Decreases in energy flow to the highway sector helped conserve the fuels. Reduction in gasoline consumption without a tax surcharge did not conserve total fuel use, while reduction with a tax surcharge did help conserve fuels.     

On the theory of economic MPC: ELOC and approximate infinite horizon EMPC

In recent years, the notion of Economic Model Predictive Control (EMPC) has gained significant interest. Despite a marked improvement in economic performance, it has been shown that this performance will degrade substantially if implemented with a horizon that is not sufficiently large. In the current effort, it is shown that if applied to a particular reaction process, EMPC performance will abruptly collapse at a critical horizon size. To alleviate this issue, we develop an Infinite Horizon EMPC (IH-EMPC) formulation. While this IH-EMPC problem is computationally intractable, it does lead to an approximation of the optimal policy. The resulting Approximate IH-EMPC (AIH-EMPC) is identical to the original finite horizon EMPC, but includes a final cost term that represents the objective function from the finite horizon to infinity. With two example systems, a chemical reactor and a power system with energy storage, it is shown that the AIH-EMPC policy is virtually insensitive to its computational horizon size.     

Large-scale regional economic development: Macroergonomics in theory and practice

Ergonomics has traditionally focused on improving such indices as productivity, health and safety, and quality of work life. Such improvements are necessary to individuals and organizations, but may not be sufficient, as emphasized by the recent focus on community ergonomics and other “macrosystem” concerns. Ergonomists have begun to apply their technologies to go beyond traditional measures to impact regional economic development. A model for ergonomics in regional economic development was developed from a successful 10-year intervention in New York State. After presenting this model in terms of organizational design and core processes, two industrial cases are summarized to help validate the approach. Two large plants and industrial employers were threatened with closure. Macroergonomic assessment, research, and intervention led to significant job retention, facilities expansion, and job creation. Within 5 years, the approach was credited with several turnarounds, retaining and expanding thousands of jobs and transforming the regional economy. © 1999 John Wiley & Sons, Inc.     

The economic impact of a transportation bottleneck: an integrated input-output and linear programming approach

A transport-constrained input-output and linear programming (IO/LP) model is proposed for the purpose of studying the impact of a transportation bottleneck in an economy. This removes the implicit assumption of no capacity constraints that characterizes the traditional demand-driven input-output model. Data for Taiwan are used for empirical experiments, and results from these experiments indicate the kinds of policy implications that might be drawn.     

GAMS: A stylistic approach to economic modelling

GAMS (General Algebraic Modelling System) is a software package which will make numerical optimization a much simpler endeavor for specialists from a wide range of disciplines. The need for writing personal fortran codes for optimizers and unfriendly fixed-formatfortran type input files is no longer necessary. This review gives an overall view of GAMS' capabilities and uses in the field of numerical optimization.     

Optimal maintenance policy for equipment subject to random deterioration and random failure A modern control theory approach

The stochastic version of Pontryagin's maximum principle is applied to determine an optimal maintenance policy of equipment subject to random deterioration. The deterioration of the equipment with age is modelled as a random process. Next the model is generalized to include random catastrophic failure of the equipment. The optimal maintenance policy is derived for two special probability distributions of time to failure of the equipment, namely, exponential and Weibull distributions Both the salvage value and deterioration rate of the equipment are treated as state variables and the maintenance as a control variable. The result is illustrated by an example.