Ecological, environmental and economic systems are examples of the dynamic processes upon which IIASA projects concentrate in the field of systems analysis. Several of these relevant problems motivate the objectives of the work of the Dynamic Systems Project. The first consists in studying, at the level of conceptual models, time changes in several classes of economic and biological macrosystems characterized by repeated interactions between elements. The research is based on a game-theoretical approach. Starting with the motives of individual and population behaviors, this approach allows one to understand the driving forces of a system's dynamics and thus, as a perspective, to outline ways to control them. A second objective of the project is to develop identification and forecasting techniques for the dynamic models of environmental processes studied within other IIASA projects. In this research, the methods of the theory of inverse problems will play an important role. Theoretical justification of solution algorithms and their implementation are expected.
In modern systems analysis, problems related to forecasting and controlling environmental and economic systems are of special interest. Dynamic models are required to analyze the time changes characteristic for such problems. Hence, the main aim of the project's research is to understand a system's dynamics, and to provide reliable algorithms for decisionmaking.
Many macrosystems in biology and economics are formed as large groups of somewhat identical individuals (animal communities, firms, etc.). The evolution of such systems is realized through micro-level interactions between individuals, and are thus determined by the behavioral rules used by individuals in elementary actions. One of the recent approaches to studying such processes consists of treating them as appropriate dynamic games. The strong features of this approach are that, first, game models explicitly reflect the conflict in a system's nature, and, second, allow one to analyze them with formal tools of mathematical game theories. The project will focus on developing new techniques for building and treating game-theoretical models for the above macrosystems; implementation of the methods of the theory of differential games will be a specific feature of the research.
Another of the project's research interests is concerned with models of spacially distributed dynamical processes in the environment. Real processes of this kind are usually affected by time-varying inputs which cannot be observed directly. Meanwhile, information on the actual input dynamics is often desirable for reliable decisionmaking. Thus, the problem of input reconstruction, via available observations of system states, arises naturally. This problem, as well as those of forecasting and control for some classes of spacially distributed systems, are planned to be investigated.
The project has two methodological objectives. The first consists of choosing mathematical models adequate to the real-life processes in question, and clarifying the basic properties of the models. In this respect, the focus will primarily be on game-theoretical analysis of bio-economical macrosystems. The relationships between long- and short-term-oriented behavior policies, characterizations of equilibria dynamics at different levels of population hierarchy, correlations between individual and corporative interests, motives for behavior modes will be the main properties considered.
The second objective is to build numerical algorithms for environment-oriented models. The problems of model identification and input reconstruction under incomplete and inaccurate state observations imply strong stability constraints upon the corresponding solution algorithms. Therefore stability analysis will be an essential element of the study. The developed dynamical models and algorithms will be tested on real-life problems treated at IIASA. This part of the work is intended to clarify the positive and negative sides of the proposed methodologies and point out directions for future investigations.
The project's approach to studying models for macrosystems will be based on methods of evolutionary and differential games. The theory of evolutionary games describes typical models for interactions between the members of large biological and economical groups, and provides many examples of large-scale population dynamics. The theory of differential games deals with dynamical systems whose parameters are controlled by different players; within this framework, mathematical techniques for finding equilibric - unimprovable for each player - control laws are developed. Application of the differential game-theoretical approach to game-evolutionary models leads naturally to the notion of an equilibric behavior, at both individual and population levels. In this way, behavior-selection principles making a gaming system fix on an equilibric dynamics - given the pool of all potentially admissible ones - can be looked for. Besides, the approach can result in methods for comparing different levels of centralization in population self-regulation.
The models for spacially distributed dynamical processes will be considered, primarily, in the traditional form of partial differential equations (PDE). Stability analysis of input reconstruction algorithms will principally be based on the approaches of the theory of illposed problems. An inversion methodology from control theory will be implemented, and algorithms for online input reconstruction and evaluation of unknown input characteristics compatible with given observation results will be investigated. Also, non-PDE-based methods for identifying and forecasting systems with uncertainties will be looked for. This research is motivated by the problems of decisionmaking under inaccurate observations, planning environment-compatible pollution regimes, and forecasting short- and long-term changes in environmental systems.
The Workshop on "Dynamics and Control" coorganized with the University of California, Berkeley, and the University of Southern California, USA and the Technical University, Vienna is planned for July 1995. It is intended to give an overview of modern approaches to control, identification and qualitative analysis of dynamical systems, with the emphasis on environmental and economical models.
Research on macrosystem dynamics will start with fixing appropriate - deterministic and stochastic - dynamical models. The models will be treated as control systems guided by several agents; thus a link to the theory of differential games will be established. The next step will be implementation of differential game-theoretical technique for the analysis of the models, and clarifying the structure of equilibric behaviors. Finally, analytic results will be interpreted in terms of initial systems and supplemented by computer illustrations. The research will be coordinated with the project on System Analysis of Technological and Economic Dynamics.
Studies on models for environmental systems will begin by specifying relevant classes of partial differential equations. Different modeling levels - starting from rough and simple - will be tried. At the next step, input reconstruction algorithms will be described and analyzed theoretically; the goal of the analysis is to establish convergence and stability properties of the algorithms, and provide bounds for approximation accuracies. Finally, the algorithms will be implemented as computer programs and tested with real data; in this experiment, directions of further development will be outlined. In a similar pattern, non-PDE-based approaches to modeling and forecasting will be developed; a particular problem will be concerned with dynamic modeling of the soil parameters responsible for the diffusion of cadmium in agricultural zones. The study will be coordinated with the Advanced Computer Applications Project and the project on Material Balance Approaches to Long-Term Environmental Policy Planning.
The expected results should fit the goals specified in the objectives. They will be presented as IIASA Working Papers. Selected, primarily theoretical, results will be submitted to journals. Theoretical statements will be illustrated by appropriate PC programs. Input reconstruction algorithms are expected to be mounted into a prototype decision support system; modeling and forecasting algorithms will be implemented as computer-based tools for model identification and scenario running experiments.
Though broadening the research area is not an explicit project goal in 1995, new areas for applications will constantly be looked for. A real possibility for applications have methods of closed-loop control used for input reconstruction problems; they naturally link the problems of decomposition and parallelization in convex optimization; in this aspect, an application to cooperative optimization procedures under informational constraints seems interesting. These issues will be tried, thus establishing new links to the project on Optimization Under Uncertainty and the project on Risk, Policy and Complexity.
The project's research staff includes Arkadii Kryazhimskii, Karl Sigmund (part-time), and Elena Samarskaia (part-time). Required would be two half-year staff members specializing on forecasting methodology for environmental systems.
Close collaborators include: Jean-Pierre Aubin, Center for Research on Decision Theory, University of Paris-Dauphine, France; Bruce Beck, D.B. Warnell School of Forest Resources, University of Georgia, Athens, USA; Helene Frankowska, Center for Research on Decision Theory, University of Paris-Dauphine, France; Sergio Rinaldi, Department of Electronics, Milano Politechnical Institute, Italy; Gyorgy Sonnevend, Institute of Mathematics, Eotvos University, Budapest, Hungary; Peyton Young, The Brookings Institution and the John Hopkins University, USA; and a research team at the Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ekaterinburg headed by Andrei Subbotin.