Alexander H. Levis

Petri net representation of decision models

Models of decision-making organizations supported by command, control, and communication systems are represented using the Petri net formalism. A small set of primitives, defining the correspondence between decision models, signals, and functions and their Petri net counterparts, is proposed. A new decision signal-routing demultiplexer is added to the Petri net formalism to represent internal decision-making in the model. Using the above primitives, any decision-making structure can be modeled by a Petri net diagram. An array is introduced that describes the interactions between decision-makers, and an algorithm is presented for the calculation of delay when synchronous protocols are used.

Challenges to control: A collective view--Report of the workshop held at the University of Santa Clara on September 18-19, 1986

During the last seven years, while structural changes have been taking place in the industrial sector of the U.S. and questions of technological leadership and technology transfer have been debated widely, new areas for research have been developing. This led the leadership of the IEEE Control Systems Society to recommend that a workshop be organized to assess the state of the art of the field and outline directions of research. An Organizing Committee, consisting of D. D. Siljak (Chairman), G. F. Franklin, A. H. Levis, and W. R. Perkins, submitted a proposal to the Systems Theory and Operations Research Program of the National Science Foundation to hold such a workshop at the University of Santa Clara, in Santa Clara, CA, on September 18-19, 1986. As part of the proposal effort, a Steering Committee was constituted to assist the organizers in selecting workshop participants and to carry out the preparalory work for the meeting. The twelve-member Steering Committee consisted of the four organizers and eight other individuals: R. W. Brockett, E. J. Davison, Y.-C. Ho, P. Kokotovic, A. J. Laub, S. 1. Marcus, W. F. Powers, and S. S. Sastry. In early 1986, the organizers issued an open call for participation in the workshop that was published in the April issue of the IEEE CONTROL SYSTEMS MAGAZINE. in addition, more than 150 letters were sent to leaders in the field, inviting them to apply for participation in the workshop. The Steering Committee was also asked to identify individuals who could provide unique perspectives. The cut-off date for applications, that included a statement of proposed contribution, was May 31. In June, during the 1986 American Control Conference, the Steering Committee met for many hours to select the participants from the many applicants and to decide on the final structure of the program. One of the decisions was to invite all the Presidential Young Investigator awardees who had applied, another was to limit the total number of participants to fifty. In addition to the Steering Committee, the following persons attended and contributed to the deliberations: K. J. Astrom, M. Athans, D. Auslander, J. S. Baras, T. Basar, G. Blankenship, S. P. Boyd, A. E. Bryson, Jr., J. Burns, J. Cassidy, J. B. Cruz, D. F. Delchamps, C. A. Desoer, R. F. Drenick, T. Edgar, J. S. Freudenberg, D. Gangsaas, J. Grizzle, A. H. Haddad, W. E. Hopkins, Jr., M. Ili-Spong, P. loannou, T. L. Johnson, T. Kailath, A. J. Krener, R. E. Larson, W. S. Levine, J. L. Melsa, J. M. Mendel, G. Meyer, J. B. Pearson, H. E. Rauch, G. N. Saridis, J. L. Speyer, J. N. Tsitsiklis, P. Varaiya, G. C. Verghese, M. Vidyasagar, A. S. Willsky, and M. Wonham. The National Science Foundation was represented by Dr. M. P. Polis, Program Director of the Systems Theory and Operations Research Program, and by Dr. G. Hazelrig, Acting Program Director of the Instrumentation, Sensing, and Measurement Systems Program. The workshop was organized into plenary sessions and breakout sessions, during which Working Groups discussed and wrote the material that forms the basis of this report. Seven keynote talks addressed the main themes of the workshop: accomplishments in the past twenty five years and definition of important current and future research problems drawn from the needs of the industrial and service sectors of the economy. The Working Groups were structured so that, while discussions could take place with few constraints, written materials could be produced by the end of each session. To that effect, each group had one or two persons designated as recorders, with the primary responsibility of keeping notes during the discussion and assisting the group leaders in preparing the Working Group draft reports. In order to provide some focus in the deliberations of the Working Groups,eight persons were asked to prepare position statements based on their own perspectives. Seven of these position papers are being published concurrently in the April 1987 issue of the IEEE CONTROL SYSTEMS MAGAZINE. The eighth one is appearing in this issue of the TRANSACTIONS as a perspectives paper. The findings of the workshop were documented in a final report; the paper that follows is the main body of that report. It was prepared by a group of Editors (A. H. Levis, S. I. Marcus, W. R. Perkins, P. Kokotovic, M. Athans, R. W. Brockett. and A. S. Willsky) on the basis of the contributions, both oral and written, of all the participants, the advocacy papers, and the keynote talks. The draft was reviewed and edited further first by the members of the Steering Committee and then by all the participants. It is indeed a collective effort-A. H. L.

On the generation of organizational architectures using Petri nets

A methodology is presented for generating architectures for decisionmaking organizations that satisfy some generic structural properties, as well as more specific designers requirements. Petri Nets are used as the basic technique to represent organizational architectures. The allowable set of interactions among the organization members is first defined, and a mathematical framework is developed to represent the interactions between organization members. The set of organizational architectures satisfying both the structural and the designers requirements is then analyzed. This set is delimited by its minimal and maximal elements and a technique is given to generate the entire set from its boundaries. Simple paths are used as the incremental unit leading from one organizational form in the set to its neighboring ones. The methodology has been implemented on a personal computer.

Feasibility Sets for Steady-State Loads in Electric Power Networks

Using mathematical programming duality, explicit conditions are found which characterize the set of substation loads that can be served with the available generation resources without overloading the transmission lines or transformers. This feasibility set is a convex polyhedron in the space of substation load vectors, when the distribution of power flow through the network is represented either by the DC load flow or the transportation flow model. The impact on the feasibility set of changes in the generation and transmission system is analyzed. This analysis is then used to construct a probabilistic supply reliability measure.

Brief paper: Modeling and analysis of teams of interacting decisionmakers with bounded rationality

A methodology for analyzing and evaluating alternative organizational structures is presented. An information theoretic framework is used in which each team member is described by a two-stage model consisting of situation assessment and response selection stages as well as interconnections with the rest of the organization. The information processing and decisionmaking load of each team member and the measure of organizational performance are depicted in the performance-workload space as implicit functions of the decision strategies of each individual member. The approach to evaluating organizational structures using the methodology for analysis analysis of an organization consisting of two decisionmakers with bounded rationality.

Human Organizations as Distributed Intelligence Systems

Abstract Human decision making organizations can serve as a paradigm for distributed intelligence systems. Elements of a mathematical theory of organizations are presented and used to analyze the behavior of organizations that have to meet stringent requirements with constraints on the cognitive and physical resources available. It is shown how the introduction of decision support systems to aid individual decisionmakers can affect in unforeseen ways systen performance

Decisionmaking organizations with acyclical information structures

An analytical model of a team of well-trained human decisionmakers executing a well-defined decisionmaking task is presented. Each team member is described by a two-stage model consisting of a situation assessment (SA) and a response selection (RS) stage. An information theoretic framework is used, in which bounded rationality is modelled as a constraint on the total rate of internal processing by each decisionmaker. Optimising and satisfying strategies are derived and their properties analysed in terms of organisational performance and individual workload. The results are applied to the analysis of two three-person organisational designs.

On the design of distributed organizational structures

Abstract The problem of designing human decision-making organizations is formulated as an organizational form problem with special structure. Petri Nets are used to represent the organizational form. An algorithmic procedure, suitable for computer-aided design, is presented and the specific algorithms that it includes are developed. The approach reduces the dimensionality of the problem to a tractable level.

Effectiveness analysis of C 3 systems

A methodology for analyzing and assessing the effectiveness of command, control, and communications (C3) systems is developed. The analysis is carried out by characterizing separately both the system and the mission in terms of attributes. These attributes are determined as functions of primitives that describe the system, the mission to be performed, and their context. The system capabilities and the mission requirements are compared in a common attribute space. This comparison leads to the evaluation of partial measures of effectiveness that are then combined to yield a global measure. The methodology is illustrated through an assessment of the effectiveness of a communications network operating in a hostile environment.

Some computational aspects of the matrix exponential

Matrix norms that satisfy the Schwarz inequality are used to determine upper bounds for the error in some common computations involving the matrix exponential function.