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The final report for the project, Mathematical Software for Linear Control and Estimation Theory, includes a list of publications, conference proceedings, and invited talks by the principal investigators. Emphasis throughout the project was placed on interdisciplinary work in control theory, numerical methods suitable for certain control problems and mathematical software to do the frequency response problem. Numerically stable methods were used, and portability of the mathematical software was stressed. (Author)

This report summarizes a scientific meeting/conference which was supported in part by a grant from the Army Research Office. The conference was held in Cambridge, MA on October 23, 24, 1998. The occasion marked the sixtieth birthday of Roger W. Brockett, and more than one hundred leading control theorists traveled to Boston to attend two days of lectures and a formal banquet. No formal conference record was published, but a volume of technical articles discussing current research related to Brockett's work was published. The book entitled Mathematical Control Theory is available from Springer-Verlag as indicated in the report.

This report summarizes a scientific meeting/conference which was supported in part by a grant from the Army Research Office. The conference was held in Cambridge, MA on October 23, 24, 1998. The occasion marked the sixtieth birthday of Roger W. Brockett, and more than one hundred leading control theorists traveled to Boston to attend two days of lectures and a formal banquet. No formal conference record was published, but a volume of technical articles discussing current research related to Brockett's work was published. The book entitled Mathematical Control Theory is available from Springer-Verlag as indicated in the report.

This report summarizes a scientific meeting/conference which was supported in part by a grant from the Army Research Office. The conference was held in Cambridge, MA on October 23, 24, 1998. The occasion marked the sixtieth birthday of Roger W. Brockett, and more than one hundred leading control theorists traveled to Boston to attend two days of lectures and a formal banquet. No formal conference record was published, but a volume of technical articles discussing current research related to Brockett's work was published. The book entitled Mathematical Control Theory is available from Springer-Verlag as indicated in the report.

Let K be a closed convex set in E superscript (m + 1) and L = (P = (P sub 0, ..., P sub m): P sub 1 = P sub 2 = ...P sub m = 0). Then for the simple problem: Minimize P sub 0 Subject to P = (P sub 0, P sub 1, ..., P sub m) epsilon the intersection of K and L, we prove a duality theorem and the convergence of a solution algorithm modeled on the duality theorem and the simplex method of linear programming respectively. Specialization of this general model to linear programming, convex programming, generalized programming, control theory, and the decomposition approach to mathematical programming yield the appropriate duality theorems and solution algorithms in each case.

A brief introduction to continuous mathematical control theory is presented. A model having two state variable accounts, cash and wheat, is defined by means of differential equations. Adjoint functions, the Hamiltonian function, and the optimum (bang-bang) policy are derived. Interpretations of the Hamiltonian and switching functions and a numerical example are given. The results are extended to the case where transaction costs and spoilage costs are incurred.

The elements of a mathematical theory for the analysis and design of organizations are presented. The focus of the research has been on information processing and decisionmakers organizations supported by Command Control and Communications(C3) systems. The mathematical framework used in modeling the individual decisonmakers, as well as the organization, is that of n-dimensional information theory. Petri Net representation of the organizational structure is used to model the interactions between organization members as well as their interactions with the C3 system. Comparison and evaluation of alternative organizational forms is accomplished by considering organizational performance, individual workload and the sets of satisfing decision strategies. A brief description of research on distributed estimation and on information storage and flow in C3 systems is also included.

A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included.

A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included.

A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included.

A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included.

Research under the following general headings was concluded: (1) Eigenvalue inequalities (Marcus, Thompson); (2) Numerical range calculations (Marcus); (3) Exact solutions of integral systems of linear equations (Newman); (4) Experiments on the ILLIAC IV, Sunnyvale, CA (Newman); (5) The Campbell Baker Hausdorff formula (Thompson); (6) Rearrangement inequalities and determinant bounds (Minc); (7) Non-linear control in 3 x 3 linear systems (Leipnik).

This report presents, in unclassified form, the mathematical theory of aircraft fire control as developed in the present state of the art. It is intended that this book will serve as a basic text for use by schools or individuals desiring background theory in the field of aircraft fire control.

Research concentrated on designing and implementing a microprocessor based concurrent computing environment consisting of a number of Intel microprocessors with IEEE floating point arithmetic implemented in hardware. The major focus of our work was the design of a concurrent tasker in software to locate code can data, monitor computation and communication and report results to the user. The construction of viable numerical algebra modules in an IEEE floating point arithmetic was and continues to be part of the research. (Author)

A bibliography is presented of publications and reports resulting from the research project.

A geometric setup for control theory is presented. The argument is developed through the study of the extremals of action functionals defined on piecewise differentiable curves, in the presence of differentiable non-holonomic constraints. Special emphasis is put on the tensorial aspects of the theory. To start with, the kinematical foundations, culminating in the so called variational equation, are put on geometrical grounds, via the introduction of the concept of infinitesimal control . On the same basis, the usual classification of the extremals of a variational problem into normal and abnormal ones is also rationalized, showing the existence of a purely kinematical algorithm assigning to each admissible curve a corresponding abnormality index, defined in terms of a suitable linear map. The whole machinery is then applied to constrained variational calculus. The argument provides an interesting revisitation of Pontryagin maximum principle and of the Erdmann-Weierstrass corner conditions, as well as a proof of the classical Lagrange multipliers method and a local interpretation of Pontryagin's equations as dynamical equations for a free (singular) Hamiltonian system. As a final, highly non-trivial topic, a sufficient condition for the existence of finite deformations with fixed endpoints is explicitly stated and proved.

A geometric setup for control theory is presented. The argument is developed through the study of the extremals of action functionals defined on piecewise differentiable curves, in the presence of differentiable non-holonomic constraints. Special emphasis is put on the tensorial aspects of the theory. To start with, the kinematical foundations, culminating in the so called variational equation, are put on geometrical grounds, via the introduction of the concept of infinitesimal control . On the same basis, the usual classification of the extremals of a variational problem into normal and abnormal ones is also rationalized, showing the existence of a purely kinematical algorithm assigning to each admissible curve a corresponding abnormality index, defined in terms of a suitable linear map. The whole machinery is then applied to constrained variational calculus. The argument provides an interesting revisitation of Pontryagin maximum principle and of the Erdmann-Weierstrass corner conditions, as well as a proof of the classical Lagrange multipliers method and a local interpretation of Pontryagin's equations as dynamical equations for a free (singular) Hamiltonian system. As a final, highly non-trivial topic, a sufficient condition for the existence of finite deformations with fixed endpoints is explicitly stated and proved.

Simple ideas, endowed from the mathematical theory of control, are used in order to analyze in general grounds the human immune system. The general principles are minimization of the pathogen load and economy of resources. They should constrain the parameters describing the immune system. In the simplest linear model, for example, where the response is proportional to the load, the annihilation rate of pathogens in any tissue should be greater than the pathogen's average rate of growth. When nonlinearities are added, a reference value for the number of pathogens is set, and a stability condition emerges, which relates strength of regular threats, barrier height and annihilation rate. The stability condition allows a qualitative comparison between tissues. On the other hand, in cancer immunity, the linear model leads to an expression for the lifetime risk, which accounts for both the effects of carcinogens (endogenous or external) and the immune response.

Simple ideas, endowed from the mathematical theory of control, are used in order to analyze in general grounds the human immune system. The general principles are minimization of the pathogen load and economy of resources. They should constrain the parameters describing the immune system. In the simplest linear model, for example, where the response is proportional to the load, the annihilation rate of pathogens in any tissue should be greater than the pathogen's average rate of growth. When nonlinearities are added, a reference value for the number of pathogens is set, and a stability condition emerges, which relates strength of regular threats, barrier height and annihilation rate. The stability condition allows a qualitative comparison between tissues. On the other hand, in cancer immunity, the linear model leads to an expression for the lifetime risk, which accounts for both the effects of carcinogens (endogenous or external) and the immune response.

Contents: Introduction; Controllability, bang-bang principle; Linear time-optimal control; The Pontryagin Maximum Principle; Dynamic programming; Game theory; Introduction to stochastic control theory; Proofs of the Pontryagin Maximum Principle. Lecture Notes Collection FreeScience.info ID937 Obtained from http://math.berkeley.edu/~evans/control.course.pdf http://www.freescience.info/go.php?pagename=books&id=937

Contents: Introduction; Controllability, bang-bang principle; Linear time-optimal control; The Pontryagin Maximum Principle; Dynamic programming; Game theory; Introduction to stochastic control theory; Proofs of the Pontryagin Maximum Principle. Lecture Notes Collection FreeScience.info ID937 Obtained from http://math.berkeley.edu/~evans/control.course.pdf http://www.freescience.info/go.php?pagename=books&id=937

Contents: Introduction; Controllability, bang-bang principle; Linear time-optimal control; The Pontryagin Maximum Principle; Dynamic programming; Game theory; Introduction to stochastic control theory; Proofs of the Pontryagin Maximum Principle. Lecture Notes Collection FreeScience.info ID937 Obtained from http://math.berkeley.edu/~evans/control.course.pdf http://www.freescience.info/go.php?pagename=books&id=937

Contents: Introduction; Controllability, bang-bang principle; Linear time-optimal control; The Pontryagin Maximum Principle; Dynamic programming; Game theory; Introduction to stochastic control theory; Proofs of the Pontryagin Maximum Principle. Lecture Notes Collection FreeScience.info ID937 Obtained from http://math.berkeley.edu/~evans/control.course.pdf http://www.freescience.info/go.php?pagename=books&id=937

Contents: Introduction; Controllability, bang-bang principle; Linear time-optimal control; The Pontryagin Maximum Principle; Dynamic programming; Game theory; Introduction to stochastic control theory; Proofs of the Pontryagin Maximum Principle. Lecture Notes Collection FreeScience.info ID937 Obtained from http://math.berkeley.edu/~evans/control.course.pdf http://www.freescience.info/go.php?pagename=books&id=937

Contents: Introduction; Controllability, bang-bang principle; Linear time-optimal control; The Pontryagin Maximum Principle; Dynamic programming; Game theory; Introduction to stochastic control theory; Proofs of the Pontryagin Maximum Principle. Lecture Notes Collection FreeScience.info ID937 Obtained from http://math.berkeley.edu/~evans/control.course.pdf http://www.freescience.info/go.php?pagename=books&id=937

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