Christopher I. Byrnes - Böcker

The mathematical theory of networks and systems has a long, and rich history, with antecedents in circuit synthesis and the analysis, design and synthesis of actuators, sensors and active elements in both electrical and mechanical systems. Fundamental paradigms such as the state-space real­ ization of an input/output system, or the use of feedback to prescribe the behavior of a closed-loop system have proved to be as resilient to change as were the practitioners who used them. This volume celebrates the resiliency to change of the fundamental con­ cepts underlying the mathematical theory of networks and systems. The articles presented here are among those presented as plenary addresses, invited addresses and minisymposia presented at the 12th International Symposium on the Mathematical Theory of Networks and Systems, held in St. Louis, Missouri from June 24 - 28, 1996. Incorporating models and methods drawn from biology, computing, materials science and math­ ematics, these articles have been written by leading researchers who are on the vanguard of the development of systems, control and estimation for the next century, as evidenced by the application of new methodologies in distributed parameter systems, linear nonlinear systems and stochastic sys­ tems for solving problems in areas such as aircraft design, circuit simulation, imaging, speech synthesis and visionics.

The problem of controlling the output of a system so as to achieve asymptotic tracking of prescribed trajectories and/or asymptotic re­ jection of undesired disturbances is a central problem in control the­ ory. A classical setup in which the problem was posed and success­ fully addressed - in the context of linear, time-invariant and finite dimensional systems - is the one in which the exogenous inputs, namely commands and disturbances, may range over the set of all possible trajectories ofa given autonomous linear system, commonly known as the exogeneous system or, more the exosystem. The case when the exogeneous system is a harmonic oscillator is, of course, classical. Even in this special case, the difference between state and error measurement feedback in the problem ofoutput reg­ ulation is profound. To know the initial condition of the exosystem is to know the amplitude and phase of the corresponding sinusoid. On the other hand, to solve the output regulation problem in this case with only error measurement feedback is to track, or attenu­ ate, a sinusoid ofknown frequency but with unknown amplitude and phase. This is in sharp contrast with alternative approaches, such as exact output tracking, where in lieu of the assumption that a signal is within a class of signals generated by an exogenous system, one instead assumes complete knowledge of the past, present and future time history of the trajectory to be tracked.

The problem of controlling the output of a system so as to achieve asymptotic tracking of prescribed trajectories and/or asymptotic re­ jection of undesired disturbances is a central problem in control the­ ory. A classical setup in which the problem was posed and success­ fully addressed - in the context of linear, time-invariant and finite dimensional systems - is the one in which the exogenous inputs, namely commands and disturbances, may range over the set of all possible trajectories ofa given autonomous linear system, commonly known as the exogeneous system or, more the exosystem. The case when the exogeneous system is a harmonic oscillator is, of course, classical. Even in this special case, the difference between state and error measurement feedback in the problem ofoutput reg­ ulation is profound. To know the initial condition of the exosystem is to know the amplitude and phase of the corresponding sinusoid. On the other hand, to solve the output regulation problem in this case with only error measurement feedback is to track, or attenu­ ate, a sinusoid ofknown frequency but with unknown amplitude and phase. This is in sharp contrast with alternative approaches, such as exact output tracking, where in lieu of the assumption that a signal is within a class of signals generated by an exogenous system, one instead assumes complete knowledge of the past, present and future time history of the trajectory to be tracked.

The mathematical theory of networks and systems has a long, and rich history, with antecedents in circuit synthesis and the analysis, design and synthesis of actuators, sensors and active elements in both electrical and mechanical systems. Fundamental paradigms such as the state-space real­ ization of an input/output system, or the use of feedback to prescribe the behavior of a closed-loop system have proved to be as resilient to change as were the practitioners who used them. This volume celebrates the resiliency to change of the fundamental con­ cepts underlying the mathematical theory of networks and systems. The articles presented here are among those presented as plenary addresses, invited addresses and minisymposia presented at the 12th International Symposium on the Mathematical Theory of Networks and Systems, held in St. Louis, Missouri from June 24 - 28, 1996. Incorporating models and methods drawn from biology, computing, materials science and math­ ematics, these articles have been written by leading researchers who are on the vanguard of the development of systems, control and estimation for the next century, as evidenced by the application of new methodologies in distributed parameter systems, linear nonlinear systems and stochastic sys­ tems for solving problems in areas such as aircraft design, circuit simulation, imaging, speech synthesis and visionics.

This volume provides a compilation of recent contributions on feedback and robust control, modeling, estimation and filtering. They were presented on the occasion of the sixtieth birthday of Anders Lindquist, who has delivered fundamental contributions to the fields of systems, signals and control for more than three decades. His contributions include seminal work on the role of splitting subspaces in stochastic realization theory, on the partial realization problem for both deterministic and stochastic systems, on the solution of the rational covariance extension problem and on system identification. Lindquist's research includes the development of fast filtering algorithms, leading to a nonlinear dynamical system which computes spectral factors in its steady state, and which provide an alternate, linear in the dimension of the state space, to computing the Kalman gain from a matrix Riccati equation. He established the separation principle for stochastic function differential equations, including some fundamental work on optimal control for stochastic systems with time lags.His recent work on a complete parameterization of all rational solutions to the Nevanlinna-Pick problem is providing a new approach to robust control design.