Directions in Mathematical Systems Theory and Optimization

For more than three decades, Anders Lindquist has delivered fundamental cont- butions to the ?elds of systems, signals and control. Throughout this period, four themes can perhaps characterize his interests: Modeling, estimation and ?ltering, feedback and robust control. His contributions to modeling 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 identi?cation. His contributions to ?ltering and estimation include the development of fast ?ltering 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. His further research on the phase portrait of this dynamical system gave a better understanding of when the Kalman ?lter will converge, answering an open question raised by Kalman. While still a student he established the separation principle for stochastic function differential equations, including some fundamental work on optimal control for stochastic systems with time lags. He continued his interest in feedback control by deriving optimal and robust control feedback laws for suppressing the effects of harmonic disturbances. Moreover, 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.

Includes supplementary material: sn.pub/extras

Texte du rabat
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.

Contenu
Systems with Lebesgue Sampling.- Acoustic Attenuation Employing Variable Wall Admittance.- Some Remarks on Linear Filtering Theory for Infinite Dimensional Systems.- A Note on Stochastic Dissipativeness.- Internal Model Based Design for the Suppression of Harmonic Disturbances.- Conditional Orthogonality and Conditional Stochastic Realization.- Geometry of Oblique Splitting Subspaces, Minimality and Hankel Operators.- Linear Fractional Transformations.- Structured Covariances and Related Approximation Questions.- Risk Sensitive Identification of ARMA Processes.- Input Tracking and Output Fusion for Linear Systems.- The Convergence of the Extended Kalman Filter.- On the Separation of Two Degree of Freedom Controller and Its Application to H ? Control for Systems with Time Delay.- The Principle of Optimality in Measurement Feedback Control for Linear Systems.- Linear System Identification as Curve Fitting.- Optimal Model Order Reduction for Maximal Real Part Norms.- Quantum Schrödinger Bridges.- Segmentation of Diffusion Tensor Imagery.- Robust Linear Algebra and Robust Aperiodicity.- On Homogeneous Density Functions.- Stabilization by Collocated Feedback.- High-Order Open Mapping Theorems.- New Integrability Conditions for Classifying Holonomic and Nonholonomic Systems.- On Spectral Analysis Using Models with Pre-specified Zeros.- Balanced State Representations with Polynomial Algebra.- Nonconvex Global Optimization Problems: Constrained Infinite-Horizon Linear-Quadratic Control Problems for Discrete Systems.