Mathematical System Theory: The Influence of R. E. Kalman

ISBN-13: 9783662085486 / Angielski / Miękka / 2014 / 605 str.

Ac Antoulas

Opis

Over the past three decades R.E. Kalman has been one of the most influential personalities in system and control theory. His ideas have been instrumental in a variety of areas. This is a Festschrift honoring his 60th birthday. It contains contributions from leading researchers in the field giving an account of the profound influence of his ideas in a number of areas of active research in system and control theory. For example, since their introduction by Kalman in the early 60's, the concepts of controllability and observability of dynamical systems with inputs, have been the corner stone of the great majority of investigations in the field.

Spis treści

List of Technical Publication of R. E. Kalman.- 1: Axiomatic Framework.- Dynamical Systems, Controllability, and Observability: A Post-Modern Point of View.- 2: Kalman Filtering.- Kalman Filtering: Whence, What and Whither?.- From Kalman Filtering to Innovations, Martingales, Scattering and Other Nice Things.- Kalman Filtering and the Advancement of Navigation and Guidance.- Quantum Kalman Filters.- 3: The LQG Problem.- LQG as a Design Theory.- State-Space H? Control Theory and the LQG Problem.- Unified Continuous and Discrete Time LQG Theory.- 4: The Realization Problem.- Linear Deterministic Realization Theory.- Stochastic Realization Theory.- 5: Linear System Theory: Module Theory.- Algebraic Methods in System Theory.- Module Theory and Linear System Theory.- Models and Modules: Kalman’s Approach to Algebraic System Theory.- Linear Realization Theory, Integer Invariants and Feedback Control.- Linear Systems Over Rings: From R. E. Kalman to the Present.- 5: Linear System Theory: Families of Systems.- Invariant Theory and Families of Dynamical Systems.- 5: Linear System Theory: Related Developments.- On the Parametrization of Input-Output Maps for Stable Linear Systems.- Algebraic System Theory, Computer Algebra and Controller Synthesis.- On the Stability of Linear Discrete System and Related Problems.- 6: Identification and Adaptive Control.- Finite Dimensional Linear Stochastic System Identification.- Identification of Dynamic Systems from Noisy Data: The Case m* = 1.- Adaptive Control.- 7: Generalizations to Nonlinear and Distributed Systems.- Kalman’s Controllability Rank Condition: From Linear to Nonlinear.- Controllability Revisited.- On the Extensions of Kalman’s Canonical Structure Theorem.- Some Remarks on the Control of Distributed Systems.- 8: Influence in Mathematics.- The State Space Method in the Study of Interpolation by Rational Matrix Functions.- The State Space Method for Solving Singular Integral Equations.- 9: Applications.- Algebraic Structure of Convolutional Codes and Algebraic System Theory.- System-Theoretic Trends in Econometrics.- Dynamical Systems That Learn Subspaces.