Minimum Entropy Control for Time-Varying Systems

ISBN-13: 9781461273660 / Angielski / Miękka / 2012 / 189 str.

Marc A. Peters; Pablo Iglesias; Marc A. Peters

Opis

This book takes the topic of H-infinity control as a point of departure, and pursues an improved controller design suggested in the mainstream of robust control. Using stochastic methods, the book is important to the circuits and systems community, alongside researchers in networking systems, operator theory and linear multivariable control.

Spis treści

1 Introduction.- 1.1 Optimal control problems.- 1.2 Minimum entropy control.- 1.3 The maximum entropy principle.- 1.4 Extensions to time-varying systems.- 1.5 Organization of the book.- 2 Preliminaries.- 2.1 Discrete-time time-varying systems.- 2.2 State-space realizations.- 2.3 Time-reverse systems.- 3 Induced Operator Norms.- 3.1 Characterizations of the induced norm.- 3.2 Time-varying hybrid systems.- 3.2.1 Sampled continuous-time systems.- 3.2.2 Continuous-time systems with piecewise constant inputs.- 3.2.3 Hybrid feedback systems.- 3.3 Computational issues.- 4 Discrete-Time Entropy.- 4.1 Entropy of a discrete-time time-varying system.- 4.2 Properties.- 4.2.1 Equivalence with the entropy integral.- 4.2.2 Entropy in terms of a state-space realization.- 4.3 Entropy and information theory.- 4.4 Entropy of an anti-causal system.- 4.5 Entropy and the W-transform.- 4.6 Entropy of a non-linear system.- 5 Connections With Related Optimal Control Problems.- 5.1 Relationship with H?control.- 5.2 Relationship with H2 control.- 5.3 Average cost functions.- 5.3.1 Average H2 cost.- 5.3.2 Average entropy.- 5.4 Time-varying risk-sensitive control.- 5.5 Problems defined on a finite horizon.- 6 Minimum Entropy Control.- 6.1 Problem statement.- 6.2 Basic results.- 6.3 Full information.- 6.3.1 Characterizing all closed-loop systems.- 6.3.2 FI minimum entropy controller.- 6.4 Full control.- 6.5 Disturbance feedforward.- 6.5.1 Characterizing all closed-loop systems.- 6.5.2 DF minimum entropy controller.- 6.6 Output estimation.- 6.7 Output feedback.- 6.8 Stability concepts.- 7 Continuous-Time Entropy.- 7.1 Classes of systems considered.- 7.2 Entropy of a continuous-time time-varying system.- 7.3 Properties.- 7.3.1 Equivalence with the entropy integral.- 7.3.2 Entropy in terms of a state-space realization.- 7.3.3 Relationship with discrete-time entropy.- 7.4 Connections with related optimal control problems.- 7.4.1 Relationship with H? control.- 7.4.2 Relationship with H2 control.- 7.4.3 Relationship with risk-sensitive control.- 7.5 Minimum entropy control.- A Proof of Theorem 6.5.- B Proof of Theorem 7.21.- Notation.