Items related to Minimum Entropy Control for Time-Varying Systems
Synopsis
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.
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