Closed-loop analysis and feedback design in the presence of limited information

Control Theory;Information Theory;Robust Control;Sensitivity Function;Stochastic Control

Li, Dapeng

关键词: Control Theory;    Information Theory;    Robust Control;    Sensitivity Function;    Stochastic Control;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/24370/Dapeng_Li.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Recent progress in communication technologies and their use in feedback control systems motivate to look deeper into the interplay of control and communication in the closed-loop feedback architecture. Among several research directions on this topic, a great deal of attention has been given to the fundamental limitations in the presence communication constraints. Entropy rate inequalities corresponding to the information flux in a typical causal closed loop have been derived towards obtaining a Bode-like integral formula.This work extends the discrete-time result to continuous-time systems. The main challenge in this extension is that Kolmogorov's entropy rate equality, which is fundamental to the derivation of the result in discrete-time case, does not hold for continuous-time systems. Mutual information rate instead of entropy rate is used to represent the information flow in the closed-loop, and a limiting relationship due to Pinsker towards obtaining the mutual information rate between two continuous time processes from their discretized sequence is used to derive the Bode-like formula. The results are further extended to switched systems and a Bode integral formula is obtained under the assumption that the switching sequence is an ergodic Markov chain. To enable simplified calculation of the resulting lower bound, some Lie algebraic conditions are developed.Besidesanalysis results, this dissertation also includes joint control/communication design for closed-loop stability of performance. We consider the stabilization problem within Linear Quadratic Regulator framework, where a control gain is chosen to minimize a linear quadratic cost functional while subject to the inputpower constraint imposed by an additive Gaussian channel which closes the loop. Also focused on Gaussian channel, the channel noise attenuation problem is addressed, by using H-infinity/H2 methodology. Similar feedback optimal estimation problemis solvedby using Kalman filtering theory.