Studies on the Convergence of Information Theory and Control Theory

摘要

In this chapter being presented the information-theoretic explanation of Bod6 Sensitivity Integral - a fundamental limitation of control theory, controllability grammian, Fisher Information and the issues of control under communication constraints. As resource-economic use of information is of prime concern in communication-constrained control problems, we need to emphasize more on informational aspect which has got direct relation with uncertainties in terms of Shannon Entropy and Mutual Information. Bode Integral which is directly related to the disturbances can be correlated with the difference of entropies between the disturbance-input and measurable output of the system. These disturbances due to communication channel-induced noises and limited bandwidth are causing the information packet-loss and delays resulting in degradation of control performances.rnControllability Gramian is a measure of control performance and Fisher Information is a measure of accuracy of estimation (which needs to be done in uncertainties caused by packet-loss and delays of the network). Hence, in order to have better controllability, we need to explore the relation between the estimation theoretic (because information losses and delays force us to resort to estimation) parameter like Fisher Information Matrix (FIM) / information theoretic parameters and the control theoretic parameters of practical importance.