On Energy-Information Balance in Automatic Control Systems Revisited

Area of Science:

• Control Systems Engineering
• Information Theory
• Optimization Theory

Background:

• The informational approach was a significant optimization method for automatic control systems from 1970-1990.
• Variational problems and information quantity functionals are key in analyzing complex systems.
• Degenerated functionals and minimax relations require advanced mathematical treatment.

Purpose of the Study:

• To revise and generalize variational problems within the informational approach for automatic control.
• To find extremals for degenerated functionals and interpret resulting minimax relations.
• To analyze balance relations in linear stationary systems and connect them to Legendre duality.

Main Methods:

• Generalization of variational problems.
• Analysis of degenerated (derivative-independent) functionals.
• Application of the Gelfand-Pinsker-Yaglom formula for information quantity.
• Investigation of linear stationary one-dimensional systems with Gaussian signals.
• Interpretation using Legendre duality.

Main Results:

• New extremals for degenerated functionals were identified.
• Minimax relations were interpreted in the context of information theory.
• Balance relations in specific linear systems were derived.
• Connections between information quantity and Legendre duality were established.

Conclusions:

• The study provides updated theoretical frameworks for informational optimization in control systems.
• The findings offer novel interpretations of minimax relations and information measures.
• The research highlights the utility of Legendre duality in analyzing information-theoretic properties of control systems.