Control and adaptation in telecommunication systems. Mathematical foundations (Q545922)

Some properties of models for complex controlled systems are discussed, as well as their classification, the peculiarities of situational and automatic control methods, the rules of system policy, and the task functions of controlled systems. Mathematical models and control principles used in telecommunication systems are described. Particularly, static and dynamic, deterministic and stochastic models of controlled systems and decision-making techniques of control modes are discussed. The methods of state variables are used to construct these models. Some optimality criteria are discussed, such as the compatibility criterion, principles of guaranteed quality, or the preference criterion. Both, algorithms of optimal control and main principles of control systems construction are considered. The principles are based on methods of Ponselle and Watt. A decomposition theorem is formulated. Methods to investigate controllability are considered. Further properties of control are discussed, such as observability, identifiability, stability and invariance. Also methods for synthesis of algorithms of recursive estimations, such as the methods of Kalman-Bucy or Robbins-Monro are considered. The peculiarities of recursive calculations of estimations are analyzed. The sensibility of Kalman-Bucy filter to deviations of chosen model from the real situation is investigated and the synthesis of state control algorithms and observation control algorithms is discussed. Instruction-based control system and control system without teacher are considered. Some examples of practical implementations of these approaches in the existed telecommunications systems are given. The following classes of taught systems are analyzed: systems with identification of the model and self-organized and self-repairing systems with re-engineering. Entropic, homeostatic and morphogenetic solutions are discussed. Neural networks and their applications in the control tasks are studied. Few examples are given for practical solutions, such as the traveling salesman problem and the Boltzmann machine. The theory and methods of multifunctional control automata are also an subject of this book. Moreover, methods of Petri nets and E-nets are discussed. The methods are useful for simulation, analysis and development of telecommunication networks.