We solve an optimal control problem for thermodynamic processes in an ideal gas. The thermodynamic state is given by a Legendrian manifold in a contact space. Pontryagin’s maximum principle is used to find an optimal trajectory (thermodynamic process) on this manifold that maximizes the work of the gas. In the case of ideal gases, it is shown that the corresponding Hamiltonian system is completely integrable and its quadrature-based solution is given.

The notion of a local infimum for the optimal control problem, which generalizes the notion of an optimal trajectory, is introduced. For a local infimum the existence theorem is proved and necessary conditions in the form of a family of ‘maximum principles’ are derived. The meaningfulness of the necessary conditions, which generalize and strengthen Pontryagin’s maximum principle, is illustrated by examples.

Design of object-oriented databases for automatic information control systems is studied. A formal method of analysis and design of optimal structures for object-oriented databases is developed on the basis of sequential interconnected formalizations of user problem domains, clustering of user information and functional requirements, design and analysis of object models for user requirements and object canonical structure of databases and design of optimal logical structures for object-oriented databases. Methods of analysis of problem domains of database users and construction of effective object canonical database structures in the form of classes, objects, and their relations and satisfying principles of abstraction, encapsulation, modularity, and hierarchy are described.

The paper aims to synthesize by Quantitative Feedback Theory (QFT) a robust controller represented as a transfer function containing two left zeros and two left poles to stabilize a model of a plasma unstable vertical position in the T-15MD tokamak (Kurchatov Institute, Moscow, Russia). Due to the relatively large overshoot and oscillations of a transient response, the two-cascade robust control system of the plasma position with PID controllers was designed by the QFT. An inner cascade controls a current in a horizontal field coil and an outer cascade stabilizes the plasma vertical position. An actuator is a model of a 6-pulse multiphase thyristor rectifier.