Profile
Optimal Control Methods for Irreversible Thermodynamic Systems and Estimations of Extreme Performance of these Systems:
- Extreme performance of heat engines and refrigerators with pregiven power input/output.
- Optimal direct and reverse transformation of heat to work in a thermodynamic system of general form.
- Extreme performance of separation processes using either mechanical or heat energy with pregiven productivity of these processes.
Particularly, processes of rectification, absorption are considered.
- Maintaining of the pregiven field of potentials (e.g. temperatures, concentrations, pressures) with the minimal energy
expenditures.
Optimal Processes in Irreversible Microeconomics:
- Accounting of irreversibility factor during investigation of economic processes; existance of wealth function and its
characteristics.
- Extreme performance of firms in time constrained economic processes.
- Extremal principle determining a stationary condition of an open economic system.
Optimal Control of Temperature Fields and Energy Saving Problems (Cooling in Supercomputers, Energy Saving in House-Building):
- Conditions of optimal thermostatting and optimal design of heat exchange systems.
- Software for multicoating walling calculation considering heat and moisture transfer between layers and existance of air spaces.
- Current systems of cooling for computers of high power shortcomings are analysed and the structure of proper system of cooling is
outlined.
Problem on Equivalence of Differential Equations:
- Local classification of linear ordinary differential equations is obtained up to replacement of variables.
- A differential invariant is found which is respondent for possibility to reduce a nonlinear ordinary differential equation of the
second order to linear form by replacement of variables.
Geometrical Conditions of Solvability of Convolution Equations:
- A criterion for solvability of convolution equations with an arbitrary second member.
- Interrelations between different definitions of complexity to given direction of a plane set.
Areas of interests
- Optimal control methods for conditional problems with restrictions of different types.
- Averaged problems of optimal control (problems including averaged values of variables or functions of variables).
- Limiting possibilities of processes in macrosystems with restricted duration or averaged intensities of fluxes.
- Differential invariants and problems of equivalence of differential equations.
Main results
- Optimum conditions in maximum principle form for variational problems with scalar argument for arbitrary structure of
restrictions.
- Optimum conditions and structure of optimum solution for averaged problems of nonlinear programming.
- Limiting possibilities of heat engines, refrigerators and heat pumps with given power.
- Limiting possibilities of separation processes.
- Heat and mass transfer regimes corresponding to minimal entropy production with given intensity of processes.
- Solution of a problem of resources exchange problem based on analogies between economic and thermodynamic systems.
- Classification of linear differential equations the n-th dimension with contact transform accuracy.
- Algorithms for choice of optimum sequence and intensity of processing of perishable materials.
Presentation Materials
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