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System Analysis Research Center

Russia, 152020, Yaroslavl region, Pereslavl-Zalessky, s.Botik, PSI RAS
Head of the center: Anatoly Tsirlin Doctor of Technical Sciences, Professor
phone: +7 (48535) 98-057, 98029


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

PowerPoint presentations





Optimal processes in macro systems (thermodynamics and economics)   12.05.2005 24 pages
Optimal control of temperature fields for cooling of supercomputer facilities and clusters and energy saving for supercomputer centers Visit delegation of HP to PSI RAS 26.09.2005 9 pages


Booklets and Leaflets



Optimal Control of Temperature Fields for Cooling of Supercomputer Facilities and Clusters and Energy Saving for Supercomputer Centers 22.05.2006
System Analysis Research Center 20.09.2005
System Analysis Research Center





Optimal Control of Temperature Fields  for Cooling of Supercomputer Facilities Clusters and Energy Saving for Supercomputer Centers 19.05.2006
System Analysis Research Center 22.09.2005




Program Systems Institute (jpg, eps)
System Analysis Research Center (jpg, eps)

Last edition: 25-01-2007 13:25


Address: Program Systems Institute of RAS
Pereslavl-Zalessky Yaroslavl Region Russia, 152020
Telephone./Fax: +7 (48535) 98-064  E-mail:    Web:

Program Systems Institute of RAS, Pereslavl-ZalesskyRussia

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