Advanced Systems Analysis (ASA) Program researchers advance methods of control theory that allow models of complex human-Earth interactions to be studied under incomplete information and uncertainty.

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The system-analytical approach using so-called attainability domains helps researchers to oversee how sensitive a model’s objective function is to selecting a particular control strategy; in particular, it allows sub-optimal (i.e., close-to-optimal) solutions to be constructed and analyzed. ASA research deals both with theoretical foundations of construction of attainability domains and applications of this approach to economy-climate models.

In [1] the problem of constructing the attainability domain of a stochastic system in the absence of variable continuity and under asymptotic constraints was considered; researchers obtained a constructive description of the attainability domain’s structure and proved its robustness with respect to relaxation of constraints.

Boundary conditions are sometimes uncertain in human-Earth systems models. ASA researchers are developing methods of constructing guaranteed controls under uncertainty and incomplete information. In 2014 first results on a new approach of guaranteed feedback control of dynamic systems were published by [2] and [3], which suggested a constructive algorithm for linear control dynamic systems.

Sensitivity of the solution toward parameters of the objective function in the problem of maximizing a time-averaged objective function was studied by [4] and [5]. An optimal solution was selected from among stationary strategies, and a special type of periodic cyclic trajectory, so-called level cycles, were derived; and phase transitions between two optimal strategies were revealed.

References

[1] Chentsov AG, Baklanov A (2014). A problem related to asymptotic attainability in the mean, *Doklady Mathematics*, 90(3):762-765 [In Russian]

[2] Kryazhimskiy AV, Strelkovskii NV (2014a). An open-loop criterion for the solvability of a closed-loop guidance problem with incomplete information. Linear control systems, Proceedings of the Steklov Institute of Mathematics (Trudy Instituta Matematiki i Mekhaniki UrO RAN), 20(3):132-147 [In Russian, English version to appear]

[3] Kryazhimskiy AV, Strelkovskii NV (2014b). A problem of guaranteed closed-loop guidance by a fixed time for a linear control system with incomplete information. Program solvability criterion, *Proceedings of the Steklov Institute of Mathematics (Trudy Instituta Matematiki i Mekhaniki UrO RAN)*, 20(4):168-177 [In Russian, English version to appear]

[4] Davydov AA, Mena-Matos H, Moreira CS (2014). Generic profit singularities in time averaged optimization for cyclic processes in polydynamical systems.* Journal of Mathematical Sciences*, 199(5):510-534

[5] Davydov AA, Mena-Matos H, Moreira CS (2015). Generic profit singularities in time averaged optimization for phase transitions in polydynamical systems. *Journal of Mathematical Analysis and Applications*, 424(1):704-726

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Program Director and Principal Research Scholar Advancing Systems Analysis Program

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International Institute for Applied Systems Analysis (IIASA)

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