1860
eng
reportzib
0
2013-05-27
2013-05-27
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A Global Approach to the Optimal Control of System Dynamics Models
The System Dynamics (SD) methodology is a framework for modeling and simulating the dynamic behavior of socioeconomic systems. Characteristic for the description of such systems is the occurrence of feedback loops together with stocks and flows. The mathematical equations that describe the system are usually ordinary differential equations and nonlinear algebraic constraints. Therefore seemingly simple systems can show a nonintuitive, unpredictable behavior over time. Controlling a dynamical system means to specify potential interventions from outside that should keep the system on the desired track, and to define an evaluation schema to compare different controls among each other, so that a "best" control can be defined in a meaningful way. The central question is how to compute such globally optimal control for a given SD model, that allows the transition of the system into a desired state with minimum effort. We propose a mixed-integer nonlinear programming (MINLP) reformulation of the System Dynamics Optimization (SDO) problem. MINLP problems can be solved by linear programming based branch-and-bound approach. We demonstrate that standard MINLP solvers are not able to solve SDO problem. To overcome this obstacle, we introduce a special-tailored bound propagation method. We apply our new method to a predator-prey model with additional hunting activity as control, and to a mini-world model with the consumption level as control. Numerical results for these test cases are presented.
1438-0064
urn:nbn:de:0297-zib-18600
Armin Fügenschuh
Armin Fügenschuh
Ingmar Vierhaus
ZIB-Report
13-28
eng
uncontrolled
System Dynamics
eng
uncontrolled
Global Optimal Control
eng
uncontrolled
Mixed-Integer Nonlinear Optimization
eng
uncontrolled
Bounds Strengthening
ORDINARY DIFFERENTIAL EQUATIONS
DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
Mathematical Optimization
Fügenschuh, Armin
https://opus4.kobv.de/opus4-zib/files/1860/ZR-13-28.pdf