2020-07-29 –, Green Track
The probabilistic optimization of dynamical systems is often framed to minimize the expectation of a given loss function. For non-linear systems, the evaluation of such a loss function and its gradient can be expensive. In this work the Koopman Operator and its computational advantages are presented using the AD-compatible DiffEqUncertainty.jl.
The probabilistic optimization of dynamical systems is often framed to minimize the expectation of a given loss function. For non-linear systems, the evaluation of such a loss function and its gradient can be expensive. Often times practitioners rely on implicit methods, such a Monte Carlo simulation, for this calculation due to ease of implementation and understanding. Alternatively, explicit methods such as the Frobenious-Perron Operator can be leveraged to directly evolve probability densities through non-linear systems. Furthermore, the adjoint to the Frobenious-Perron Operator, the Koopman Operator, can be leveraged to the same ends. In this work we will demonstrate how the adjoint property of the Koopman Operator provides significant computational advantages over alternative methods for calculating expectations. We also demonstrate how this Koopman-based approach is AD-compatible. Building on Julia's differential equation ecosystem, this Koopman-based approach is available in DiffEqUncertainty.jl
Adam Gerlach is a Research Aerospace Engineer in the Control Sciences Center of Excellence at the Air Force Research Laboratory (AFRL). His research interests are in intelligent systems, decision making under uncertainty, decentralized cooperative control.
Adam received his Ph.D. in aerospace engineering from the University of Cincinnati in 2014 focused on Controls, Dynamics, and Intelligent Systems.