MLC Tactics and Strategy
In this chapter, we provide good practices for applying machine learning control (MLC) to a real-world flow control experiment. The recipes include common experimental challenges, like defining a cost function, implementing MLC on the computer, and dealin
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MLC Tactics and Strategy
Heavy is the brick of reality on the strawberry cake of our illusions. Gilles “Boulet” Roussel, cartoonist, Translated from his Twitter account Bouletcorp, 10th December 2013
If the ideal MLC experiment existed, this chapter would not be needed. The literature contains many examples of control methods that fail the translation from a numerical study to the corresponding experimental demonstration. MLC removes one of the major obstacles: the discrepancy between the employed model and the physical reality of the experiment. Nonetheless there still exist many pitfalls that lead to disappointing results. Often, these results relate to the difference between the idealized experiment and reality. Through our first applications of MLC in experiments we have explored many pitfalls and have developed a mitigation strategy. This chapter guides experimental control demonstrations with MLC. The advice may also apply to numerical studies.
7.1 The Ideal Flow Control Experiment The ideal flow control experiment—or any other control experiment—does not exist. If it existed, it would have the following properties: Full knowledge about the dynamics: The evolution equation da/dt = F(a, b) and the parameters of the dynamics F, like the Reynolds or Mach number, are exactly known. A corollary is that reproducibility is guaranteed. Accurate measurements: The measurement equation s = G(a, b) is known with perfect precision and the signals s(t) are accurately recorded. Ideal cost function: The cost function J (a, b) describes the quantity which shall be optimized and which can be measured in the experiment. © Springer International Publishing Switzerland 2017 T. Duriez et al., Machine Learning Control – Taming Nonlinear Dynamics and Turbulence, Fluid Mechanics and Its Applications 116, DOI 10.1007/978-3-319-40624-4_7
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7 MLC Tactics and Strategy
Known noise: Any noise terms affecting the dynamics, the measurement equation or the cost function are accurately modeled and accounted for. A corollary is the reproducibility of arbitrary ensemble averages. Controllability: Any desired final state a of the system can be reached with finite actuation in finite time. At a minimum, the achieved change of cost function due to MLC is so impressive, that the results merit a career promotion and convince the funding agencies to invest more money. Infinitely powerful computer: The control law b = K(s) is computed instantaneously. At minimum, the actuation command is computed with predictable small time delay. No aging: Of course, the ideal experiment never breaks, nor suffers slowly drifting external parameters such as atmospheric pressure and temperature, nor is effected by opening and closing doors of the room, nor experiences any changes which are not reflected in the dynamics F, in the measurement function G and in the cost function J . Infinite resources: The perfect experiment can be operated until the cost function value is converged and until MLC is converged to the globally optimal control law. Arguably, the
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