Cluster regression model for flow control

In the realm of big data, discerning patterns in nonlinear systems affected by external control inputs is increasingly challenging. Our approach blends the coarse-graining strengths of centroid-based unsupervised clustering with sparse regression in a way to enhance the closed-loop feedback control of nonlinear dynamical systems. A key innovation in our method is the employment of cluster coefficients through cluster decomposition of time-series measurements. Capturing the dynamics of these coefficients enables the construction of a deterministic model for the observed states of the system. This model is able to predict the dynamics of periodic and chaotic systems, under the influence of external control inputs. Demonstrated in both the low-dimensional Lorenz system and the high-dimensional scenario of a flexible plate immersed in a fluid flow, our model showcases its ability to pinpoint critical system features and adaptability in reaching any observed state. A distinctive feature of our control strategy is the novel hopping technique between clusters, which successfully averts lobe switching in the Lorenz system and accelerates vortex shedding in fluid–structure interaction systems while maintaining the mean aerodynamic characteristics. Such a data-centric control design becomes evident in a myriad of applications, ranging from energy harvesting devices to mitigating emissions through drag control.