Cluster regression model for control of nonlinear dynamics

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 the clarity of sparse regression in a unique way to enhance the closed-loop feedback control of nonlinear dynamical systems. A key innovation in our methodology is the employment of cluster coefficients via a cluster decomposition of time-series measurement data. This approach transcends the conventional emphasis on the proximity of time series measurements to cluster centroids, offering a more nuanced representation of the dynamics within phase space. Capturing the evolving dynamics of these coefficients enable the construction of a robust, deterministic model for the observed states of the system. This model excels in capturing a wide range of dynamics, including periodic and chaotic behaviors, 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 fluid flow, our model showcases its ability to pinpoint critical system features and its adaptability in reaching any observed state. A distinctive feature of our control strategy is the novel hopping technique between cluster states, which successfully averts lobe switching in the Lorenz system and accelerates vortex shedding in fluid-structure interaction systems while maintaining the mean aerodynamic characteristics.