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A convex data-driven approach for nonlinear control synthesis

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Document pages: 6 pages

Abstract: We consider a class of nonlinear control synthesis problems where theunderlying mathematical models are not explicitly known. We propose adata-driven approach to stabilize the systems when only sample trajectories ofthe dynamics are accessible. Our method is founded on the density functionbased almost everywhere stability certificate that is dual to the Lyapunovfunction for dynamic systems. Unlike Lyapunov based methods, density functionslead to a convex formulation for a joint search of the control strategy and thestability certificate. This type of convex problem can be solved efficiently byinvoking the machinery of the sum of squares (SOS). For the data-driven part,we exploit the fact that the duality results in the stability theory of thedynamical system can be understood using linear Perron-Frobenius and Koopmanoperators. This connection allows us to use data-driven methods developed toapproximate these operators combined with the SOS techniques for the convexformulation of control synthesis. The efficacy of the proposed approach isdemonstrated through several examples.

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