A Convex Data-Driven Approach for Nonlinear Control Synthesis

We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. propose data-driven approach to stabilize systems when only sample trajectories dynamics accessible. Our method is built on density-function-based stability certificate that dual Lyapunov function for dynamic systems. Unlike Lyapunov-based methods, density functions lead convex formulation joint search strategy and certificate. This type problem can be solved efficiently using machinery sum squares (SOS). For part, we exploit fact duality results in theory understood through lens Perron–Frobenius Koopman operators. allows us use methods approximate these operators combine them with SOS techniques establish synthesis. The efficacy proposed demonstrated several examples.