Poincaré map Identification of Switched Nonlinear Systems Using SINDy Method

This paper presents an extended approach for the identification and characterization of limit cycles in switched nonlinear dynamical systems using the Poincaré map and the Sparse Identification of Nonlinear Dynamics (SINDy) technique. We can effectively unravel critical insights from the complex behavior exhibited by switched nonlinear systems. This extended technique of Poincaré map identification using the SINDy method allows us to comprehensively comprehend the system’s evolution during mode transitions across specific intersections. The proposed method plays a pivotal role in both stabilizing switched systems and conducting a comprehensive analysis of their limit cycles. Indeed, the precise identification of Poincaré maps enables exploration of the system stability and its periodicity patterns, offering invaluable tools for controlling switched nonlinear systems. These insights hold significant promise for making well-informed decisions across a wide range of practical applications.