State transition learning with limited data for safe control of switched nonlinear systems

Switching dynamics are prevalent in real-world systems, arising from either intrinsic changes or responses to external influences, which can be appropriately modeled by switched systems. Control synthesis for switched systems, especially integrating safety constraints, is recognized as a significant and challenging topic. This study focuses on devising a learning-based control strategy for switched nonlinear systems operating under arbitrary switching law. It aims to maintain stability and uphold safety constraints despite limited system data. To achieve these goals, we employ the control barrier function method and Lyapunov theory to synthesize a controller that delivers both safety and stability performance. To overcome the difficulties associated with constructing the specific control barrier and Lyapunov function and take advantage of switching characteristics, we create a neural control barrier function and a neural Lyapunov function separately for control policies through a state transition learning approach. These neural barrier and Lyapunov functions facilitate the design of the safe controller. The corresponding control policy is governed by learning from two components: policy loss and forward state estimation. The effectiveness of the developing scheme is verified through simulation examples.