Data-Driven Risk-Averse Safe Control for Nonlinear Parameter-Varying Systems

This letter presents a data-driven risk-averse control strategy for stochastic nonlinear systems. The presented controller consists of two components: 1) A gain-scheduling control to ensure the invariance of the safe set by leveraging the concept of $\lambda $ -contractivity, and 2) a nonlinear control to mitigate or eliminate the impact of the system's nonlinearities on set invariance. To formalize a data-driven approach, closed-loop data-driven representations of both the gain scheduling and nonlinear dynamics are provided. These representations are then leveraged to impose $\lambda $ -contractivity using a semidefinite programming (SDP) problem. The decision variables are optimized to minimize the variance of the system's state distribution, ensuring that the system remains within the safe set with a specified probability. Additional constraints are incorporated to ensure robustness against unmeasured noise and residual nonlinearities. Simulation result validates the proposed approach, demonstrating its potential to enhance both safety and performance in stochastic nonlinear systems by managing gain scheduling, nonlinear dynamics, and uncertainty in a risk-aware manner.