Risk-Informed Model-Free Safe Control of Linear Parameter-Varying Systems

This paper presents a risk-informed data-driven safe control design approach for a class of stochastic uncertain nonlinear discrete-time systems. The nonlinear system is modeled using linear parameter-varying (LPV) systems. A model-based probabilistic safe controller is first designed to guarantee probabilistic <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lambda$</tex>-contractivity (i.e., stability and invariance) of the LPV system with respect to a given polyhedral safe set. To obviate the requirement of knowing the LPV system model and to bypass identifying its open-loop model, its closed-loop data-based representation is provided in terms of state and scheduling data as well as a decision variable. It is shown that the variance of the closed-loop system, as well as the probability of safety satisfaction, depends on the decision variable and the noise covariance. A minimum-variance direct data-driven gain-scheduling safe control design approach is presented next by designing the decision variable such that all possible closed-loop system realizations satisfy safety with the highest confidence level. This minimum-variance approach is a control-oriented learning method since it minimizes the variance of the state of the closed-loop system with respect to the safe set, and thus minimizes the risk of safety violation. Unlike the certainty-equivalent approach that results in a risk-neutral control design, the minimum-variance method leads to a risk-averse control design. It is shown that the presented direct risk-averse learning approach requires weaker data richness conditions than existing indirect learning methods based on system identification and can lead to a lower risk of safety violation. Two simulation examples along with an experimental validation on an autonomous vehicle are provided to show the effectiveness of the presented approach.