  In this paper, we introduce a data-driven framework for synthesis of
provably-correct controllers for general nonlinear switched systems under
complex specifications. The focus is on systems with unknown disturbances whose
effects on the dynamics of the system is nonlinear. The specifications are
assumed to be given as linear temporal logic over finite traces (LTLf)
formulas. Starting from observations of either the disturbance or the state of
the system, we first learn an ambiguity set that contains the unknown
distribution of the disturbances with a user-defined confidence. Next, we
construct a robust Markov decision process (RMDP) as a finite abstraction of
the system. By composing the RMDP with the automaton obtained from the LTLf
formula and performing optimal robust value iteration on the composed RMDP, we
synthesize a strategy that yields a high probability that the uncertain system
satisfies the specifications. Our empirical evaluations on systems with a wide
variety of disturbances show that the strategies synthesized with our approach
lead to high satisfaction probabilities and validate the theoretical
guarantees.
