  In this paper we study the problem of synthesizing optimal control policies
for uncertain continuous-time nonlinear systems from syntactically co-safe
linear temporal logic (scLTL) formulas. We formulate this problem as a sequence
of reach-avoid optimal control sub-problems. We show that the resulting hybrid
optimal control policy guarantees the satisfaction of a given scLTL formula by
constructing a barrier certificate. Since solving each optimal control problem
may be computationally intractable, we take a learning-based approach to
approximately solve this sequence of optimal control problems online without
requiring full knowledge of the system dynamics. Using Lyapunov-based tools, we
develop sufficient conditions under which our approximate solution maintains
correctness. Finally, we demonstrate the efficacy of the developed method with
a numerical example.
