Title: Automata Theory Meets Approximate Dynamic Programming: Optimal
Control with Temporal Logic Constraints

Speaker: Ivan Papusha (Caltech) 
 
Abstract: We investigate the synthesis of optimal controllers for
continuous-time and continuous-state systems under temporal logic
specifications. We consider a setting in which the specification can be
expressed as a deterministic, finite automaton (the specification
automaton) with transition costs, and the optimal system behavior is
captured by a cost function that is integrated over time.
Specifically, we construct a dynamic programming problem over the
product of the underlying continuous-time, continuous-state system and
the discrete specification automaton. This dynamic programming
formulation relies on the optimal substructure of the additive
transition costs over the product of the system and specification
automaton. Furthermore, we propose synthesis algorithms based on
approximate dynamic programming for both linear and nonlinear systems
under temporal logic constraints. We show that, for linear systems
under co-safe temporal logic constraints, this approximate dynamic
programming solution reduces to a semidefinite program.