  Enforcing state and input constraints during reinforcement learning (RL) in
continuous state spaces is an open but crucial problem which remains a
roadblock to using RL in safety-critical applications. This paper leverages
invariant sets to update control policies within an approximate dynamic
programming (ADP) framework that guarantees constraint satisfaction for all
time and converges to the optimal policy (in a linear quadratic regulator
sense) asymptotically. An algorithm for implementing the proposed constrained
ADP approach in a data-driven manner is provided. The potential of this
formalism is demonstrated via numerical examples.
