Deep Reinforcement Learning Based Networked Control with Network Delays for Signal Temporal Logic Specifications

We apply deep reinforcement learning (DRL) to design of a networked controller with network delays to complete a temporal control task that is described by a signal temporal logic (STL) formula. STL is useful to deal with a specification with a bounded time interval for a dynamical system. In general, an agent needs not only the current system state but also the past behavior of the system to determine a desired control action for satisfying the given STL formula. Additionally, we need to consider the effect of network delays for data transmissions. Thus, we propose an extended Markov decision process using past system states and control actions, which is called a $\tau d$-MDP, so that the agent can evaluate the satisfaction of the STL formula considering the network delays. Thereafter, we apply a DRL algorithm to design a networked controller using the $\tau d$-MDP. Through simulations, we also demonstrate the learning performance of the proposed algorithm.