# Meeting Details

Title: Optimal Response Control for Systems Modeled with Symbolic Transfer Functions The Pritchard Lab Seminar Chris Griffin, Applied Research Laboratory, Penn State Transfer function modeling is a standard technique in classical Linear Time Invariant and Statistical Process Control. The work of Box and Jenkins was seminal in developing methods for identifying parameters associated with classical (r,s,k) transfer functions. Discrete event systems are often used for modeling hybrid control structures and high-level decision problems, such as discrete time, discrete strategy repeated games. For these games, a discrete transfer function in the form of an accurate hidden Markov model of input-output relations could be used to derive optimal response strategies. In this talk, we discuss work in identifying symbolic transfer functions for discrete event dynamic systems. We assume an underlying input/output system that is purely symbolic and stochastic. Our models are defined by three parameters, (L1, L2, k), just as the Box-Jenkins models. Here L1 is the maximal input history lengths to consider, L2 is the maximal output history length to consider, and $k$ is the response lag. We show how to use algorithms for estimating the symbolic transfer functions and Markov Decision Processes to find an optimal symbolic control function for the symbolic system. We use a repeated game as an example of a symbolic input/output dynamical system.