Optimal Process Control of Symbolic Transfer Functions

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. Computing systems are often fundamentally discrete and feedback control in these situations may require discrete event systems for modeling control structures and process flow. In these situations, a discrete transfer function in the form of an accurate hidden Markov model of input/output relations can be used to derive optimally responding controllers. In this paper, we extend work begun by the authors in identifying symbolic transfer functions for discrete event dynamic systems (Griffin et al. Determining A Purely Symbolic Transfer Function from Symbol Streams: Theory and Algorithms. In Proc. 2008 American Control Conference, pgs. 1166-1171, Seattle, WA, June 11-13, 2008). We assume an underlying input/output system that is purely symbolic and stochastic. We show how to use algorithms for estimating a symbolic transfer function and then use a Markov Decision Processes representation to find an optimal symbolic control function for the symbolic system.