Multiple Model Adaptive controller for Partially-Observed Boolean Dynamical Systems

This paper is concerned with developing an adaptive controller for Partially-Observed Boolean Dynamical Systems (POBDS). Assuming that partial knowledge about the system can be modeled by a finite number of candidate models, then simultaneous identification and control of a POBDS is achieved using the combination of a state-feedback controller and a Multiple-Model Adaptive Estimation (MMAE) technique. The proposed method contains two main steps: first, in the offline step, the stationary control policy for the underlying Boolean dynamical system is computed for each candidate model. Then, in the online step, an optimal Bayesian estimator is modeled using a bank of Boolean Kalman Filters (BKFs), each tuned to a candidate model. The result of the offline step along with the estimated state by the bank of BKFs specify the control input that should be applied at each time point. The performance of the proposed adaptive controller is investigated using a Boolean network model constructed from melanoma gene expression data observed through RNA-seq measurements.