Bayesian Inference for Feedback Control. I: Theory

The control of water-resources systems can be extremely complicated because of the difficulty in accurately modeling such systems. Many systems are controlled manually by operators with subjective, ad hoc rules. Other system controls are based on statistical methods such as forecasting. Even though considerable theoretical knowledge and mathematical models of such systems exist, they are rarely used in feedback control of such systems. Combining these three control techniques is difficult because they use different types of information. A new procedure is developed that combines these sources of information as an extension of Bayesian inference. The method, Bayesian error analysis, uses Bayesian likelihoods to characterize parameter-estimation errors so that any modeling bias can be removed from the estimates. Learning methods are used to develop Bayesian likelihood tables. Prior probabilities can come from historical data or from subjective estimates. The method is demonstrated in a companion paper.