Intelligent control and optimization under uncertainty with application to hydro power

A control that makes the best change in control settings in response to inputs of sensors measuring the state of the system, we refer to as intelligent. Instead of ‘hard-wiring’ response based on protocols, priorities, and pre-selected, pre-programmed ground rules that do not necessarily produce the best changes of the control settings, we show how best rules can be generated and modified by the computer during the course of controlling the system, and how learning plays an important role in the real-time implementation of an intelligent control system. The problem of finding the best control of a system is the same as optimizing a multi-stage mathematical program under uncertainty. Our formulation allows one to take into account uncertainty of the true values that the sensors are measuring, as well as uncertainties about the system response to the changes in the control settings. A feasible solution of the system is called optimum if it maximizes the expected objective value while hedging against the myriad of possible contingencies (or taking advantage of favorable events) that may arise in the future; typically these can number in the thousands, millions, or even billions. We have developed a special approach, a composite of Benders decomposition and importance sampling, to efficiently solve the extremely large mathematical programs that model the myriads of possible future events. The dual of the multistage formulation measures the impact of future (down-stream) responses, which the algorithm ‘passes back’ up-stream to the model's ‘present time’ in the form of ‘cuts’ or necessary conditions for the up-stream controls to follow in order to optimally control the system. These cuts, automatically generated and modified, form a set of general ground rules, or principles, which the computer learns, remembers, and calls upon to intelligently control the real system.