Effective information for offline stochastic feedback and optimal control of dynamic systems
The paper deals with the modeling of the impact of uncertain future events on decision making in a random medium. The concepts of effective information called EIH (Effective Information Horizon) and EIS (Effective Information Parameter Space) are introduced. The main results of the paper are the following: 1) one can use a substantially restricted amount of information to optimally control offline a real system or to offline evaluate the system performance under a feedback control rule; 2) at the same time, it is proven that ignoring the uncertain events, whose expectation lie in the time interval \([T\), EIH], necessarily results in a nonoptimal solution of the problem. There are several numerical examples. The first two demonstrate that the length of the EIH is quite limited, being of the same order of magnitude as the planning horizon length. The EIS is also limited, covering the most probable parameter realizations. The third example demonstrates both a possible violation of the problem constraints and deterioration of the performance measure, when neglecting information beyond the planning horizon.
scientific article; zbMATH DE number 1997727