Optimal filtering and control-Theory, practice, and intuition

Most of the current knowledge on the quadratic optimization of linear, stochastically influenced dynamic systems rests in a dozen or so key papers written in the last twenty years. With scarce exception, these papers treat the general theory and employ a certain traditional assumptions which seem simple enough to remove -- until one actually tries to remove them for a practical application. This paper will discuss the available methods, and develop new ones where necessary, for relaxing three of these assumptions: namely, that for time-domain design the environment introduce only white noise, that the noise statistics and plant parameters be known rather precisely, and that the command-response and disturbance-rejection properties of the system not both be important. Four equivalent implementations of the optimal control will be derived, of which one, a model-feedback design very similar to those long offered heuristically for adaptive flight control, has important sensitivity and stability advantages under environment and plant-parameter uncertainties.