Schade, C.M., “Optimal Regulation of Physiological Systems via Real Time Adaptive Model Synthesis,” (TRNo.6792-2), Stanford Electronics Laboratories, Stanford, California, 1971.
Optimal control algorithms that use an adaptive non-recursive digital filter model for on-line closed-loop blood pressure regulation have been developed. This Automatic Therapeutic Control System was designed specifically for the regulation of physiological systems, but the design assumptions are such that it should prove very useful for a much broader class of control problems.
An Adaptive Model Control system has been developed, the analysis of which is presented in two parts: (1) the real-time adaptive model synthesis procedure, and (2) the optimal forward-time controller.
The Adaptive modeling process is accomplished by the rapidly converging O-LMS Algorithm. The conditions necessary to guarantee convergence for deterministic inputs are presented. Mean-Square Error bounds are presented for zero mean and nonzero mean additive-output noise systems and also for the low-order approximation problem.
The optimal forward-time controller is described. It not only makes efficient use of the mathematical properties of the non-recursive digital filter model (that is, the filter gains and the state of the filter), but also meets the time and memory constraints of a minicomputer used on-line for this control problem. The future control inputs are determined by a doubly constrained quadratic function which is solved to minimize the mean-square control error.
The results of an experimental run are included in which these algorithms were used to regulate the blood pressure of a dog that had been artificially placed in a hypotensive state (shock). The results of this and similar experiments have been very successful from both an engineering and medical point of view, and if the necessary arrangements can be made with the local hospitals, this system will be used in the near future as part of an intensive care unit.