Control Subject to Human Behavioral Disturbances: Anticipating Behavioral Influences in the Control of Diabetes

This project addresses the design of cyber-physical systems that respond to behavioral disturbances introduced by human users. The primary motivating example of this research is the design of "artificial pancreas" algorithms for the control of blood glucose in patients with Type 1 diabetes who require external insulin throughout the day to maintain glucose homeostasis. Whereas individual patients have their own preferences with regard to the degree of automation needed (with some desiring fully automatic delivery of insulin, others wanting only advice), the control problem itself is largely defined in terms of the uncertainties associated with daily activities: meals and exercise.

From recent clinical studies of fully automated control of diabetes, it is clear that deterministic model predictive methods can effectively deal with the measurement and actuation delays associated with current-generation continuous glucose monitors and insulin pumps. However, it is also clear that outside of the controlled environment of a clinical research center it is necessary to make special accommodations for spurious human behavioral disturbances. Specifically, (i) system disturbances, such as meals and exercise, may have to be announced by the patient (requiring an intrusion upon the patient's lifestyle), (ii) it may be necessary to integrate specialized algorithms for detecting meals and exercise (which are prone to errors and introduce delay), and/or (iii) the system may need to be de-tuned so that unannounced meals and exercise can be safely absorbed by the system.

In this work, we take the view that stochastic methods can play a significant role in bridging the gap between model predictive control and uncertain system disturbances caused by human behavior. In particular, we assert that many system disturbances can be modeled (i) as random processes, but not as zero-mean white noise processes, and (ii) as occurring with statistical regularity, but not as periodic. Accordingly, we are developing new mathematical models of human behavioral disturbances. Our premise is that appropriate statistical characterizations of routine behavior allow us to derive new control algorithms that anticipate behavioral disturbances and improve upon the existing (deterministic) model predictive methods currently being evaluated for human-subject clinical experiments without compromising safety.

Estimating Behavioral Disturbances via Deconvolution: In this work, we have been developing computational approaches to estimating human behavioral disturbances implicitly by reconciling continuous sensor data (e.g. a diabetic patient's continuous BG monitoring data) with known actuation signals (e.g. a patient's insulin pump log file). Implicit methods are important since humans are prone to reporting behaviors inaccurately (e.g. patient meal diaries). The opportunity to recover human behavioral disturbances stems from the fact that the model-predictive control algorithms often used for closed-loop control are typically implemented with simple linear time-invariant models relating behavioral disturbances and actuation signals to output measurements. With an LTI system model it is possible to recover behavioral influences via deconvolution, the output of which we refer to as the "net effect" which refers to the collective effect of behavioral events that either (i) we do not have a record of, such as meals, or (ii) the LTI system model cannot account for, like dawn phenomenon. One challenge to address in this regard is that the inverse solution is not unique and has to be computed as the solution to a regularized optimization problem. Since the inverse has to account for true nonlinear and time-varying effects (e.g. circadian rhythm), the unknown input isn't necessarily zero-mean or sparse. The approach we have taken to address these challenges is to introduce an "outer-loop" optimization of system model parameters based on the "shape" of the L2-regularized inverse solution reflecting a priori knowledge about the unknown disturbance signal.

Closed-Loop Control of Diabetes with Multiple Disturbance Function Hypotheses: In this work, our goal is to use the deconvolution methods above to create an implicit characterization of patient behavior and thereby improve closed-loop control of diabetes. The idea is that by maintaining a "history" of past net effect curves, we can employ them as a set of hypotheses that explain the measurements that we are observing today. Thus, if the patient's net effect behavior is highly consistent, we have actionable information about the future. The technical approach follows the "open-loop feedback control" (OLFC) methodology explored in the preceding years of the project. First, based on all of the continuous monitoring data up to the present time, we compute the posterior probability of each hypothesis, making it possible to recognize and act, through an optimal insulin delivery strategy, on days with different net effect curves. Next, we compute in real time an optimal "open loop" schedule for insulin delivery based on the posterior probabilities of all of the hypotheses. (This is "open loop" in the sense that the computation is done as though there will be no future observations.) Retrospective analysis of patient data over approximately one month shows that the OLFC approach can significantly reduce the probability of out- of-range blood glucose measurements throughout the day.