We give a brief review of the developments in several classical problems of sequential analysis and their applications to biomedicine, economics and engi- neering. Even though it can only focus on a limited number of topics, the review shows that sequential analysis is still a vibrant subject after six decades of contin- ual development, with fresh ideas brought in from various fields of application and through interactions with other branches of statistics and probability. We conclude with some remarks on the opportunities and challenges ahead.

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Sequential analysis: some classical problems and new challenges

Automated control of blood glucose (BG) concentration is a long-sought goal for type 1 diabetes therapy. We have developed a closed-loop control system that uses frequent measurements of BG concentration along with subcutaneous delivery of both the fast-acting insulin analog lispro and glucagon (to imitate normal physiology) as directed by a computer algorithm. The algorithm responded only to BG concentrations and incorporated a pharmacokinetic model for lispro. Eleven subjects with type 1 diabetes and no endogenous insulin secretion were studied in 27-hour experiments, which included three carbohydrate-rich meals. In six subjects, the closedloop system achieved a mean BG concentration of 140 mg/dl, which is below the mean BG concentration target of _154 mg/dl recommended by the American Diabetes Association. There were no instances of treatmentrequiring hypoglycemia. Five other subjects exhibited hypoglycemia that required treatment; however, these individuals had slower lispro absorption kinetics than the six subjects that did not become hypoglycemic. The time-to-peak plasma lispro concentrations of subjects that exhibited hypoglycemia ranged from 71 to 191 min (mean, 117 ± 48 min) versus 56 to 72 min (mean, 64 ± 6 min) in the group that did not become hypoglycemic (aggregate mean of 84 min versus 31 min longer than the algorithm’s assumption of 33 min, P = 0.07). In an additional set of experiments, adjustment of the algorithm’s pharmacokinetic parameters (time-to-peak plasma lispro concentration set to 65 min) prevented hypoglycemia in both groups while achieving an aggregate mean BG concentration of 164 mg/dl. These results demonstrate the feasibility of safe BG control by a bihormonal artificial endocrine pancreas.

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A Bihormonal Closed-Loop Artificial Pancreas for Type 1 Diabetes

https://hal.archives-ouvertes.fr/hal-00259532/document

Survey paper: Optimal experimental design and some related control problems

Background:In order to stave off deleterious complications of the disease, the ultimate task for people with diabetes is to maintain their blood glucose in euglycemic range. Despite technological advancements, conventional open-loop therapy often results in prolonged hyperglycemia and episodic hypoglycemia, in addition to necessitating carbohydrate counting, frequent glucose monitoring, and drug administration. The logical conclusion in the evolution of exogenous insulin therapy is to develop an automated closed-loop control system.Methods:Eleven closed-loop control experiments were conducted in four anesthetized diabetic pigs, with carbohydrate loads simulated by intravenous glucose administration through ear-vein catheters. Type 1 diabetes-like pathology was induced using intravenous administration of cytotoxin streptozotocin. The augmented model-predictive control algorithm accounts for the accumulation of subcutaneous insulin, which is critical in avoiding excessive insulin dosing.Results:Control resu...

/pdf/adaptive-closed-loop-control-provides-blood-glucose-2afm4lzl7c.pdf

Adaptive Closed-Loop Control Provides Blood-Glucose Regulation Using Dual Subcutaneous Insulin and Glucagon Infusion in Diabetic Swine:

A recursive least-squares algorithm with slowly decreasing weights for linear stochastic systems is found to have self-convergence property, i.e., it converges to a certain random vector almost surely irrespective of the control law design. Such algorithms enjoy almost the same nice asymptotic properties as the standard least-squares. This universal convergence result combined with a method of random regularization then easily can be applied to construct a self-convergent and uniformly controllable estimated model and thus may enable us to form a general framework for adaptive control of possibly nonminimum phase autoregressive-moving average with exogenous input (ARMAX) systems. As an application, we give a simple solution to the well-known stochastic adaptive pole-placement and linear-quadratic-Gaussian (LQG) control problems in the paper.

Self-convergence of weighted least-squares with applications to stochastic adaptive control

Based on the recently established results on self-tuning regulators originally proposed by Astrom and Wittenmark, this paper presents various novel and extended results on least squares based adaptive minimum variance control for linear stochastic systems. These results establish self-optimality, self-tuning property, and the best possible convergence rate of the control law in a variety of situations of interest.

Lei Guo

Papers

Further Results on Least Squares Based Adaptive Minimum Variance Control