Excessive weight gain during pregnancy is a significant public health concern and has been the recent focus of novel, control systems-based interventions. Healthy Mom Zone (HMZ) is an intervention study that aims to develop and validate an individually tailored and intensively adaptive intervention to manage weight gain for overweight or obese pregnant women using control engineering approaches. Motivated by the needs of the HMZ, this dissertation presents how to use system identification and state estimation techniques to assist in dynamical systems modeling and further enhance the performance of the closed-loop control system for interventions.

Underreporting of energy intake (EI) has been found to be an important consideration that interferes with accurate weight control assessment and the effective use of energy balance (EB) models in an intervention setting. To better understand underreporting, a variety of estimation approaches are developed; these include back-calculating energy intake from a closed-form of the EB model, a Kalman-filter based algorithm for recursive estimation from randomly intermittent measurements in real time, and two semi-physical identification approaches that can parameterize the extent of systematic underreporting with global/local modeling techniques. Each approach is analyzed with intervention participant data and demonstrates potential of promoting the success of weight control.

In addition, substantial efforts have been devoted to develop participant-validated models and incorporate into the Hybrid Model Predictive Control (HMPC) framework for closed-loop interventions. System identification analyses from Phase I led to modifications of the measurement protocols for Phase II, from which longer and more informative data sets were collected. Participant-validated models obtained from Phase II data significantly increase predictive ability for individual behaviors and provide reliable open-loop dynamic information for HMPC implementation. The HMPC algorithm that assigns optimized dosages in response to participant real time intervention outcomes relies on a Mixed Logical Dynamical framework which can address the categorical nature of dosage components, and translates sequential decision rules and other clinical considerations into mixed-integer linear constraints. The performance of the HMPC decision algorithm was tested with participant-validated models, with the results indicating that HMPC is superior to "IF-THEN" decision rules.

Increasing interest in individualized treatment strategies for prevention and treatment of health disorders has created a new application domain for dynamic modeling and control. Standard population-level clinical trials, while useful, are not the most suitable vehicle for understanding the dynamics of dosage changes to patient response. A secondary analysis of intensive longitudinal data from a naltrexone intervention for fibromyalgia examined in this dissertation shows the promise of system identification and control. This includes datacentric identification methods such as Model-on-Demand, which are attractive techniques for estimating nonlinear dynamical systems from noisy data. These methods rely on generating a local function approximation using a database of regressors at the current operating point, with this process repeated at every new operating condition. This dissertation examines generating input signals for data-centric system identification by developing a novel framework of geometric distribution of regressors and time-indexed output points, in the finite dimensional space, to generate sufficient support for the estimator. The input signals are generated while imposing “patient-friendly” constraints on the design as a means to operationalize single-subject clinical trials. These optimization-based problem formulations are examined for linear time-invariant systems and block-structured Hammerstein systems, and the results are contrasted with alternative designs based on Weyl's criterion. Numerical solution to the resulting nonconvex optimization problems is proposed through semidefinite programming approaches for polynomial optimization and nonlinear programming methods. It is shown that useful bounds on the objective function can be calculated through relaxation procedures, and that the data-centric formulations are amenable to sparse polynomial optimization. In addition, input design formulations are formulated for achieving a desired output and specified input spectrum. Numerical examples illustrate the benefits of the input signal design formulations including an example of a hypothetical clinical trial using the drug gabapentin. In the final part of the dissertation, the mixed logical dynamical framework for hybrid model predictive control is extended to incorporate a switching time strategy, where decisions are made at some integer multiple of the sample time, and manipulation of only one input at a given sample time among multiple inputs. These are considerations important for clinical use of the algorithm.