Optimal input signal design for data-centric identification and control with applications to behavioral health and medicine
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.