Humans learn to interact with many complex dynamic systems such as helicopters, bicycles, and automobiles. This dissertation develops a subsystem identification method to model the control strategies that human subjects use in experiments where they interact with dynamic systems. This work provides new results on the control strategies that humans learn. We present a novel subsystem identification algorithm, which can identify unknown linear time-invariant feedback and feedforward subsystems interconnected with a known linear time-invariant subsystem. These subsystem identification algorithms are analyzed in the cases of noiseless and noisy data. We present results from human-in-the-loop experiments, where human subjects in- teract with a dynamic system multiple times over several days. Each subject’s control behavior is assumed to have feedforward (or anticipatory) and feedback (or reactive) components, and is modeled using experimental data and the new subsystem identifi- cation algorithms. The best-fit models of the subjects’ behavior suggest that humans learn to control dynamic systems by approximating the inverse of the dynamic system in feedforward. This observation supports the internal model hypothesis in neuro- science. We also examine the impact of system zeros on a human’s ability to control a dynamic system, and on the control strategies that humans employ.

Humans learn to interact with many complex physical systems. For example, humans learn to fly aircraft, operate drones, and drive automobiles. We present results from human-in-the-loop (HITL) experiments, where human subjects interact with dynamic systems while performing command-following tasks multiple times over a one-week period. We use a new subsystem identification (SSID) algorithm to estimate the control strategies (feedforward, feedforward delay, feedback, and feedback delay) that human subjects use during their trials. We use experimental and SSID results to examine the effects of system characteristics (e.g., system zeros, relative degree, system order, phase lag, time delay), reference command, and command-following objectives on humans command-following performance and on the control strategies that the humans learn. Results suggest that nonminimum-phase zeros, relative degree, phase lag, and time delay tend to make dynamic systems difficult for human to control. Subjects can generalize their control strategies from one task to another and use prediction of the reference command to improve their command-following performance. However, this dissertation also provides evidence that humans can learn to improve performance without prediction. This dissertation also presents a new SSID algorithm to model the control strategies that human subjects use in HITL experiments where they interact with dynamic systems. This SSID algorithm uses a two-candidate-pool multi-convex-optimization approach to identify feedback-and-feedforward subsystems with time delay that are interconnected in closed loop with a known subsystem. This SSID method is used to analyze the human control behavior in the HITL experiments discussed above.