(484c) An Integrated System Identification and Hybrid Model Predictive Control Strategy for Optimized Interventions for Physical Activity

Insufficient levels of physical activity (PA) among adults is one of the main contributors to the rise of chronic illnesses in society such as cancer, heart disease, obesity, and diabetes. Alternatively, engagement in sustained levels of PA has been shown to reduce the risk of these illnesses or delay their onset [1,2]; a 51% decrease in all- cause mortality risk among adults is associated with an increase in the number of daily steps from 4,000 to 8,000 steps per day. Despite the availability of this information to the public, engagement in sufficient PA levels remains low in the general population. Control system engineering has ushered in paradigm shifts in many fields, and the adoption of dynamic modeling and control strategies in the behavioral medicine field has proven to be of great promise [3]. The benefits of control system engineering approaches to behavioral medicine include, system identification of dynamic behavioral models and controller design for decision-making framework that can be utilized to implement optimized personalized interventions, and ultimately assist in disseminating novel interventions to combat unhealthy behaviors, and promote healthy ones.

Prior and existing work in our laboratory has resulted in control-oriented PA interventions (Just Walk and Your Move) which are inspired by a fluid analogy dynamic model of the Social Cognitive Theory (SCT) [4], and where the goal is for participants to achieve and sustain 10,000 steps/day. This is accomplished by providing participants with daily “ambitious but doable” step goals aiming to increase the daily step count to reach and maintain the setpoint. Participants are also given financial incentives, in the form of expected points which turn into granted points when daily step goals are achieved. These interventions rely on mobile and wearable technology to measure the behavior of interest (the number of daily steps) along with environmental and contextual conditions (like anticipated stress and weather). In Just Walk the intervention was conducted in an open-loop setting, where judiciously designed multisine input signals were utilized for daily goals and expected points, in order to gather informative experimental data which can be used to estimate dynamical models for the desired behavior. In Your Move PA intervention, an improved system identification experiment takes place at the beginning of the intervention. Once sufficient cycles of multisine input data are gathered, a dynamic model for each participant is estimated from the data, and utilized as the control model for a Kalman-filter based hybrid MPC (HMPC), which serves as the decision-making framework throughout the closed-loop phases of the intervention. The integrated process of system identification and control is referred to as the Control Optimization Trial (COT) [5]. The closed-loop portion consists of two phases: an initiation phase to reach the desired setpoint, followed by a maintenance phase that reduces the use of points to maintain a desired behavior.

In this work, we rely on an AutoRegressive with eXternal inputs (ARX) models with regularization to model the walking behavior of Just Walk participants. We generate multiple combinations of estimation and validation data by organizing the experimental data into sub-experiments based on input signal cycles, which enables reducing bias from emphasis created by selected time portions of the data, and also strengthens model validity. Estimated models are deployed as the control model for the Kalman filter based, three degree-of-freedom (3DoF) HMPC formulation in simulations to test the ability of the integrated COT framework for delivering PA interventions. Diverse control strategies, like a lower constraint on goals attainment (GA = Behavior – Goal), and low target for the expected points in the maintenance phase to avoid dependency on financial rewards for maintaining engagement in healthy PA levels are examined. Slack variables are added to the HMPC formulation to avoid infeasibility, when the lower constraint on GA is not met. Moreover, through 3DoF filtering intuitive tuning is accomplished, where parameters for the filters can be adjusted independently to handle the speed of response for setpoint tracking, and measured and unmeasured disturbance rejection. Simulation results illustrate the effectiveness of the intervention design and devised HMPC strategies in delivering personalized, optimized PA interventions. This is a preliminary yet an essential step towards experimental evaluation of the analyzed constrained HMPC strategies in real-life conditions, as is currently underway in Your Move [5].

References:

[1] Katzmarzyk, P. T., Friedenreich, C., Shiroma, E. J., & Lee, I.-M. (2021). Physical inactivity and non-communicable disease burden in low-income, middle-income and high-income countries. British Journal of Sports Medicine, 56(2), 101–106. https://doi.org/10.1136/bjsports-2020-103640

[2] Saint-Maurice, P. F., Troiano, R. P., Bassett, D. R., Graubard, B. I., Carlson, S. A., Shiroma, E. J., Fulton, J. E., & Matthews, C. E. (2020). Association of Daily Step Count and step intensity with mortality among US adults. JAMA, 323(12), 1151. https://doi.org/10.1001/jama.2020.1382

[3] Rivera, D.E., Hekler, E.B., Savage, J.S., Downs, D.S. (2018). Intensively Adaptive Interventions Using Control Systems Engineering: Two Illustrative Examples. In: Collins, L., Kugler, K. (eds) Optimization of Behavioral, Biobehavioral, and Biomedical Interventions. Statistics for Social and Behavioral Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-91776-4_5

[4] Martin, C. A., Rivera, D. E., Hekler, E. B., Riley, W. T., Buman, M. P., Adams, M. A., & Magann, A. B. (2020). Development of a control-oriented model of social cognitive theory for optimized mhealth behavioral interventions. IEEE Transactions on Control Systems Technology, 28(2), 331–346. https://doi.org/10.1109/tcst.2018.2873538

[5] Optimizing individualized and adaptive mhealth interventions via control systems engineering methods. (n.d.). From https://reporter.nih.gov/search/g7QkpEP3VUS-bXgSgfT-GA/project-details/10051197
R01CA244777: National Institute of Health, National Cancer Institute.