(288c) Data-Centric Modeling and Predictive Control for Nonlinear Hybrid Systems, with Application to Adaptive Behavioral Interventions

In adaptive interventions, the dosage of intervention components (such as frequency of counseling visits, medication, or intensity of therapy) is assigned to participants based on measurements of outcome response over time. Adaptive interventions are receiving increasing attention in the field of behavioral health as a means to improve the prevention and treatment of chronic, relapsing disorders, such as drug abuse, smoking, and obesity [1-2]. In practice, these problems represent hybrid control systems because dosages of intervention components must be assigned to discrete values on the basis of decision policies that apply feedback and/or feedforward action. The dynamics of these systems can be complex and highly uncertain, with many factors that contribute to these dynamics not well understood. Moreover, these interventions have to be implemented on a population that may display significant levels of interindividual variability. Data-driven modeling and control formulations which achieve robust performance can contribute substantially towards delivering optimized interventions under real-world conditions.

Identification theory for continuous systems is well understood in the literature (see for example [3]). However, hybrid system identification is challenging due to the fact that the model parameters depend on the mode or location [4-5]. A number of identification approaches for linear hybrid systems have been proposed in the literature [5-8]. An identification scheme for nonlinear hybrid systems has been presented in [4]. However, it addresses only a particular class of nonlinear hybrid systems that are linear and separable in the discrete variables. Moreover, the locations or modes of the hybrid systems are assumed to be known beforehand.

We develop in this paper a data-centric modeling and predictive control scheme for nonlinear hybrid systems using Model-on-Demand (MoD) [9]. These represent nonlinear, black-box estimation method which enhance the classical local modeling problem. This method obtain a local model around a current operating point using only a subset of data from a point of interest determined by a fixed structure of regression vectors. In MoD, an adaptive bandwidth selector determines the size of data within a user-defined bandwidth limit (upper and lower bound). The data is weighted using a kernel or weighting function, and model parameters are obtained by solving a linear least squares problem at each time step. Because MoD estimation uses only small portions of data relevant to the region of interest to determine a model, it automatically considers the current operating location of the hybrid system in estimates of the model parameters; hence estimation of locations or modes governed by autonomous discrete events is achieved automatically. The local model is then converted into a mixed logical dynamical (MLD) system [10] representation. This model is used to formulate model predictive control algorithm that offers multiple-degree-of-freedom tuning parameters such that speed of setpoint tracking and speed of disturbance rejection (measured and unmeasured) which can be adjusted independently for each controlled output of the system [11].

The effectiveness of the proposed data-centric predictive control algorithm for nonlinear hybrid systems is demonstrated on a hypothetical adaptive behavioral intervention problem inspired by Fast Track, a real-life preventive intervention for improving parental function and reducing conduct disorder in at-risk children [12]. Simulation results confirm that the proposed approach is able to assign suitable dosages to each participant family in order to achieve a desired goal of parental function in the presence of unknown disturbances. The performance of the proposed approach is compared with a hybrid MPC controller relying on a fixed ARX model. The hybrid MoD-MPC controller yields comparatively lower 2-norm error (i.e., parental function deviation from its desired goal) for a given intervention energy. As a result, it uses less intervention resources by assigning intervention dosages in an improved manner according to the needs and characteristics of the participant family. We find that the proposed algorithm is useful for optimizing the class of adaptive intervention problems exhibiting both nonlinear and hybrid character.

References

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