Korkut Bekiroglu

Designing adaptive intensive interventions using methods from engineering

OBJECTIVE Adaptive intensive interventions are introduced, and new methods from the field of control engineering for use in their design are illustrated. METHOD A detailed step-by-step explanation of how control engineering methods can be used with intensive longitudinal data to design an adaptive intensive intervention is provided. The methods are evaluated via simulation. RESULTS Simulation results illustrate how the designed adaptive intensive intervention can result in improved outcomes with less treatment by providing treatment only when it is needed. Furthermore, the methods are robust to model misspecification as well as the influence of unobserved causes. CONCLUSIONS These new methods can be used to design adaptive interventions that are effective yet reduce participant burden.

Parsimonious model identification via atomic norm minimization

During the past few years a considerably research effort has been devoted to the problem of identifying parsimonious models from experimental data. Since this problem is generically non-convex, these approaches typically rely on relaxations such as Group Lasso or nuclear norm minimization. However, while these approaches usually work well in practice, there is no guarantee that using these surrogates will lead to the simplest model explaining the experimental data. In addition, incorporating stability constraints into the formalism entails a substantial increase in the computational complexity. Alternatively stability and model order constraints can be handled directly using a moments based approach. However, presently this approach is limited to relatively small sized problems, due to its computational complexity. Motivated by these difficulties, recently a new approach has been proposed based on the idea of representing the response of an LTI system as a linear combination of suitably chosen objects (atoms) and the observation that minimizing the atomic norm leads to sparse representations. In this paper we cover the fundamentals of this new approach and show that it leads to a very efficient algorithm, that avoids the need for using regularization steps and automatically incorporates stability constraints. In addition, this approach can be extended to accommodate non-uniform sampling and (unknown) initial conditions. These results are illustrated with several examples, including identification of a very lightly damped structure from time and frequency domain measurements.

Control Engineering Methods for the Design of Robust Behavioral Treatments

In this paper, a robust control approach is used to address the problem of adaptive behavioral treatment design. Human behavior (e.g., smoking and exercise) and reactions to treatment are complex and depend on many unmeasurable external stimuli, some of which are unknown. Thus, it is crucial to model human behavior over many subject responses. We propose a simple (low order) uncertain affine model subject to uncertainties whose response covers the most probable behavioral responses. The proposed model contains two different types of uncertainties: uncertainty of the dynamics and external perturbations that patients face in their daily life. Once the uncertain model is defined, we demonstrate how least absolute shrinkage and selection operator (lasso) can be used as an identification tool. The lasso algorithm provides a way to directly estimate a model subject to sparse perturbations. With this estimated model, a robust control algorithm is developed, where one relies on the special structure of the uncertainty to develop efficient optimization algorithms. This paper concludes by using the proposed algorithm in a numerical experiment that simulates treatment for the urge to smoke.

A robust MPC approach to the design of behavioural treatments

The objective of this paper is to provide some initial results on the application of control tools to the problem treatment design. Human behavior and reaction to treatment is complex and dependent on many unmeasurable external stimuli. Therefore, to the best of our knowledge, it cannot be described by simple models. Hence, one of the main messages in this paper is that, to design a treatment (controller) one cannot rely on exact models. More precisely, to be able to design effective treatments, we propose to use “simple” uncertain affine models whose response “covers” the most probable subject responses. So, we propose a simple model that contains two different types of uncertainties: one aimed at uncertainty of the dynamics and another aimed at approximating external perturbations that patients face in their daily life. With this model at hand, we design a robust model predictive controller, where one relies on the special structure of the uncertainty to develop efficient optimization algorithms.

A Randomized Algorithm for Parsimonious Model Identification

Identifying parsimonious models is generically a “hard” nonconvex problem. Available approaches typically rely on relaxations such as Group Lasso or nuclear norm minimization. Moreover, incorporating stability and model order constraints into the formalism in such methods entails a substantial increase in computational complexity. Motivated by these challenges, in this paper we present algorithms for parsimonious linear time invariant system identification aimed at identifying low-complexity models which i) incorporate a priori knowledge on the system (e.g., stability), ii) allow for data with missing/nonuniform measurements, and iii) are able to use data obtained from several runs of the system with different unknown initial conditions. The randomized algorithms proposed are based on the concept of atomic norm and provide a numerically efficient way to identify sparse models from large amounts of noisy data.

Vision based control of an autonomous blimp with actuator saturation using pulse-width modulation

This paper demonstrates an effective way to track any targeted object with unmanned aerial vehicle (UAV) by using Continuously Adaptive Mean Shift (Camshift) Algorithm, Proportional-Derivative (PD) controller and Pulse Width modulation (PWM). The approach proposed in this paper is applied to a blimp equipped with a Wireless video Camera and radio controlled propellers. When determining the model that best describes the behaviour of the blimp, it was found that a good approximation of the behaviour is accomplished by a model that includes saturations in velocity and actuation. The controller proposed is designed in two steps: first, one determines a PD controller that satisfies the specifications for the model without saturations. Then, PWM is used to address the effect of nonlinearities.

Low-order model identification of MIMO systems from noisy and incomplete data

In this paper, we provide preliminary results aimed at solving the following problem: Given a priori information on Multi-Input/Multi-Output (MIMO) plant, namely constraints on the pole location, and scattered input/output data, find the lowest order model that is compatible with both the a priori assumptions and the collected data. By combining concepts from signal sparsification and subspace identification, algorithms are developed that can determine a low order model from data that is both corrupted by measurement noise and has missing measurements. Effectiveness of the proposed approach is shown by an academic example.