Sunil Deshpande

A control engineering approach for designing an optimized treatment plan for fibromyalgia

Control engineering offers a systematic and efficient means for optimizing the effectiveness of behavioral interventions. In this paper, we present an approach to develop dynamical models and subsequently, hybrid model predictive control schemes for assigning optimal dosages of naltrexone as treatment for a chronic pain condition known as fibromyalgia. We apply system identification techniques to develop models from daily diary reports completed by participants of a naltrexone intervention trial. The dynamic model serves as the basis for applying model predictive control as a decision algorithm for automated dosage selection of naltrexone in the face of the external disturbances. The categorical/discrete nature of the dosage assignment creates a need for hybrid model predictive control (HMPC) schemes. Simulation results that include conditions of significant plant-model mismatch demonstrate the performance and applicability of hybrid predictive control for optimized adaptive interventions for fibromyalgia treatment involving naltrexone.

Towards Patient-Friendly Input Signal Design for Optimized Pain Treatment Interventions

Abstract We examine some of the challenges associated with generating input signals for identifying dynamics in pain treatment interventions while imposing “patient-friendly” constraints on the design. Standard clinical trials, while providing some useful information, are not the most suitable vehicle for understanding the dynamic response of dosage changes to participant response. Meanwhile, much of the work in classical input design, even that which incorporates “plant-friendly” considerations, may not result in clinically acceptable trials for human participants. In this paper, we describe some of the issues involved and suggest various approaches (leading ultimately to optimization-based formulations) to obtain input signals with desired spectral properties under time-domain constraints of importance to clinical practice. Numerical examples are shown to illustrate the proposed method with a hypothetical clinical trial of the drug gabapentin for the treatment of neuropathic pain.

A control systems engineering approach for adaptive behavioral interventions: illustration with a fibromyalgia intervention.

The term adaptive intervention has been used in behavioral medicine to describe operationalized and individually tailored strategies for prevention and treatment of chronic, relapsing disorders. Control systems engineering offers an attractive means for designing and implementing adaptive behavioral interventions that feature intensive measurement and frequent decision-making over time. This is illustrated in this paper for the case of a low-dose naltrexone treatment intervention for fibromyalgia. System identification methods from engineering are used to estimate dynamical models from daily diary reports completed by participants. These dynamical models then form part of a model predictive control algorithm which systematically decides on treatment dosages based on measurements obtained under real-life conditions involving noise, disturbances, and uncertainty. The effectiveness and implications of this approach for behavioral interventions (in general) and pain treatment (in particular) are demonstrated using informative simulations.

A system identification approach for improving behavioral interventions based on Social Cognitive Theory

Mobile and wireless health (mHealth) interventions offer the opportunity for applying control engineering and system identification concepts in behavioral change settings. Social Cognitive Theory provides a recognized theoretical framework that can be applied to explain changes in behavior over time. Based on earlier work describing a dynamical model of this theory, a semi-physical system identification approach is developed in this paper for interventions associated with improving physical activity. An initial informative experiment that relies on prior knowledge from similar interventions is first designed to obtain basic insights regarding the dynamics of the system. Based on these results a second, optimized experiment is developed which solves a constrained optimization problem to find the intervention component profiles needed to mirror a desired behavioral pattern and to provide sufficient information that allows a more precise estimation of the parameters. A simulation study is presented to illustrate the design procedure.

Hybrid model predictive control for sequential decision policies in adaptive behavioral interventions

Control engineering offers a systematic and efficient method to optimize the effectiveness of individually tailored treatment and prevention policies known as adaptive or “just-in-time” behavioral interventions. The nature of these interventions requires assigning dosages at categorical levels, which has been addressed in prior work using Mixed Logical Dynamical (MLD)-based hybrid model predictive control (HMPC) schemes. However, certain requirements of adaptive behavioral interventions that involve sequential decision making have not been comprehensively explored in the literature. This paper presents an extension of the traditional MLD framework for HMPC by representing the requirements of sequential decision policies as mixed-integer linear constraints. This is accomplished with user-specified dosage sequence tables, manipulation of one input at a time, and a switching time strategy for assigning dosages at time intervals less frequent than the measurement sampling interval. A model developed for a gestational weight gain (GWG) intervention is used to illustrate the generation of these sequential decision policies and their effectiveness for implementing adaptive behavioral interventions involving multiple components.

Optimal input signal design for data-centric estimation methods

Data-centric estimation methods such as Model-on-Demand and Direct Weight Optimization form attractive techniques for estimating unknown functions from noisy data. These methods rely on generating a local function approximation from a database of regressors at the current operating point with the process repeated at each new operating point. This paper examines the design of optimal input signals formulated to produce informative data to be used by local modeling procedures. The proposed method specifically addresses the distribution of the regressor vectors. The design is examined for a linear time-invariant system under amplitude constraints on the input. The resulting optimization problem is solved using semidefinite relaxation methods. Numerical examples show the benefits in comparison to a classical PRBS input design.

LPV system identification using a separable least squares support vector machines approach

In this article, an algorithm to identify LPV State Space models for both continuous-time and discrete-time systems is proposed. The LPV state space system is in the Companion Reachable Canonical Form. The output vector coefficients are linear combinations of a set of a possibly infinite number of nonlinear basis functions dependent on the scheduling signal, the state matrix is either time invariant or a linear combination of a finite number of basis functions of the scheduling signal and the input vector is time invariant. This model structure, although simple, can describe accurately the behaviour of many nonlinear SISO systems by an adequate choice of the scheduling signal. It also partially solves the problems of structural bias caused by inaccurate selection of the basis functions and high variance of the estimates due to over-parameterisation. The use of an infinite number of basis functions in the output vector increases the flexibility to describe complex functions and makes it possible to learn the underlying dependencies of these coefficients from the data. A Least Squares Support Vector Machine (LS-SVM) approach is used to address the infinite dimension of the output coefficients. Since there is a linear dependence of the output on the output vector coefficients and, on the other hand, the LS-SVM solution is a nonlinear function of the state and input matrix coefficients, the LPV system is identified by minimising a quadratic function of the output function in a reduced parameter space; the minimisation of the error is performed by a separable approach where the parameters of the fixed matrices are calculated using a gradient method. The derivatives required by this algorithm are the output of either an LTI or an LPV (in the case of a time-varying SS matrix) system, that need to be simulated at every iteration. The effectiveness of the algorithm is assessed on several simulated examples.

Constrained Optimal Input Signal Design for Data-Centric Estimation Methods

This technical note examines the design of constrained input signals for data-centric estimation methods which systematically generate a local function approximation from a database of regressors at a current operating point. The proposed method addresses the optimal distribution of regressor vectors under constraints for a linear time-invariant (LTI) system. The resulting nonconvex optimization problems are solved using semidefinite relaxation methods. Numerical examples illustrate the benefits and usefulness of the proposed input signal design formulations.

A data-centric system identification approach to input signal design for Hammerstein systems

This paper examines the design of input signals for identification of Hammerstein systems in a data-centric framework by addressing the optimal distribution of regressors. Data-centric estimation methods such as Model-on-Demand (MoD) generate local function approximations from a database of regressors at the current operating point. The data-centric input signal design formulation aims to develop sufficient support in the regressor space for the MoD estimator, while addressing time-domain constraints on the input and output signals. A numerical example is shown to highlight the benefit of proposed design over classical Pseudo Random Binary Sequence (PRBS), Multi Level Pseudo Random Sequence (MLPRS) and uniform random input designs.

Identification of affine linear parameter varying models for adaptive interventions in fibromyalgia treatment

There is good evidence that naltrexone, an opioid antagonist, has a strong neuroprotective role and may be a potential drug for the treatment of fibromyalgia. In previous work, some of the authors used experimental clinical data to identify input-output linear time invariant models that were used to extract useful information about the effect of this drug on fibromyalgia symptoms. Additional factors such as anxiety, stress, mood, and headache, were considered as additive disturbances. However, it seems reasonable to think that these factors do not affect the drug actuation, but only the way in which a participant perceives how the drug actuates on herself. Under this hypothesis the linear time invariant models can be replaced by State-Space Affine Linear Parameter Varying models where the disturbances are seen as a scheduling signal signal only acting at the parameters of the output equation. In this paper a new algorithm for identifying such a model is proposed. This algorithm minimizes a quadratic criterion of the output error. Since the output error is a linear function of some parameters, the Affine Linear Parameter Varying system identification is formulated as a separable nonlinear least squares problem. Likewise other identification algorithms using gradient optimization methods several parameter derivatives are dynamical systems that must be simulated. In order to increase time efficiency a canonical parametrization that minimizes the number of systems to be simulated is chosen. The effectiveness of the algorithm is assessed in a case study where an Affine Parameter Varying Model is identified from the experimental data used in the previous study and compared with the time-invariant model.