Matching Items (7)
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- All Subjects: System identification
- All Subjects: Dynamical Systems
- Creators: Platte, Rodrigo
- Creators: Si, Jennie
Description
Increasing interest in individualized treatment strategies for prevention and treatment of health disorders has created a new application domain for dynamic modeling and control. Standard population-level clinical trials, while useful, are not the most suitable vehicle for understanding the dynamics of dosage changes to patient response. A secondary analysis of intensive longitudinal data from a naltrexone intervention for fibromyalgia examined in this dissertation shows the promise of system identification and control. This includes datacentric identification methods such as Model-on-Demand, which are attractive techniques for estimating nonlinear dynamical systems from noisy data. These methods rely on generating a local function approximation using a database of regressors at the current operating point, with this process repeated at every new operating condition. This dissertation examines generating input signals for data-centric system identification by developing a novel framework of geometric distribution of regressors and time-indexed output points, in the finite dimensional space, to generate sufficient support for the estimator. The input signals are generated while imposing “patient-friendly” constraints on the design as a means to operationalize single-subject clinical trials. These optimization-based problem formulations are examined for linear time-invariant systems and block-structured Hammerstein systems, and the results are contrasted with alternative designs based on Weyl's criterion. Numerical solution to the resulting nonconvex optimization problems is proposed through semidefinite programming approaches for polynomial optimization and nonlinear programming methods. It is shown that useful bounds on the objective function can be calculated through relaxation procedures, and that the data-centric formulations are amenable to sparse polynomial optimization. In addition, input design formulations are formulated for achieving a desired output and specified input spectrum. Numerical examples illustrate the benefits of the input signal design formulations including an example of a hypothetical clinical trial using the drug gabapentin. In the final part of the dissertation, the mixed logical dynamical framework for hybrid model predictive control is extended to incorporate a switching time strategy, where decisions are made at some integer multiple of the sample time, and manipulation of only one input at a given sample time among multiple inputs. These are considerations important for clinical use of the algorithm.
ContributorsDeśapāṇḍe, Sunīla (Author) / Rivera, Daniel E. (Thesis advisor) / Peet, Matthew M. (Committee member) / Si, Jennie (Committee member) / Tsakalis, Konstantinos S. (Committee member) / Arizona State University (Publisher)
Created2014
Description
This thesis describes an approach to system identification based on compressive sensing and demonstrates its efficacy on a challenging classical benchmark single-input, multiple output (SIMO) mechanical system consisting of an inverted pendulum on a cart. Due to its inherent non-linearity and unstable behavior, very few techniques currently exist that are capable of identifying this system. The challenge in identification also lies in the coupled behavior of the system and in the difficulty of obtaining the full-range dynamics. The differential equations describing the system dynamics are determined from measurements of the system's input-output behavior. These equations are assumed to consist of the superposition, with unknown weights, of a small number of terms drawn from a large library of nonlinear terms. Under this assumption, compressed sensing allows the constituent library elements and their corresponding weights to be identified by decomposing a time-series signal of the system's outputs into a sparse superposition of corresponding time-series signals produced by the library components. The most popular techniques for non-linear system identification entail the use of ANN's (Artificial Neural Networks), which require a large number of measurements of the input and output data at high sampling frequencies. The method developed in this project requires very few samples and the accuracy of reconstruction is extremely high. Furthermore, this method yields the Ordinary Differential Equation (ODE) of the system explicitly. This is in contrast to some ANN approaches that produce only a trained network which might lose fidelity with change of initial conditions or if facing an input that wasn't used during its training. This technique is expected to be of value in system identification of complex dynamic systems encountered in diverse fields such as Biology, Computation, Statistics, Mechanics and Electrical Engineering.
ContributorsNaik, Manjish Arvind (Author) / Cochran, Douglas (Thesis advisor) / Kovvali, Narayan (Committee member) / Kawski, Matthias (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2011
Description
There is increasing interest in the medical and behavioral health communities towards developing effective strategies for the treatment of chronic diseases. Among these lie adaptive interventions, which consider adjusting treatment dosages over time based on participant response. Control engineering offers a broad-based solution framework for optimizing the effectiveness of such interventions. In this thesis, an approach is proposed to develop dynamical models and subsequently, hybrid model predictive control schemes for assigning optimal dosages of naltrexone, an opioid antagonist, as treatment for a chronic pain condition known as fibromyalgia. System identification techniques are employed to model the dynamics from the daily diary reports completed by participants of a blind naltrexone intervention trial. These self-reports include assessments of outcomes of interest (e.g., general pain symptoms, sleep quality) and additional external variables (disturbances) that affect these outcomes (e.g., stress, anxiety, and mood). Using prediction-error methods, a multi-input model describing the effect of drug, placebo and other disturbances on outcomes of interest is developed. This discrete time model is approximated by a continuous second order model with zero, which was found to be adequate to capture the dynamics of this intervention. Data from 40 participants in two clinical trials were analyzed and participants were classified as responders and non-responders based on the models obtained from system identification. The dynamical models can be used by a model predictive controller for automated dosage selection of naltrexone using feedback/feedforward control actions in the presence of external disturbances. The clinical requirement for categorical (i.e., discrete-valued) drug dosage levels creates a need for hybrid model predictive control (HMPC). The controller features a multiple degree-of-freedom formulation that enables the user to adjust the speed of setpoint tracking, measured disturbance rejection and unmeasured disturbance rejection independently in the closed loop system. The nominal and robust performance of the proposed control scheme is examined via simulation using system identification models from a representative participant in the naltrexone intervention trial. The controller evaluation described in this thesis gives credibility to the promise and applicability of control engineering principles for optimizing adaptive interventions.
ContributorsDeśapāṇḍe, Sunīla (Author) / Rivera, Daniel E. (Thesis advisor) / Si, Jennie (Committee member) / Tsakalis, Konstantinos (Committee member) / Arizona State University (Publisher)
Created2011
Description
This thesis considers the application of basis pursuit to several problems in system identification. After reviewing some key results in the theory of basis pursuit and compressed sensing, numerical experiments are presented that explore the application of basis pursuit to the black-box identification of linear time-invariant (LTI) systems with both finite (FIR) and infinite (IIR) impulse responses, temporal systems modeled by ordinary differential equations (ODE), and spatio-temporal systems modeled by partial differential equations (PDE). For LTI systems, the experimental results illustrate existing theory for identification of LTI FIR systems. It is seen that basis pursuit does not identify sparse LTI IIR systems, but it does identify alternate systems with nearly identical magnitude response characteristics when there are small numbers of non-zero coefficients. For ODE systems, the experimental results are consistent with earlier research for differential equations that are polynomials in the system variables, illustrating feasibility of the approach for small numbers of non-zero terms. For PDE systems, it is demonstrated that basis pursuit can be applied to system identification, along with a comparison in performance with another existing method. In all cases the impact of measurement noise on identification performance is considered, and it is empirically observed that high signal-to-noise ratio is required for successful application of basis pursuit to system identification problems.
ContributorsThompson, Robert C. (Author) / Platte, Rodrigo (Thesis advisor) / Gelb, Anne (Committee member) / Cochran, Douglas (Committee member) / Arizona State University (Publisher)
Created2012
Description
A continuously and stably stratified fluid contained in a square cavity subjected to harmonic body forcing is studied numerically by solving the Navier-Stokes equations under the Boussinesq approximation. Complex dynamics are observed near the onset of instability of the basic state, which is a flow configuration that is always an exact analytical solution of the governing equations. The instability of the basic state to perturbations is first studied with linear stability analysis (Floquet analysis), revealing a multitude of intersecting synchronous and subharmonic resonance tongues in parameter space. A modal reduction method for determining the locus of basic state instability is also shown, greatly simplifying the computational overhead normally required by a Floquet study. Then, a study of the nonlinear governing equations determines the criticality of the basic state's instability, and ultimately characterizes the dynamics of the lowest order spatial mode by the three discovered codimension-two bifurcation points within the resonance tongue. The rich dynamics include a homoclinic doubling cascade that resembles the logistic map and a multitude of gluing bifurcations.
The numerical techniques and methodologies are first demonstrated on a homogeneous fluid contained within a three-dimensional lid-driven cavity. The edge state technique and linear stability analysis through Arnoldi iteration are used to resolve the complex dynamics of the canonical shear-driven benchmark problem. The techniques here lead to a dynamical description of an instability mechanism, and the work serves as a basis for the remainder of the dissertation.
The numerical techniques and methodologies are first demonstrated on a homogeneous fluid contained within a three-dimensional lid-driven cavity. The edge state technique and linear stability analysis through Arnoldi iteration are used to resolve the complex dynamics of the canonical shear-driven benchmark problem. The techniques here lead to a dynamical description of an instability mechanism, and the work serves as a basis for the remainder of the dissertation.
ContributorsYalim, Jason (Author) / Welfert, Bruno D. (Thesis advisor) / Lopez, Juan M. (Thesis advisor) / Jones, Donald (Committee member) / Tang, Wenbo (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2019
Description
The three-dimensional flow contained in a rapidly rotating circular
split cylinder is studied numerically solving the Navier--Stokes
equations. The cylinder is completely filled with fluid
and is split at the midplane. Three different types of boundary
conditions were imposed, leading to a variety of instabilities and
complex flow dynamics.
The first configuration has a strong background rotation and a small
differential rotation between the two halves. The axisymmetric flow
was first studied identifying boundary layer instabilities which
produce inertial waves under some conditions. Limit cycle states and
quasiperiodic states were found, including some period doubling
bifurcations. Then, a three-dimensional study was conducted
identifying low and high azimuthal wavenumber rotating waves due to
G’ortler and Tollmien–-Schlichting type instabilities. Over most of
the parameter space considered, quasiperiodic states were found where
both types of instabilities were present.
In the second configuration, both cylinder halves are in exact
counter-rotation, producing an O(2) symmetry in the system. The basic state flow dynamic
is dominated by the shear layer created
in the midplane. By changing the speed rotation and the aspect ratio
of the cylinder, the flow loses symmetries in a variety of ways
creating static waves, rotating waves, direction reversing waves and
slow-fast pulsing waves. The bifurcations, including infinite-period
bifurcations, were characterized and the flow dynamics was elucidated.
Additionally, preliminary experimental results for this case are
presented.
In the third set up, with oscillatory boundary conditions, inertial
wave beams were forced imposing a range of frequencies. These beams
emanate from the corner of the cylinder and from the split at the
midplane, leading to destructive/constructive interactions which
produce peaks in vorticity for some specific frequencies. These
frequencies are shown to be associated with the resonant Kelvin
modes. Furthermore, a study of the influence of imposing a phase
difference between the oscillations of the two halves of the cylinder
led to the interesting result that different Kelvin
modes can be excited depending on the phase difference.
split cylinder is studied numerically solving the Navier--Stokes
equations. The cylinder is completely filled with fluid
and is split at the midplane. Three different types of boundary
conditions were imposed, leading to a variety of instabilities and
complex flow dynamics.
The first configuration has a strong background rotation and a small
differential rotation between the two halves. The axisymmetric flow
was first studied identifying boundary layer instabilities which
produce inertial waves under some conditions. Limit cycle states and
quasiperiodic states were found, including some period doubling
bifurcations. Then, a three-dimensional study was conducted
identifying low and high azimuthal wavenumber rotating waves due to
G’ortler and Tollmien–-Schlichting type instabilities. Over most of
the parameter space considered, quasiperiodic states were found where
both types of instabilities were present.
In the second configuration, both cylinder halves are in exact
counter-rotation, producing an O(2) symmetry in the system. The basic state flow dynamic
is dominated by the shear layer created
in the midplane. By changing the speed rotation and the aspect ratio
of the cylinder, the flow loses symmetries in a variety of ways
creating static waves, rotating waves, direction reversing waves and
slow-fast pulsing waves. The bifurcations, including infinite-period
bifurcations, were characterized and the flow dynamics was elucidated.
Additionally, preliminary experimental results for this case are
presented.
In the third set up, with oscillatory boundary conditions, inertial
wave beams were forced imposing a range of frequencies. These beams
emanate from the corner of the cylinder and from the split at the
midplane, leading to destructive/constructive interactions which
produce peaks in vorticity for some specific frequencies. These
frequencies are shown to be associated with the resonant Kelvin
modes. Furthermore, a study of the influence of imposing a phase
difference between the oscillations of the two halves of the cylinder
led to the interesting result that different Kelvin
modes can be excited depending on the phase difference.
ContributorsGutierrez Castillo, Paloma (Author) / Lopez, Juan M. (Thesis advisor) / Herrmann, Marcus (Committee member) / Platte, Rodrigo (Committee member) / Welfert, Bruno (Committee member) / Tang, Wenbo (Committee member) / Arizona State University (Publisher)
Created2017
DescriptionUnderstanding the evolution of opinions is a delicate task as the dynamics of how one changes their opinion based on their interactions with others are unclear.
ContributorsWeber, Dylan (Author) / Motsch, Sebastien (Thesis advisor) / Lanchier, Nicolas (Committee member) / Platte, Rodrigo (Committee member) / Armbruster, Dieter (Committee member) / Fricks, John (Committee member) / Arizona State University (Publisher)
Created2021