Estimation of constant and time-varying dynamic parameters of HIV infection in a nonlinear differential equation model

Modeling viral dynamics in HIV/AIDS studies has resulted in a deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear differential equations have been proposed and well developed over the past few decades. However, it is quite challenging to use experimental or clinical data to estimate the unknown parameters (both constant and time-varying parameters) in complex nonlinear differential equation models. Therefore, investigators usually fix some parameter values, from the literature or by experience, to obtain only parameter estimates of interest from clinical or experimental data. However, when such prior information is not available, it is desirable to determine all the parameter estimates from data. In this paper we intend to combine the newly developed approaches, a multi-stage smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares (SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear differential equation model. In particular, to the best of our knowledge, this is the first attempt to propose a comparatively thorough procedure, accounting for both efficiency and accuracy, to rigorously estimate all key kinetic parameters in a nonlinear differential equation model of HIV dynamics from clinical data. These parameters include the proliferation rate and death rate of uninfected HIV-targeted cells, the average number of virions produced by an infected cell, and the infection rate which is related to the antiviral treatment effect and is time-varying. To validate the estimation methods, we verified the identifiability of the HIV viral dynamic model and performed simulation studies.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS290 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Motion Planning of Uncertain Ordinary Differential Equation Systems

This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems. Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs. The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space

Electron density retrieval from truncated Radio Occultation GNSS data

This paper summarizes the definition and validation of two complementary new strategies, to invert incomplete Global Navigation Satellite System Radio-Occultation (RO) ionospheric measurements, such as the ones to be provided by the future EUMETSAT Polar System Second Generation. It will provide RO measurements with impact parameter much below the Low Earth Orbiters' height (817 km): from 500 km down approximately. The first presented method to invert truncated RO data is denoted as Abel-VaryChap Hybrid modeling from topside Incomplete Global Navigation Satellite System RO data, based on simple First Principles, very precise, and well suited for postprocessing. And the second method is denoted as Simple Estimation of Electron density profiles from topside Incomplete RO data, is less precise, but yields very fast estimations, suitable for Near Real-Time determination. Both techniques will be described and assessed with a set of 546 representative COSMIC/FORMOSAT-3 ROs, with relative errors of 7% and 11% for Abel-VaryChap Hybrid modeling from topside Incomplete Global Navigation Satellite System RO data and Simple Estimation of Electron density profiles from topside Incomplete RO data, respectively, with 20 min and 15 s, respectively, of computational time per occultation in our Intel I7 PC.Peer ReviewedPostprint (published version

Adaptive hybrid optimization strategy for calibration and parameter estimation of physical models

A new adaptive hybrid optimization strategy, entitled squads, is proposed for complex inverse analysis of computationally intensive physical models. The new strategy is designed to be computationally efficient and robust in identification of the global optimum (e.g. maximum or minimum value of an objective function). It integrates a global Adaptive Particle Swarm Optimization (APSO) strategy with a local Levenberg-Marquardt (LM) optimization strategy using adaptive rules based on runtime performance. The global strategy optimizes the location of a set of solutions (particles) in the parameter space. The LM strategy is applied only to a subset of the particles at different stages of the optimization based on the adaptive rules. After the LM adjustment of the subset of particle positions, the updated particles are returned to the APSO strategy. The advantages of coupling APSO and LM in the manner implemented in squads is demonstrated by comparisons of squads performance against Levenberg-Marquardt (LM), Particle Swarm Optimization (PSO), Adaptive Particle Swarm Optimization (APSO; the TRIBES strategy), and an existing hybrid optimization strategy (hPSO). All the strategies are tested on 2D, 5D and 10D Rosenbrock and Griewank polynomial test functions and a synthetic hydrogeologic application to identify the source of a contaminant plume in an aquifer. Tests are performed using a series of runs with random initial guesses for the estimated (function/model) parameters. Squads is observed to have the best performance when both robustness and efficiency are taken into consideration than the other strategies for all test functions and the hydrogeologic application

Global Exponential Attitude Tracking Controls on SO(3)

This paper presents four types of tracking control systems for the attitude dynamics of a rigid body. First, a smooth control system is constructed to track a given desired attitude trajectory, while guaranteeing almost semi-global exponential stability. It is extended to achieve global exponential stability by using a hybrid control scheme based on multiple configuration error functions. They are further extended to obtain robustness with respect to a fixed disturbance using an integral term. The resulting robust, global exponential stability for attitude tracking is the unique contribution of this paper, and these are developed directly on the special orthogonal group to avoid singularities of local coordinates, or ambiguities associated with quaternions. The desirable features are illustrated by numerical examples

Disturbance Observer-based Robust Control and Its Applications: 35th Anniversary Overview

Disturbance Observer has been one of the most widely used robust control tools since it was proposed in 1983. This paper introduces the origins of Disturbance Observer and presents a survey of the major results on Disturbance Observer-based robust control in the last thirty-five years. Furthermore, it explains the analysis and synthesis techniques of Disturbance Observer-based robust control for linear and nonlinear systems by using a unified framework. In the last section, this paper presents concluding remarks on Disturbance Observer-based robust control and its engineering applications.Comment: 12 pages, 4 figure