Harish J. Palanthandalam-Madapusi

Recursive input reconstruction with a delay

The unknown inputs in a dynamical system may represent unknown external drivers, input uncertainty, state uncertainty, or instrument faults and thus unknown-input reconstruction has several wide-spread applications. In this paper we consider recursive reconstruction of unknown inputs with a delay for both square and non-square systems. That is, we develop filters that use current measurements to estimate past states and reconstruct past inputs. We further develop convergence results for these filters and show that the convergence of these filters are related to multivariable zeros of the systems. Finally we also show that existing unbiased minimum-variance filters are special cases of the proposed filters.

Constitutive-Law Modeling of Microfilaments From Their Discrete-Structure Simulations—A Method Based on an Inverse Approach Applied to a Static Rod Model

Twisting and bending deformations are crucial to the biological functions of several microfilaments such as DNA molecules. Although continuum-rod models have emerged as efficient tools to describe the nonlinear dynamics of these deformations, a major roadblock in the continuum–mechanics-based description of microfilaments is the accurate modeling of the constitutive law, which follows from their atomistic-level structure and interactions. In this paper, we present a method for estimating the constitutive law using a static rod model and deformed configuration data generated from discrete-structure simulations. Furthermore, we illustrate the method on a filament with an artificial discrete-structure. We simulate its deformation in response to a prescribed loading using a multibody dynamics (MBD) solver. Using position data generated from the MBD solver, we first estimate the curvature of the filament, and subsequently use it to estimate the effective relationship between the restoring moment and curvature.

Clinical Facts Along With a Feedback Control Perspective Suggest That Increased Response Time Might Be the Cause of Parkinsonian Rest Tremor

Vrutangkumar V. Shah SysIDEA Lab, Mechanical Engineering, Indian Institute of Technology Gandhinagar, Gandhinagar 382355, India e-mail: shah_vrutangkumar@iitgn.ac.in Sachin Goyal 1 Assistant Professor Department of Mechanical Engineering, University of California, Merced, CA 95343 e-mail: sachin.goyal@ucmerced.edu Harish J. Palanthandalam- Madapusi Assistant Professor SysIDEA Lab, Mechanical Engineering, Indian Institute of Technology Gandhinagar, Gandhinagar 382355, India e-mail: harish@iitgn.ac.in Clinical Facts Along With a Feedback Control Perspective Suggest That Increased Response Time Might Be the Cause of Parkinsonian Rest Tremor Parkinson’s disease (PD) is a neurodegenerative disorder characterized by increased response times leading to a variety of biomechanical symptoms, such as tremors, stoop- ing, and gait instability. Although the deterioration in biomechanical control can intui- tively be related to sluggish response times, how the delay leads to such biomechanical symptoms as tremor is not yet understood. Only recently has it been explained from the perspective of feedback control theory that delay beyond a threshold can be the cause of Parkinsonian tremor (Palanthandalam-Madapusi and Goyal, 2011, “Is Parkinsonian Tremor a Limit Cycle?” J. Mech. Med. Biol., 11(5), pp. 1017–1023). The present paper correlates several observations from this perspective to clinical facts and reinforces them with simple numerical and experimental examples. Thus, the present work provides a framework toward developing a deeper conceptual understanding of the mechanism behind PD symptoms. Furthermore, it lays a foundation for developing tools for diagno- sis and progress tracking of the disease by identifying some key trends. [DOI: 10.1115/1.4034050] Introduction Patients suffering from PD experience a variety of biomechani- cal symptoms including tremors, stooping, rigidity, and gait insta- bility [1]. Since the discovery of this disease in 1817 [2], the connections between these apparently unrelated biomechanical symptoms have puzzled researchers and have led to a range of hypotheses and conjectures about the source of these symptoms [3,4], and it is not clear whether there is a single underlying expla- nation for these symptoms [5,6]. PD is a neurodegenerative disor- der and is also characterized by a permanent increase in response time in both voluntary and involuntary motor responses. The impairment of response time in PD was first noted in Ref. [7], stat- ing, “recent measurements with special apparatus for muscular response to a single visual stimulus have given the figures of 0.24 s for normal individuals and 0.36 s for the subjects with paralysis agitans.” Several detailed studies since then have come up with similar conclusions [8–11]. This has added another dimension to the mystery surrounding the symptoms. Although the deterioration in biomechanical control can intui- tively be related to sluggish response times, how the increase in response time leads to such biomechanical symptoms as tremors is not yet understood [12]. In fact, it is argued that Parkinsonian tremor may have a pathophysiology different from most other symptoms of the disease [3,4]. Neuroprosthetic therapies such as deep brain stimulation [13] suppress Parkinsonian tremor, how- ever, the fundamental mechanism behind these therapies is also unresolved [14]. On another front, empirical mathematical models are proposed, which can simulate Parkinsonian tremor, for instance, a limit- Corresponding author. Contributed by the Design Engineering Division of ASME for publication in the J OURNAL OF C OMPUTATIONAL AND N ONLINEAR D YNAMICS . Manuscript received November 25, 2015; final manuscript received June 24, 2016; published online September 1, 2016. Assoc. Editor: Sotirios Natsiavas. cycle-exhibiting system such as the Van Der Pol oscillator can be fit to experimentally measured data [15]. But such an approach lacks physical underpinnings and does not provide any insights into some of the other key features of Parkinsonian tremor. For example, why a PD patient trying to keep still would exhibit trem- ors (referred to as rest tremors) [1], whereas these tremors would often disappear during voluntary motion [3], is not explained by such models. Recently, arguments based on a control-system anal- ogy were used to support the hypothesis that Parkinsonian tremor may indeed be a limit-cycle oscillation [16] and established a direct logical connection between increased response time and limit-cycle behavior of Parkinsonian tremor. Since then, similar connections between increased time delays and limit-cycle oscil- lations in human biomechanics (although not necessarily in the context of PD) have also been drawn [17–19]. In this paper, we exploit this link between increased time delays (observed as an increase in response times) and Parkinsonian tremors to address two specific objectives (see Fig. 1). First, we wish to draw qualitative observations based on this hypothesis that are supported by clinical facts, explained using feedback con- trol theory, and reproduced by simple numerical and experimental Fig. 1 The contributions of this work Journal of Computational and Nonlinear Dynamics C 2017 by ASME Copyright V JANUARY 2017, Vol. 12 / 011007-1 Downloaded From: https://computationalnonlinear.asmedigitalcollection.asme.org/ on 09/10/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use

Diagnosis of Parkinson's disease: A limit cycle approach

Parkinsons disease is characterized by increased reaction times in both voluntary and involuntary motor responses and often results in unintended oscillatory motion of body parts, termed as Parkinsonian tremor. A simple and efficient method for diagnosing Parkinsons disease is still not available and furthermore, on the correct diagnosis of Parkinsons disease, estimating the severity of the disease is challenging. This is particularly important since the medications typically prescribed to address the symptoms of Parkinsons disease have adverse side effects and thus the dosages have to be finely optimized. In this paper, based on a systems theory perspective and a recently suggested control-system analogy [11], a simple method for the diagnosis of Parkinsons disease is explored. This paper also discusses the possibility of developing a low-cost diagnostic device and strategies for the same. Future work will focus on using data from real patients to validate the hypotheses and results in this paper.

Backward-in-time input reconstruction

Input reconstruction is the problem of reconstructing unknown inputs to the system, be it deterministic or stochastic or a combination of both, from knowledge of plant model and the output measurements alone. Being a fundamental and long-standing problem, the literature on this topic is extensive, but is also somewhat fragmented. Furthermore, connections between feasibility of input reconstruction and zeros of the system have been established in the literature. In this paper, we explore possible methods to reconstruct inputs for systems with non-minimum phase zeros. Although the existing literature suggests that in the presence of non-minimum phase zeros, any estimator will yield an error that grows in time, we are able to overcome this problem by developing an estimator that goes backward in time.

Command following using an input reconstruction approach

The idea we explore in this paper is whether we can use input reconstruction methods for control problems. In input reconstruction problems, the outputs of a dynamical system are known, and the objective is to reconstruct the inputs to the system that caused the measured outputs. Command following problems can be viewed from a similar perspective. The desired outputs of the system are known and the control inputs that would yield those desired outputs have to be determined. In that sense, by implicitly assuming that a control input exists such that the output of the system will be equal to the desired output, one can use input reconstruction to determine the corresponding control inputs by pretending that the the desired outputs are the actual outputs of the system. With this end in view we explore a few control schemes based on the filter-based approach to input reconstruction and demonstrate the efficacy of these methods with illustrative numerical examples.

LETTER TO EDITORS — SOLVING FOR CANTILEVER EQUILIBRIA AS INITIAL VALUE PROBLEMS

Large nonlinear deformations of the Kirchhoff rod involving bending and twistingare traditionally simulated by solving the equations of rod equilibria directly fordeflections or displacement fields, often using finite element methods. In thisapproach, solving for the deformations of the rod subject to loading conditionsensues solving a boundary value problem irrespective of the numerical methodschosen for solving such problems. This note highlights an alternative approach thatsimplifies solving for the deformations. This alternative approach leads to an initialvalue problem for cantilever-type (fixed-free) boundary conditions with material-fixed loads.The alternative approach builds upon the following form of the equations ofKirchhoff rod equilibria

Computational Rod Model With User-Defined Nonlinear Constitutive Laws

Author(s): Fatehiboroujeni, Soheil; Palanthandalam-Madapusi, Harish J; Goyal, Sachin | Abstract: Computational rod models have emerged as efficient tools to simulate the bending and twisting deformations of a variety of slender structures in engineering and biological applications. The dynamics of such deformations, however, strongly depends on the constitutive law in bending and torsion that, in general, may be nonlinear, and vary from material to material. Jacobian-based computational rod models require users to change the Jacobian if the functional form of the constitutive law is changed, and hence are not user-friendly. This paper presents a scheme that automatically modifies the Jacobian based on any user-defined constitutive law without requiring symbolic differentiation. The scheme is then used to simulate force-extension behavior of a coiled spring with a softening constitutive law.

Revisiting trackability for linear time-invariant systems

The paper revisits a fundamental and important concept of trackability that deals with the ability of a system to track reference commands. While drawing on the literature, on related concepts, a new treatment is provided in the context of LTI systems. Conditions are provided for checking the trackability of systems. This work may form the basis for further in-depth investigation on these concepts both for linear and non-linear systems.

Estimating Constitutive Law of a Filament From its Deformed Shapes Using Input Reconstruction

Twisting and bending dynamics of biological filaments such as DNA play a central role in their biological activity including gene expression. The elastic rod model is an efficient tool to simulate such deformations. However, the accuracy of elastic rod predictions depend strongly on the constitutive law, which follows from the atomistic structure of the DNA molecule and is known to be nonlinear and to vary along the length according to the base pair sequence of the DNA. Unfortunately, it is impractical to derive the constitutive law analytically from the atomistic structure. Identification of the nonlinear sequence-dependent constitutive law from experimental data and feasible molecular dynamics simulations remains a significant challenge. In this paper, we extend earlier work by employing techniques based on input reconstruction and state estimation filters to estimate the constitutive law using molecular dynamics data of deformations in bio-filaments.Copyright