System identification of rhythmic hybrid dynamical systems via discrete time harmonic transfer functions

Ankaralı, Mustafa Mert; Cowan, Noah J.

doi:10.1109/cdc.2014.7039515

Cited by 11 publications

(22 citation statements)

References 15 publications

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“…Our method is based on existing theory for linear time-periodic systems (e.g., Wereley and Hall, 1990; Möllerstedt and Bernhardsson, 2000; Sandberg et al, 2005) extended for general limit-cycle systems in which perturbations can reset the phase of the oscillator. Our method assumes that the system has smooth dynamics (see Ankarali and Cowan, 2014 for a method designed for hybrid LTP systems). The goal of the analysis is to describe the effect of u ( t ), a visual scene velocity or motor position perturbation, on y ( t ), a kinematic or sEMG response variable.…”

Section: Methodsmentioning

confidence: 99%

Using a System Identification Approach to Investigate Subtask Control during Human Locomotion

Logan

Kiemel

Jeka

2017

Front. Comput. Neurosci.

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Here we apply a control theoretic view of movement to the behavior of human locomotion with the goal of using perturbations to learn about subtask control. Controlling one's speed and maintaining upright posture are two critical subtasks, or underlying functions, of human locomotion. How the nervous system simultaneously controls these two subtasks was investigated in this study. Continuous visual and mechanical perturbations were applied concurrently to subjects (n = 20) as probes to investigate these two subtasks during treadmill walking. Novel application of harmonic transfer function (HTF) analysis to human motor behavior was used, and these HTFs were converted to the time-domain based representation of phase-dependent impulse response functions (ϕIRFs). These ϕIRFs were used to identify the mapping from perturbation inputs to kinematic and electromyographic (EMG) outputs throughout the phases of the gait cycle. Mechanical perturbations caused an initial, passive change in trunk orientation and, at some phases of stimulus presentation, a corrective trunk EMG and orientation response. Visual perturbations elicited a trunk EMG response prior to a trunk orientation response, which was subsequently followed by an anterior-posterior displacement response. This finding supports the notion that there is a temporal hierarchy of functional subtasks during locomotion in which the control of upper-body posture precedes other subtasks. Moreover, the novel analysis we apply has the potential to probe a broad range of rhythmic behaviors to better understand their neural control.

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Section: Methodsmentioning

confidence: 99%

Using a System Identification Approach to Investigate Subtask Control during Human Locomotion

Logan

Kiemel

Jeka

2017

Front. Comput. Neurosci.

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“…This follows sinceŪ d = K in the z-domain corresponds to a single cosine input signal for the time-domain signal. (We write the input as in (19) (14). To achieve our goal, we first write the steady-state solutions for each output signal as…”

Section: Transforming To a Real-valued State-space Modelmentioning

confidence: 99%

“…Most existing literature on LTP system identification [2,11], including our own prior work on identification of legged locomotion [12][13][14], focuses on using input-output HTF representations rather than state space. In addition, there are also contributions to state-space-based system identification for LTP systems [15,16], analogous to subspace identificatioṅ techniques commonly used for linear time-invariant (LTI) systems [17].…”

Section: Introductionmentioning

confidence: 99%

Frequency-Domain Subspace Identification of Linear Time-Periodic (LTP) Systems

Uyanik

Saranlı

Ankaralı

et al. 2019

IEEE Trans. Automat. Contr.

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This paper proposes a new methodology for subspace-based state-space identification for linear time-periodic (LTP) systems. Since LTP systems can be lifted to equivalent linear time-invariant (LTI) systems, we first lift input-output data from the unknown LTP system as if it was collected from an equivalent LTI system. Then, we use frequency-domain subspace identification methods to find an LTI system estimate. Subsequently, we propose a novel method to obtain a time-periodic realization for the estimated lifted LTI system by exploiting the specific parametric structure of Fourier series coefficients of the frequency-domain lifting method. Our method can be used to both obtain state-space estimates for unknown LTP systems as well as to obtain Floquet transforms for known LTP systems.

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“…Initial formulations of this type of systems are generally modeled as nonlinear hybrid dynamical * Correspondence: uyanik@jhu.edu This work is licensed under a Creative Commons Attribution 4.0 International License. systems that include some state-dependent scheduling functions [12][13][14][15]. However, a vast majority of the system identification studies for such systems focus on their local behavior around a periodic orbit.…”

Section: Introductionmentioning

confidence: 99%

State-space identification of switching linear discrete time-periodic systems with known scheduling signals

Uyanik

Hamzaçebi

Ankaralı

2019

Turk J Elec Eng & Comp Sci

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In this paper, we propose a novel frequency domain state-space identification method for switching linear discrete time-periodic (LDTP) systems with known scheduling signals. The state-space identification problem of linear time-invariant (LTI) systems has been widely studied both in the time and frequency domains. Indeed, there have been several studies that also concentrated on state-space identification of both continuous and discrete linear time-periodic (LTP) systems. The focus in this study is the family of LDTP systems that switch among a finite set of subsystems triggered by known periodic scheduling signals. We address the state-space identification of such systems in frequency domain using input-output data. We also assume that full state measurements are available for the identification process.The major difference of our study is that we explicitly model the known scheduling signals responsible for switching, which greatly reduces the parametric complexity as well as potentially increases the estimation accuracy by avoiding overfitting. In our identification framework, we gather the Fourier transformations of input-output data, known periodic scheduling signals, and state-space system dimensions and fuse them in a linear regression framework. Later, we estimate the Fourier series coefficients of the time-periodic system and input matrices using a least-squares solution. Finally, we illustrate the effectiveness of our method using a switching LDTP system that is based on the damped Mathieu equation.

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System identification of rhythmic hybrid dynamical systems via discrete time harmonic transfer functions

Cited by 11 publications

References 15 publications

Using a System Identification Approach to Investigate Subtask Control during Human Locomotion

Using a System Identification Approach to Investigate Subtask Control during Human Locomotion

Frequency-Domain Subspace Identification of Linear Time-Periodic (LTP) Systems

State-space identification of switching linear discrete time-periodic systems with known scheduling signals

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