Related Experiment Video
Updated: Jul 17, 2026
06:44
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
Published on: September 23, 2025
Identification of Linear Time Varying Systems using Basis Pursuit
Sreemoyi Sanyal1, Sunil Kukreja, Eric Perreault
1Department of Electrical and Computer Engineering, University of Calgary, 2500 University Dr. NW, Calgary, AB, T2N 1N4 Canada, sanyals@ucalgary.ca.
Summary
This study introduces a new algorithm for identifying time-varying systems by combining temporal expansion with Least Absolute Shrinkage and Selection Operator (Lasso) for improved parameter estimation. The method effectively detects changes in human elbow dynamic stiffness post-perturbation.
Area of Science:
- Engineering
- Control Systems
- Biomedical Engineering
Background:
- System identification models dynamic systems using input/output measurements.
- Linear time-varying systems require specialized identification techniques.
- Existing temporal expansion methods suffer from high parameter counts and noise sensitivity.
Purpose of the Study:
- To present a novel algorithm for identifying linear time-varying systems.
- To reduce parameter estimation variance and noise sensitivity.
- To demonstrate the algorithm's efficacy in detecting changes in human elbow dynamics.
Main Methods:
- The proposed algorithm combines temporal expansion of parameters with a basis function set.
- Least Absolute Shrinkage and Selection Operator (Lasso) is employed for term selection.
- The algorithm constructs a parsimonious model with minimal non-zero terms.
Main Results:
- The Lasso-based term selection significantly reduces the number of estimated parameters.
- The novel algorithm exhibits lower estimation variances compared to traditional methods.
- The algorithm successfully identified changes in human elbow dynamic stiffness after perturbation.
Conclusions:
- The developed algorithm offers an effective approach for identifying time-varying systems.
- Combining temporal expansion with Lasso provides a robust and less noisy identification method.
- This technique has practical applications in biomechanics, such as analyzing joint stiffness changes.
Related Concept Videos
01:23Linear time-invariant Systems
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
01:21Linear Approximation in Time Domain
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
01:29Application of Linearization and Approximation
A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
01:26Linear Approximation in Frequency Domain
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
01:26Linearization and Approximation
Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
01:27Linear Differential Equations
The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law yields a...