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Related Concept Videos

State Space Representation01:27

State Space Representation

301
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
301
State Space to Transfer Function01:21

State Space to Transfer Function

314
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
314
Transfer Function to State Space01:23

Transfer Function to State Space

420
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
420
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

130
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,...
130
Linear time-invariant Systems01:23

Linear time-invariant Systems

447
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...
447
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

152
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence...
152

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Idiographic Lapse Prediction With State Space Modeling: Algorithm Development and Validation Study.

Eric Pulick1, John Curtin2, Yonatan Mintz1

  • 1Department of Industrial and Systems Engineering, College of Engineering, University of Wisconsin-Madison, Madison, WI, United States.

JMIR Formative Research
|June 3, 2025
PubMed
Summary
This summary is machine-generated.

State space models (SSMs) offer superior risk prediction for mental health conditions like alcohol use disorder (AUD) compared to traditional machine learning. These idiographic models personalize patient care, improving outcomes with sufficient data.

Keywords:
alcohol use disorderdigital healthdigital therapeuticsmHealthmental healthmobile healthpersonalized medicinesubstance use disorder

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Area of Science:

  • Mental Health
  • Digital Health
  • Predictive Modeling

Background:

  • Mental health conditions require long-term patient monitoring and personalized treatment.
  • Digital sensing and predictive modeling can enhance clinician capacity and personalize care.
  • Idiographic approaches, which fit personalized models to individual patients, are of particular interest.

Purpose of the Study:

  • To bridge risk prediction and idiographic time-series modeling in mental health.
  • To propose state space modeling (SSM) as an alternative to machine learning (ML) classifiers for patient risk prediction.
  • To evaluate SSMs against ML classifiers for predicting lapses in alcohol use disorder (AUD).

Main Methods:

  • A 3-month observational study of 148 participants in early AUD recovery.
  • Idiographic state space models (SSMs) were trained using daily ecological momentary assessment (EMA) data.
  • SSM predictive performance was compared to logistic regression and gradient-boosted ML classifiers using AUROC for lapse prediction at 3, 7, and same-day intervals.

Main Results:

  • SSMs demonstrated superior mean AUROC performance compared to ML classifiers with 30 or more days of EMA data.
  • With sufficient data (≥30 days), SSMs showed high probabilities of best performance for predicting same-day, 3-day, and 7-day lapses.
  • Predictive performance varied with limited data (15 days), with SSMs outperforming ML for same-day lapse prediction.

Conclusions:

  • SSMs present a compelling alternative to traditional ML for mental health risk prediction.
  • SSMs support idiographic model fitting for rare outcomes and offer enhanced predictive performance.
  • The SSM framework can be extended beyond risk prediction to optimize treatment selection for various mental health conditions.