modular-state-space-model-260714078

name	modular-state-space-model-260714078
description	Model human perception, cognition, and decision dynamics as a modular perception-cognition-decision pipeline state-space model. Provides mathematical formulation, stability conditions, and application to rehabilitation control. Use when you need interpretable dynamical models linking neural mechanisms to behavior.
metadata	{"arxiv_id":"2607.14078","authors":["Sven Schoonebeek","Carlo Cenedese","Anahita Jamshidnejad"],"categories":["eess.SY","q-bio.NC","cs.SY"]}

Modular State-Space Model of Human Perception, Cognition, and Decision Dynamics (arXiv:2607.14078)

Overview

This skill encapsulates the methodology from arXiv:2607.14078 for modeling human behavior as a perception-cognition-decision pipeline using coupled state-space models. It provides the mathematical framework for attentional selection, predictive inference, cognitive-state evolution, intention formation, and action selection, linking sensory inputs to observable behavior through latent neural states. The skill includes stability analysis conditions and demonstrates application in a rehabilitation control scenario.

Core Components

1. Perception-Cognition-Decision Pipeline

The model decomposes behavior into five coupled subprocesses:

• Attentional selection: filters sensory inputs
• Predictive inference: generates predictions about sensory input
• Cognitive-state evolution: updates internal beliefs and goals
• Intention formation: selects goals and prepares actions
• Action selection: executes motor commands

Each subprocess is represented as a state-space model with explicit input-output mappings.

2. Mathematical Formulation

For each subprocess (i), we define:

• State vector (x_i \in \mathbb{R}^{n_i})
• Input (u_i) (from previous subsystem or sensory input)
• Output (y_i) (to next subsystem or behavior)
• Dynamics: (x_{i,k+1} = A_i x_{i,k} + B_i u_{i,k} + w_{i,k})
• Measurement: (y_{i,k} = C_i x_{i,k} + v_{i,k})

Coupling occurs through the interconnections:

• Sensory input → Attentional selection
• Attentional output → Predictive inference
• Predictive inference → Cognitive-state evolution
• Cognitive-state evolution → Intention formation
• Intention formation → Action selection → Observable behavior

3. Stability and Performance Properties

The paper establishes sufficient conditions for:

• Boundedness: states remain bounded for bounded inputs
• Lipschitz regularity: Lipschitz continuity of state transition maps
• Forward invariance: certain sets remain invariant under dynamics
• Contraction of perceptual inference: contraction mapping under constant input
• Input-to-state stability (ISS): cognitive state dynamics are ISS with respect to inputs

These properties ensure the model is well-behaved and suitable for control applications.

4. Application: Rehabilitation Control

A closed-loop rehabilitation case study demonstrates:

• Using the model to predict patient motor capabilities from partial feedback
• A receding-horizon model predictive controller adjusts task difficulty
• The model-based controller sustains task participation and reduces cumulative cost compared to baseline strategies
• This illustrates how the model enables model-based control in human-centered settings

Workflow

Step 1: Define Subsystems

Identify the relevant subprocesses for your application (attention, prediction, cognition, intention, action) and define their state, input, and output dimensions.

Step 2: Specify Dynamics

Choose appropriate state-space matrices (A, B, C) for each subsystem based on known neurocognitive mechanisms or identified from data.

Step 3: Couple Subsystems

Connect the outputs of each subsystem to the inputs of the next according to the perception-cognition-decision pipeline.

Step 4: Analyze Stability

Verify that the chosen parameters satisfy the sufficient conditions for boundedness, Lipschitz regularity, and input-to-state stability.

Step 5: Simulate and Validate

Simulate the model with synthetic or empirical data to ensure it produces interpretable changes in perceptual tracking, cognitive amplification, intention expression, and action decisiveness.

Step 6: Apply to Control (Optional)

Design a model-based controller (e.g., MPC) that uses the model's predictions to influence behavior, such as adapting task difficulty in rehabilitation.

Resources

scripts/

• simulate_pipeline.py: Example simulation of the coupled state-space model
• analyze_stability.py: Checks stability conditions for given system matrices

references/

• math_details.md: Detailed derivations of the state-space equations and coupling terms
• stability_conditions.md: List of sufficient conditions for boundedness and ISS
• rehabilitation_case.md: Detailed description of the rehabilitation control experiment

assets/

• diagram_pipeline.png: Block diagram of the perception-cognition-decision pipeline
• template_controller.m: MATLAB template for MPC controller design

Usage Notes

• Validate subsystem dimensions before coupling
• Use numerical integration (e.g., Euler or Runge-Kutta) for simulation
• For parameter estimation, consider subspace identification or expectation-maximization
• The model is particularly useful when interpretability of latent states is required

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Activation: modular state-space model, perception cognition decision, behavioral modeling, human-centered control, arXiv:2607.14078