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Distributed MPC

Distributed MPC

Model Predictive Control for large-scale systems using distributed optimization and coordination between multiple local controllers to achieve global objectives.

Family: Model Predictive Control Status: šŸ“‹ Planned

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Overview

Distributed MPC extends the predictive control framework to handle large-scale systems by decomposing them into smaller subsystems and coordinating multiple local controllers. Unlike centralized MPC, which solves a single large optimization problem, Distributed MPC solves multiple smaller problems in parallel and coordinates their solutions to achieve global objectives.

This approach is essential for systems that are too large for centralized control, geographically distributed, or have privacy/security constraints. Distributed MPC can handle systems with thousands of variables and constraints while maintaining real-time performance. The key challenge is to design coordination mechanisms that ensure global optimality and stability while maintaining computational efficiency.

Mathematical Formulation

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Key Properties

Distributed Optimization

min_{U_i} J_i(x_i, U_i, U_{-i})

Each subsystem solves local optimization problem

Coordination

U_i ā† f(U_{-i}, x_i)

Local solutions coordinated through information exchange

Scalability

O(N Ɨ nĀ³) vs O(NĀ³nĀ³)

Computational complexity scales linearly with subsystems

Key Properties

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  • Distributed Optimization

    Each subsystem solves local optimization problem

  • Coordination

    Local solutions coordinated through information exchange

  • Scalability

    Computational complexity scales linearly with subsystems

  • Privacy

    Local information remains private to each subsystem

  • Fault Tolerance

    System remains operational if some subsystems fail

Implementation Approaches

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Distributed MPC using consensus algorithm for coordination

Complexity:

  • Time: O(N Ɨ nĀ³)
  • Space: O(N Ɨ nĀ²)

Advantages

  • Scalable to large-scale systems

  • Maintains privacy of local information

  • Fault-tolerant and robust

  • Parallel computation reduces computational burden

Disadvantages

  • May not achieve global optimality

  • Requires communication between subsystems

  • Convergence not guaranteed in all cases

  • Complex coordination mechanisms

Complete Implementation

The full implementation with error handling, comprehensive testing, and additional variants is available in the source code:

Complexity Analysis

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Time & Space Complexity Comparison

Approach Time Complexity Space Complexity Notes
Consensus-based Distributed MPC O(N Ɨ nĀ³) O(N Ɨ nĀ²) Complexity scales linearly with number of subsystems N

Performance Considerations

  • Distributed approach enables real-time control of large systems

  • Communication overhead depends on network topology

  • Memory requirements scale with local subsystem size

Use Cases & Applications

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Application Categories

Smart Grids

  • Power System Control: Coordinated control of distributed generators

  • Load Management: Distributed demand response and load balancing

  • Microgrids: Coordinated control of renewable energy sources

  • Energy Storage: Distributed battery management systems

Transportation Systems

  • Traffic Control: Coordinated traffic signal control

  • Vehicle Platooning: Distributed control of vehicle formations

  • Air Traffic Management: Coordinated aircraft trajectory control

  • Railway Systems: Distributed train scheduling and control

Manufacturing Systems

  • Production Lines: Coordinated control of manufacturing processes

  • Supply Chain: Distributed inventory and production management

  • Quality Control: Coordinated quality assurance across production

  • Maintenance: Distributed predictive maintenance scheduling

Building Systems

  • HVAC Control: Coordinated temperature and ventilation control

  • Energy Management: Distributed energy optimization in buildings

  • Lighting Control: Coordinated lighting systems

  • Security Systems: Distributed surveillance and access control

Environmental Systems

  • Water Distribution: Coordinated control of water networks

  • Waste Management: Distributed waste collection and processing

  • Air Quality: Coordinated control of air pollution sources

  • Ecosystem Management: Distributed environmental monitoring

Educational Value

  • Control Theory: Distributed control and coordination

  • Optimization: Distributed optimization and consensus algorithms

  • System Analysis: Large-scale system decomposition and analysis

  • Communication: Networked control systems and information exchange

References & Further Reading

:material-book: Core Textbooks

:material-book:
Model Predictive Control: Theory, Computation, and Design
2017 ā€¢ Nob Hill Publishing ā€¢ ISBN 978-0-9759377-0-9
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:material-book:
Architectures for distributed and hierarchical model predictive control
2009 ā€¢ Journal of Process Control ā€¢ Volume 19, pages 723-731

:material-library: Distributed MPC Theory

:material-book:
Distributed Model Predictive Control Made Easy
2014 ā€¢ Springer ā€¢ ISBN 978-94-007-7006-5
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:material-book:
Cooperative distributed model predictive control
2010 ā€¢ Systems & Control Letters ā€¢ Volume 59, pages 460-469

:material-web: Online Resources

:material-link:
Distributed MPC
Wikipedia article on MPC
:material-link:
Distributed Control Systems
Control Engineering article on distributed MPC
:material-link:
Consensus Algorithms
MATLAB documentation on consensus algorithms

:material-code-tags: Implementation & Practice

:material-link:
MPC Toolbox
MATLAB Model Predictive Control Toolbox
:material-link:
YALMIP
MATLAB toolbox for optimization modeling
:material-link:
CVXPY
Python-embedded modeling language for convex optimization

Interactive Learning

Try implementing the different approaches yourself! This progression will give you deep insight into the algorithm's principles and applications.

Pro Tip: Start with the simplest implementation and gradually work your way up to more complex variants.

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Related Algorithms in Model Predictive Control:

  • Economic MPC - Model Predictive Control that optimizes economic objectives rather than tracking performance, focusing on profit maximization and cost minimization in process industries.

  • Robust MPC - Model Predictive Control that handles model uncertainty and disturbances through robust optimization techniques to ensure constraint satisfaction and stability.

  • Linear MPC - Model Predictive Control for linear time-invariant systems formulated as a Quadratic Programming problem with efficient real-time solution.

  • Nonlinear MPC - Model Predictive Control for nonlinear systems using Sequential Quadratic Programming to handle complex dynamics and constraints.

  • Model Predictive Control - Advanced control strategy that uses system models to predict future behavior and optimize control actions over a finite horizon while handling constraints.

  • Learning MPC - Model Predictive Control that learns system dynamics and improves performance through data-driven approaches, combining machine learning with predictive control.