Learning MPC
Learning MPC
Model Predictive Control that learns system dynamics and improves performance through data-driven approaches, combining machine learning with predictive control.
Family: Model Predictive Control Status: š Planned
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Overview
Learning MPC combines the predictive control framework with machine learning techniques to learn system dynamics and improve control performance over time. Unlike traditional MPC, which relies on pre-specified system models, Learning MPC uses data-driven approaches to identify system behavior and adapt the control strategy accordingly.
This approach is particularly valuable when system models are unknown, complex, or time-varying. Learning MPC can handle nonlinear systems, adapt to changing conditions, and improve performance through experience. The key challenge is to balance exploration (learning about the system) with exploitation (using learned knowledge for control) while maintaining stability and constraint satisfaction.
Mathematical Formulation¶
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Key Properties
Data-driven Learning
fĢ ā Learn(D)
Learns system dynamics from data
Adaptive Control
U_k ā MPC(x(k), fĢ)
Adapts control strategy based on learned model
Uncertainty Quantification
fĢ(x,u) Ā± Ļ(x,u)
Provides uncertainty bounds for robust control
Key Properties¶
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Data-driven Learning
Learns system dynamics from collected data
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Adaptive Control
Adapts control strategy based on learned knowledge
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Uncertainty Quantification
Provides uncertainty bounds for robust control
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Exploration vs Exploitation
Balances learning with control performance
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Online Learning
Continuously updates models during operation
Implementation Approaches¶
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Learning MPC using neural networks for system identification
Complexity:
- Time: O(NĀ³ + M)
- Space: O(NĀ² + M)
Advantages
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Learns system dynamics from data
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Adapts to changing system conditions
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Handles unknown or complex systems
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Improves performance over time
Disadvantages
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Requires sufficient data for learning
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May be unstable during learning phase
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Computationally intensive due to learning
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Requires careful tuning of learning parameters
Complete Implementation
The full implementation with error handling, comprehensive testing, and additional variants is available in the source code:
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Main implementation with neural network learning:
src/algokit/mpc/learning_mpc.py -
Comprehensive test suite including learning performance tests:
tests/unit/mpc/test_learning_mpc.py
Complexity Analysis¶
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Time & Space Complexity Comparison
| Approach | Time Complexity | Space Complexity | Notes |
|---|---|---|---|
| Neural Network Learning MPC | O(NĀ³ + M) | O(NĀ² + M) | Complexity depends on prediction horizon N and model size M |
Performance Considerations
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Learning adds computational overhead
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Model complexity affects prediction accuracy
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Memory requirements scale with data size
Use Cases & Applications¶
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Application Categories
Robotics and Mechatronics
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Manipulator Control: Learning robot dynamics for precise control
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Mobile Robot Navigation: Learning terrain and obstacle dynamics
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Humanoid Robots: Learning balance and locomotion patterns
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Industrial Robots: Learning task-specific dynamics
Automotive Systems
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Autonomous Vehicles: Learning vehicle dynamics and traffic patterns
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Engine Control: Learning combustion dynamics and fuel efficiency
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Vehicle Dynamics: Learning tire and suspension characteristics
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Hybrid Vehicles: Learning energy management strategies
Process Industries
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Chemical Plants: Learning reactor dynamics and catalyst behavior
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Oil Refineries: Learning distillation column dynamics
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Power Plants: Learning boiler and turbine characteristics
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Manufacturing: Learning production process dynamics
Aerospace Systems
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Flight Control: Learning aircraft dynamics and aerodynamic effects
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Spacecraft Guidance: Learning orbital dynamics and perturbations
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UAV Control: Learning flight dynamics and environmental effects
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Satellite Control: Learning attitude dynamics and disturbances
Energy Systems
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Smart Grids: Learning power system dynamics and demand patterns
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Renewable Energy: Learning wind and solar power generation
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Battery Management: Learning battery aging and charging dynamics
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Microgrids: Learning distributed energy resource dynamics
Educational Value
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Control Theory: Learning-based control and adaptive systems
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Machine Learning: Neural networks and system identification
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Optimization: Real-time optimization with learned models
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System Analysis: Data-driven modeling and uncertainty quantification
References & Further Reading¶
:material-book: Core Textbooks
:material-library: Learning MPC Theory
:material-web: Online Resources
:material-code-tags: Implementation & Practice
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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Navigation¶
Related Algorithms in Model Predictive Control:
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Distributed MPC - Model Predictive Control for large-scale systems using distributed optimization and coordination between multiple local controllers to achieve global objectives.
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Economic MPC - Model Predictive Control that optimizes economic objectives rather than tracking performance, focusing on profit maximization and cost minimization in process industries.
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Robust MPC - Model Predictive Control that handles model uncertainty and disturbances through robust optimization techniques to ensure constraint satisfaction and stability.
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Linear MPC - Model Predictive Control for linear time-invariant systems formulated as a Quadratic Programming problem with efficient real-time solution.
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Nonlinear MPC - Model Predictive Control for nonlinear systems using Sequential Quadratic Programming to handle complex dynamics and constraints.
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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.