Model Predictive Control
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.
Family: Model Predictive Control Status: 📋 Planned
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Overview
Model Predictive Control (MPC) is an advanced control strategy that uses a mathematical model of the system to predict future behavior and optimize control actions over a finite prediction horizon. Unlike traditional control methods, MPC explicitly handles constraints on inputs, outputs, and states while optimizing a performance objective.
The key principle of MPC is the receding horizon approach: at each time step, the controller solves an optimization problem over a finite prediction horizon, implements only the first control action, and then shifts the horizon forward by one time step. This approach provides excellent performance for complex systems with constraints and is widely used in process industries, automotive, aerospace, and robotics applications.
Mathematical Formulation¶
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Key Properties
Predictive Control
U_k = argmin J(x(k), U_k)
Optimizes control sequence over finite horizon
Receding Horizon
u(k) = U_k[0]
Implements only first control action and shifts horizon
Constraint Handling
g(x,u) ≤ 0, h(x,u) = 0
Explicitly handles system constraints
Key Properties¶
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Predictive Control
Uses system model to predict future behavior
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Constraint Handling
Explicitly handles constraints on inputs, outputs, and states
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Receding Horizon
Optimizes over finite horizon and implements only first action
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Multivariable Control
Naturally handles systems with multiple inputs and outputs
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Real-time Optimization
Solves optimization problem at each time step
Implementation Approaches¶
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Standard MPC implementation with linear system model and quadratic cost
Complexity:
- Time: O(N³)
- Space: O(N²)
Advantages
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Handles constraints explicitly
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Multivariable control capability
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Predictive control with model-based optimization
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Widely applicable to many systems
Disadvantages
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Requires accurate system model
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Computationally intensive for large horizons
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May not guarantee stability without additional constraints
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 basic and advanced variants:
src/algokit/mpc/model_predictive_control.py -
Comprehensive test suite including performance tests:
tests/unit/mpc/test_model_predictive_control.py
Complexity Analysis¶
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Time & Space Complexity Comparison
| Approach | Time Complexity | Space Complexity | Notes |
|---|---|---|---|
| Basic MPC Controller | O(N³) | O(N²) | Complexity depends on prediction horizon N and system dimensions |
Performance Considerations
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MPC requires real-time optimization within sampling period
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Computational complexity scales with prediction horizon
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Memory requirements scale with system dimensions
Use Cases & Applications¶
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Application Categories
Process Industries
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Chemical Plants: Temperature, pressure, and composition control
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Oil Refineries: Distillation column control and optimization
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Power Plants: Boiler and turbine control
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Pulp and Paper: Process control and quality optimization
Automotive Systems
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Engine Control: Fuel injection and ignition timing optimization
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Vehicle Dynamics: Trajectory tracking and stability control
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Hybrid Vehicles: Energy management and power distribution
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Autonomous Driving: Path planning and vehicle control
Aerospace Applications
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Flight Control: Aircraft attitude and trajectory control
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Spacecraft Guidance: Orbital maneuvers and docking
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UAV Control: Autonomous flight and mission execution
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Satellite Control: Attitude and orbit maintenance
Robotics
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Manipulator Control: Joint trajectory tracking
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Mobile Robot Navigation: Path planning and obstacle avoidance
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Humanoid Robots: Balance and locomotion control
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Industrial Robots: Pick and place operations
Energy Systems
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Smart Grids: Power flow optimization and demand response
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Renewable Energy: Wind and solar power management
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Battery Management: Charging and discharging optimization
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Microgrids: Distributed energy resource coordination
Educational Value
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Control Theory: Advanced predictive control concepts
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Optimization: Real-time optimization for control applications
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System Modeling: Understanding system dynamics and constraints
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Multivariable Control: Handling multiple inputs and outputs
References & Further Reading¶
:material-book: Core Textbooks
:material-library: 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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Learning MPC - Model Predictive Control that learns system dynamics and improves performance through data-driven approaches, combining machine learning with predictive control.