Adaptive Control
Adaptive Control
Control strategy that automatically adjusts controller parameters based on real-time system identification and performance evaluation.
Family: Control Algorithms Status: 📋 Planned
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Overview
Adaptive Control is a control strategy that automatically adjusts controller parameters based on real-time system identification and performance evaluation. Unlike fixed-parameter controllers like PID, adaptive controllers continuously learn and adapt to changing system dynamics, making them ideal for systems with unknown or time-varying parameters.
This approach is particularly valuable in aerospace applications, robotics, process control, and other domains where system characteristics may change over time or are initially unknown. Adaptive controllers can handle parameter uncertainties, environmental changes, and system degradation while maintaining desired performance.
Mathematical Formulation¶
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Key Properties
Online Learning
θ̂(t) = θ̂(t-1) + γ(t) φ(t) e(t)
Continuously updates parameters during operation
Lyapunov Stability
V̇(t) ≤ 0
Ensures system stability during adaptation
Convergence
lim_{t→∞} θ̃(t) = 0
Parameters converge to true values under certain conditions
Key Properties¶
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Online Learning
Continuously updates parameters during operation
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Robustness
Handles parameter uncertainties and system changes
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Self-tuning
Automatically adjusts to maintain performance
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Stability Guarantees
Lyapunov-based stability guarantees
Implementation Approaches¶
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Adaptive controller that forces plant output to track reference model output
Complexity:
- Time: O(n²)
- Space: O(n²)
Advantages
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Automatic parameter adaptation
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Handles unknown system parameters
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Robust to parameter variations
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Theoretical stability guarantees
Disadvantages
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More complex than fixed controllers
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Requires persistent excitation for convergence
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May have slower initial response
Combines system identification with controller design
Complexity:
- Time: O(n³)
- Space: O(n²)
Advantages
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Automatic controller design
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Handles time-varying systems
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Combines identification and control
Disadvantages
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Computationally intensive
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Requires careful tuning of identification parameters
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May be unstable during learning phase
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 MRAC and self-tuning variants:
src/algokit/control/adaptive_control.py -
Comprehensive test suite including stability tests:
tests/unit/control/test_adaptive_control.py
Complexity Analysis¶
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Time & Space Complexity Comparison
| Approach | Time Complexity | Space Complexity | Notes |
|---|---|---|---|
| Model Reference Adaptive Control | O(n²) | O(n²) | Time complexity dominated by matrix operations in RLS update |
Performance Considerations
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Adaptive controllers require more computation than fixed controllers
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Memory requirements grow with number of parameters
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Convergence time depends on excitation conditions
Use Cases & Applications¶
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Application Categories
Aerospace Systems
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Flight Control: Adapting to changing aircraft dynamics
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Satellite Control: Handling fuel consumption and mass changes
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Missile Guidance: Adapting to target maneuvers
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Spacecraft Docking: Handling uncertain contact dynamics
Robotics and Automation
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Robot Control: Adapting to payload changes and wear
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Manufacturing: Handling material property variations
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Autonomous Vehicles: Adapting to road conditions and vehicle dynamics
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Manipulation: Handling unknown object properties
Process Control
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Chemical Plants: Handling catalyst degradation
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Power Systems: Adapting to load variations
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Water Treatment: Handling varying water quality
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Food Processing: Adapting to ingredient variations
Biomedical Systems
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Drug Delivery: Adapting to patient response
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Prosthetics: Learning user movement patterns
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Pacemakers: Adapting to heart condition changes
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Rehabilitation: Adapting to patient progress
Marine and Offshore
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Ship Control: Handling wave and current variations
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Underwater Vehicles: Adapting to changing buoyancy
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Offshore Platforms: Handling environmental changes
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Submarine Control: Adapting to depth and speed changes
Educational Value
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System Identification: Learning to estimate system parameters online
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Adaptive Control Theory: Understanding Lyapunov stability and convergence
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Real-time Learning: Implementing learning algorithms in control systems
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Robustness Analysis: Understanding performance under uncertainty
References & Further Reading¶
:material-book: Core Textbooks
:material-library: Adaptive Control
: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 Control Algorithms:
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H-Infinity Control - Robust control design methodology that minimizes the worst-case performance of a system under bounded disturbances and uncertainties.
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Sliding Mode Control - Robust control strategy that forces the system state to reach and remain on a predefined sliding surface, regardless of parameter uncertainties and external disturbances.
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Robust Control - Comprehensive control design methodology that ensures system stability and performance despite model uncertainties, parameter variations, and external disturbances.
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PID Control - Fundamental feedback control algorithm combining proportional, integral, and derivative actions to achieve desired system behavior.