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Control theory is a branch of engineering and mathematics that deals with the behavior of [[dynamical systems]] with inputs, and how their behavior is modified by feedback. Here's a comprehensive list of various branches and sub-disciplines within control theory:

1. Classical Control Theory¶

PID Control (Proportional, Integral, Derivative)
Root Locus Methods
Frequency Response Methods
Bode Plots
Nyquist Criteria
State-Space Analysis
Stability Analysis (Routh-Hurwitz, etc.)

2. Modern Control Theory¶

State Space Representations
State Feedback Control
Observer Design
Optimal Control
LQR (Linear Quadratic Regulator)
Kalman Filters
Robust Control
Model Predictive Control (MPC)
H-infinity Control

3. Nonlinear Control¶

Lyapunov Stability Theory
Feedback Linearization
Sliding Mode Control
Backstepping
Bifurcation Theory
Chaos Control

4. Adaptive Control¶

Model Reference Adaptive Control (MRAC)
Self-Tuning Regulators
Gain Scheduling
Robust Adaptive Control

5. Stochastic Control¶

Stochastic Processes
Stochastic Estimation
Stochastic Optimal Control
Markov Decision Processes

6. Distributed Control Systems¶

Multi-Agent Systems
Decentralized Control
Networked Control Systems
Cooperative Control

7. Discrete-Time Control Systems¶

Digital Control
Sampled-Data Control Systems
Z-Transform Methods
Discrete-Time State Space Methods

8. Optimal Control¶

Dynamic Programming
Pontryagin's Maximum Principle
Variational Methods
Linear Quadratic Gaussian Control (LQG)

9. Predictive Control¶

Model Predictive Control (MPC)
Receding Horizon Control
Explicit Model Predictive Control

10. Robust Control¶

Uncertainty Modeling
H-infinity Methods
μ-Synthesis
Robust Adaptive Control

11. Intelligent Control¶

Fuzzy Logic Control
Neural Network Control
Expert Systems
Genetic Algorithms in Control

12. Feedback Control¶

Feedback Loop Design
Sensitivity and Stability Margins
Closed-Loop Control Systems

13. Process Control¶

Industrial Process Control
PID Tuning
Process Identification
Batch Process Control

14. Aerospace Control¶

Flight Control Systems
Spacecraft Attitude Control
Missile Guidance Systems
UAV (Unmanned Aerial Vehicle) Control

15. Automotive Control Systems¶

Engine Control
Vehicle Dynamics Control
Autonomous Vehicle Control

16. Biomedical Control Systems¶

Drug Delivery Systems
Biological Systems Control
Prosthetics and Orthotics Control

17. Energy Systems Control¶

Smart Grid Control
Renewable Energy Systems
Battery Management Systems

18. Quantum Control¶

Quantum Feedback Control
Quantum Error Correction
Control of Quantum Systems

Control theory is a vital area of engineering and mathematics, with applications ranging from everyday appliances like air conditioners to advanced systems like autonomous vehicles and spacecraft. The field is continuously evolving, incorporating new technologies and methodologies to address increasingly complex control challenges.

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