Basic Control Theory for Biologists

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Basic Control Theory for Biologists

• Tau-Mu Yi and Brian Ingalls
• (Notes and Slides)

www.cds.caltech.edu/tmy/tutorial.htm
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What is Control Theory?

• Principles and methods used to design
  engineering systems that maintain desirable
  performance by automatically adapting to changes
  in the environment.
• More specifically, control theory is concerned
  with designing strategies that ensure the robust
  performance of a system.
• Examples of control systems are everywhere.

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Control Sensing Computation Actuation
Feedback
Car
Actuate Gas Pedal
Sense Speed
Plant
Compute Control Action
Goals Stability, Performance, Robustness
From Richard Murray
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Biological Example of Feedback Control
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What is the Big Deal about Control?

• The real world is full of internal and external
  disturbances.
• Complex, high-performance systems are difficult
  to control.
• Instabilities can have catastrophic consequences.
• The more complex the system, the more important
  are issues concerning control.
• Control structures contribute greatly to the
  complexity of real-world systems.

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Control Theory and Biology

• Biological systems are extremely complex,
  efficient, robust, and high-performance.
• Issues of control are paramount.
• Biological networks are dominated by feedback
  loops.
• Control theory is important for both engineering
  and reverse-engineering feedback systems.

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Biochemical Network E. Coli Metabolism
Regulatory Interactions
From John Doyle
from EcoCYC by Peter Karp
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Definitions

• Signal
• Model
• Dynamical Model
• System/Network
• Control
• Feedback control
• Robustness

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Outline

• Section 1 Introduction to Feedback Control (45
  minutes)
• Section 2 Metabolic Control Theory (30 minutes).
  
• Break (20 minutes)
• Section 3 Homeostasis and Integral Control (30
  minutes)
• Section 4 Limits of Control (30 minutes)
• Section 5 System Identification (20 minutes)