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Control, Estimation, and Cyber-Physical Systems

Manual: General · Subject: Engineering

Develops modern control theory, state estimation, optimal control, and secure cyber-physical design.

Feedback, Observability, and Robustness

Core Control Ideas

Control engineering studies how to influence system behavior through feedback. In state-space form, x˙=Ax+Bu\dot{x} = Ax + Bu and y=Cx+Duy = Cx + Du. The central questions are stabilizability, observability, robustness, and performance under uncertainty.

Essential Terms

Feedback
Using measured output to adjust control inputs
Observability
Whether internal states can be inferred from outputs
Controllability
Whether states can be driven to desired values
Robustness
Performance under model mismatch and disturbances
Kalman filter
A recursive estimator for linear-Gaussian systems

Which property determines whether the internal state can be reconstructed from output measurements?

Why is robustness a central concern in engineering control?

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Cyber-Physical Risk

As engineered systems become networked and software-defined, vulnerabilities in sensing, communication, and actuation can become safety-critical.

Classical vs. Modern Control

Classical control

  • Frequency-domain methods
  • Strong intuition for SISO systems

Modern control

  • State-space representation
  • Scales better to MIMO and optimal design

Which estimator is most associated with linear systems under Gaussian noise?

What is one key feature of a cyber-physical system?