InteractiveMap of Control Theory

Learning roadmaps

Pick a path, follow the loop

Ordered sequences that take you from first principles to advanced, learning-based control.

Beginner Classical Path

  1. 1First-principles modeling
  2. 2Transfer functions & block diagrams
  3. 3Step, impulse, and sine responses
  4. 4PID control
  5. 5Root locus, Bode, Nyquist & stability margins
  6. 6Routh-Hurwitz, Z-transform methods, lead-lag compensation & loop shaping

State-Space Path

  1. 1Linear state-space models
  2. 2Controllability & observability
  3. 3Full-state feedback & pole placement
  4. 4LQR, Riccati equations & LQG
  5. 5Observers, Kalman filtering & separation principle
  6. 6MIMO design, MPC, constrained control & safety filters

Robotics & Autonomy Path

  1. 1Nonlinear state-space models
  2. 2Motion planning: holonomic & nonholonomic
  3. 3RRT and A* path planning
  4. 4PRM, trajectory optimization & feasible planning
  5. 5Sensor fusion: IMU, GPS & camera
  6. 6Mapping, tracking, MHE & safety constraints

Digital Control Path

  1. 1Sampling, reconstruction, aliasing & hold devices
  2. 2Difference equations, z-transforms, pulse transfer functions & z-plane geometry
  3. 3Discrete equivalents: numerical integration, zero-pole matching & hold equivalents
  4. 4Digital design: emulation, direct z-plane design, deadbeat control, discrete PID & pole assignment
  5. 5Sample-rate selection, multirate effects, delays, quantization, round-off, limit cycles & dither
  6. 6Implementation: A/D, D/A, controller realization, embedded interfaces, reliability & HIL validation

Advanced Control Path

  1. 1Lyapunov stability
  2. 2Nonlinear control: feedback linearization, backstepping, sliding mode, passivity
  3. 3Optimal control: PMP, HJB, dynamic programming, DDP & iLQR
  4. 4Robust control: H-infinity, mu-synthesis, structured singular values, LFTs
  5. 5Adaptive control: MRAC, self-tuning, auto-tuning, robust adaptive control
  6. 6Multi-agent, safety-critical & learning-based control

Stochastic Estimation Path

  1. 1Probability, stochastic processes & spectral density
  2. 2Least squares, recursive least squares & Wiener filtering
  3. 3Discrete-time Kalman filtering
  4. 4Continuous-time Kalman-Bucy filtering
  5. 5Square-root, information, constrained & H-infinity filters
  6. 6EKF, UKF, particle filters, smoothing & multiple-model estimation

MIMO & Robust Design Path

  1. 1SISO loop shaping, sensitivity & performance limitations
  2. 2MIMO state-space models, singular values & RGA
  3. 3Uncertainty models, LFTs & structured singular value analysis
  4. 4Robust stability and robust performance
  5. 5H-infinity synthesis, mu-synthesis & LMIs
  6. 6Control structure design, model reduction & case studies

References

Books, papers, courses & software

The full resource index now has 4 groups and 44 entries, including the textbook references from the README.

Open resource index

Textbooks & Learning Resources

25 entries

Open Texts & Course Notes

8 entries

Classic Papers & Surveys

6 entries

Open Software & Benchmarks

5 entries