Ordinary Differential Equations (16): Fundamentals of Control Theory

Tue, 12 Mar 2024 09:00:00 +0000

When you steer a car you constantly correct based on lane position. A thermostat compares room temperature with the setpoint and adjusts a heater. A rocket gimbal nudges its thrust vector to keep the booster vertical. Strip away the hardware and the same idea remains: measure, compare, act. Control theory is the mathematics of that loop — and its native language is the ordinary differential equation.

This chapter shows how the entire ODE toolkit — Laplace transforms (Ch 4), linear systems (Ch 6), eigenvalue stability (Ch 7), nonlinear stability (Ch 8) — collapses into a single unified discipline whose job is no longer to describe dynamics, but to design them.

State Space on Chen Kai Blog

Ordinary Differential Equations (16): Fundamentals of Control Theory